Has an uncomfortable truth been suppressed?

Update to post, added 11th September. As expected, there is another side to the story discussed below. See this statement about the decision by the Mathematical Intelligencer and this one about the decision taken by the New York Journal of Mathematics.

Further update, added 15th September. The author has also made a statement.

I was disturbed recently by reading about an incident in which a paper was accepted by the Mathematical Intelligencer and then rejected, after which it was accepted and published online by the New York Journal of Mathematics, where it lasted for three days before disappearing and being replaced by another paper of the same length. The reason for this bizarre sequence of events? The paper concerned the “variability hypothesis”, the idea, apparently backed up by a lot of evidence, that there is a strong tendency for traits that can be measured on a numerical scale to show more variability amongst males than amongst females. I do not know anything about the quality of this evidence, other than that there are many papers that claim to observe greater variation amongst males of one trait or another, so that if you want to make a claim along the lines of “you typically see more males both at the top and the bottom of the scale” then you can back it up with a long list of citations.

You can see, or probably already know, where this is going: some people like to claim that the reason that women are underrepresented at the top of many fields is simply that the top (and bottom) people, for biological reasons, tend to be male. There is a whole narrative, much loved by many on the political right, that says that this is an uncomfortable truth that liberals find so difficult to accept that they will do anything to suppress it. There is also a counter-narrative that says that people on the far right keep on trying to push discredited claims about the genetic basis for intelligence, differences amongst various groups, and so on, in order to claim that disadvantaged groups are innately disadvantaged rather than disadvantaged by external circumstances.

I myself, as will be obvious, incline towards the liberal side, but I also care about scientific integrity, so I felt I couldn’t just assume that the paper in question had been rightly suppressed. I read an article by the author that described the whole story (in Quillette, which rather specializes in this kind of story), and it sounded rather shocking, though one has to bear in mind that since the article is written by a disgruntled author, there is almost certainly another side to the story. In particular, he is at pains to stress that the paper is simply a mathematical theory to explain why one sex might evolve to become more variable than another, and not a claim that the theory applies to any given species or trait. In his words, “Darwin had also raised the question of why males in many species might have evolved to be more variable than females, and when I learned that the answer to his question remained elusive, I set out to look for a scientific explanation. My aim was not to prove or disprove that the hypothesis applies to human intelligence or to any other specific traits or species, but simply to discover a logical reason that could help explain how gender differences in variability might naturally arise in the same species.”

So as I understood the situation, the paper made no claims whatsoever about the real world, but simply defined a mathematical model and proved that in this model there would be a tendency for greater variability to evolve in one sex. Suppressing such a paper appeared to make no sense at all, since one could always question whether the model was realistic. Furthermore, suppressing papers on this kind of topic simply plays into the hands of those who claim that liberals are against free speech, that science is not after all objective, and so on, claims that are widely believed and do a lot of damage.

I was therefore prompted to look at the paper itself, which is on the arXiv, and there I was met by a surprise. I was worried that I would find it convincing, but in fact I found it so unconvincing that I think it was a bad mistake by Mathematical Intelligencer and the New York Journal of Mathematics to accept it, but for reasons of mathematical quality rather than for any controversy that might arise from it. To put that point more directly, if somebody came up with a plausible model (I don’t insist that it should be clearly correct) and showed that subject to certain assumptions about males and females one would expect greater variability to evolve amongst males, then that might well be interesting enough to publish, and certainly shouldn’t be suppressed just because it might be uncomfortable, though for all sorts of reasons that I’ll discuss briefly later, I don’t think it would be as uncomfortable as all that. But this paper appears to me to fall well short of that standard.

To justify this view, let me try to describe what the paper does. Its argument can be summarized as follows.

1. Because in many species females have to spend a lot more time nurturing their offspring than males, they have more reason to be very careful when choosing a mate, since a bad choice will have more significant consequences.

2. If one sex is more selective than the other, then the less selective sex will tend to become more variable.

To make that work, one must of course define some kind of probabilistic model in which the words “selective” and “variable” have precise mathematical definitions. What might one expect these to be? If I hadn’t looked at the paper, I think I’d have gone for something like this. An individual A of one sex will try to choose as desirable a mate B as possible amongst potential mates that would be ready to accept A as a mate. To be more selective would simply mean to make more of an effort to optimize the mate, which one would model in some suitable probabilistic way. One feature of this model would presumably be that a less attractive individual would typically be able to attract less desirable mates.

I won’t discuss how variability is defined, except to say that the definition is, as far as I can see, reasonable. (For normal distributions it agrees with standard deviation.)

The definition of selectivity in the paper is extremely crude. The model is that individuals of one sex will mate with individuals of the other sex if and only if they are above a certain percentile in the desirability scale, a percentile that is the same for everybody. For instance, they might only be prepared to choose a mate who is in the top quarter, or the top two thirds. The higher the percentile they insist on, the more selective that sex is.

When applied to humans, this model is ludicrously implausible. While it is true that some males have trouble finding a mate, the idea that some huge percentage of males are simply not desirable enough (as we shall see, the paper requires this percentage to be over 50) to have a chance of reproducing bears no relation to the world as we know it.

I suppose it is just about possible that an assumption like this could be true of some species, or even of our cave-dwelling ancestors — perhaps men were prepared to shag pretty well anybody, but only some small percentage of particularly hunky men got their way with women — but that isn’t the end of what I find dubious about the paper. And even if we were to accept that something like that had been the case, it would be a huge further leap to assume that what made somebody desirable hundreds of thousands of years ago was significantly related to what makes somebody good at, say, mathematical research today.

Here is one of the main theorems of the paper, with a sketch of the proof. Suppose you have two subpopulations P and Q within one of the two sexes, with P being of more varied attractiveness than Q. And suppose that the selectivity cutoff for the other sex is that you have to be in the top 40 percent attractiveness-wise. Then because P is more concentrated on the extremes than Q, a higher proportion of subpopulation P will be in that percentile. (This can easily be made rigorous using the notion of variability in the paper.) By contrast, if the selectivity cutoff is that you have to be in the top 60 percent, then a higher proportion of subpopulation Q will be chosen.

I think we are supposed to conclude that subpopulation P is therefore favoured over subpopulation Q when the other sex is selective, and not otherwise, and therefore that variability amongst males tends to be selected for, because females tend to be more choosy about their mates.

But there is something very odd about this. Those poor individuals at the bottom of population P aren’t going to reproduce, so won’t they die out and potentially cause population P to become less variable? Here’s what the paper has to say.

Thus, in this discrete-time setting, if one sex remains selective from each generation to the next, for example, then in each successive generation more variable subpopulations of the opposite sex will prevail over less variable subpopulations with comparable average desirability. Although the desirability distributions themselves may evolve, if greater variability prevails at each step, that suggests that over time the opposite sex will tend toward greater variability.

Well I’m afraid that to me it doesn’t suggest anything of the kind. If females have a higher cutoff than males, wouldn’t that suggest that males would have a much higher selection pressure to become more desirable than females? And wouldn’t the loss of all those undesirable males mean that there wasn’t much one could say about variability? Imagine for example if the individuals in P were all either extremely fit or extremely unfit. Surely the variability would go right down if only the fit individuals got to reproduce. And if you’re worrying that the model would in fact show that males would tend to become far superior to females, as opposed to the usual claim that males are more spread out both at the top and at the bottom, let’s remember that males inherit traits from both their fathers and their mothers, as do females, an observation that, surprisingly, plays no role at all in the paper.

What is the purpose of the strange idea of splitting into two subpopulations and then ignoring the fact that the distributions may evolve (and why just “may” — surely “will” would be more appropriate)? Perhaps the idea is that a typical gene (or combination of genes) gives rise not to qualities such as strength or intelligence, but to more obscure features that express themselves unpredictably — they don’t necessarily make you stronger, for instance, but they give you a bigger range of strength possibilities. But is there the slightest evidence for such a hypothesis? If not, then why not just consider the population as a whole? My guess is that you just don’t get the desired conclusion if you do that.

I admit that I have not spent as long thinking about the paper as I would need to in order to be 100% confident of my criticisms. I am also far from expert in evolutionary biology and may therefore have committed some rookie errors in what I have written above. So I’m prepared to change my mind if somebody (perhaps the author?) can explain why the criticisms are invalid. But as it looks to me at the time of writing, the paper isn’t a convincing model, and even if one accepts the model, the conclusion drawn from the main theorem is not properly established. Apparently the paper had a very positive referee’s report. The only explanation I can think of for that is that it was written by somebody who worked in evolutionary biology, didn’t really understand mathematics, and was simply pleased to have what looked like a rigorous mathematical backing for their theories. But that is pure speculation on my part and could be wrong.

I said earlier that I don’t think one should be so afraid of the genetic variability hypothesis that one feels obliged to dismiss all the literature that claims to have observed greater variability amongst males. For all I know it is seriously flawed, but I don’t want to have to rely on that in order to cling desperately to my liberal values.

So let’s just suppose that it really is the case that amongst a large number of important traits, males and females have similar averages but males appear more at the extremes of the distribution. Would that help to explain the fact that, for example, the proportion of women decreases as one moves up the university hierarchy in mathematics, as Larry Summers once caused huge controversy by suggesting? (It’s worth looking him up on Wikipedia to read his exact words, which are more tentative than I had realized.)

The theory might appear to fit the facts quite well: if men and women are both normally distributed with the same mean but men have a greater variance than women, then a randomly selected individual from the top x percent of the population will be more and more likely to be male the smaller x gets. That’s just simple mathematics.

But it is nothing like enough reason to declare the theory correct. For one thing, it is just as easy to come up with an environmental theory that would make a similar prediction. Let us suppose that the way society is organized makes it harder for women to become successful mathematicians than for men. There are all sorts of reasons to believe that this is the case: relative lack of role models, an expectation that mathematics is a masculine pursuit, more disruption from family life (on average), distressing behaviour by certain male colleagues, and so on. Let’s suppose that the result of all these factors is that the distribution of whatever it takes for women to make a success of mathematics has a slightly lower mean than that for men, but roughly the same variance, with both distributions normal. Then again one finds by very basic mathematics that if one picks a random individual from the top x percent, that individual will be more and more likely to be male as x gets smaller. But in this case, instead of throwing up our hands and saying that we can’t fight against biology, we will say that we should do everything we can to compensate for and eventually get rid of the disadvantages experienced by women.

A second reason to be sceptical of the theory is that it depends on the idea that how good one is at mathematics is a question of raw brainpower. But that is a damaging myth that puts many people off doing mathematics who could have enjoyed it and thrived at it. I have often come across students who astound me with their ability to solve problems far more quickly than I can, (not all of them male). Some of them go on to be extremely successful mathematicians, but not all. And some who seem quite ordinary go on to do extraordinary things later on. It is clear that while an unusual level of raw brainpower, whatever that might be, often helps, it is far from necessary and far from sufficient for becoming a successful mathematician: it is part of a mix that includes dedication, hard work, enthusiasm, and often a big slice of luck. And as one gains in experience, one gains in brainpower — not raw any more, but who cares whether it is hardware or software? So even if it turned out that the genetic variability hypothesis was correct and could be applied to something called raw mathematical brainpower, a conclusion that would be very hard to establish convincingly (it’s certainly not enough to point out that males find it easier to visualize rotating 3D objects in their heads), that still wouldn’t imply that it is pointless to try to correct the underrepresentation of women amongst the higher ranks of mathematicians. When I was a child, almost all doctors and lawyers were men, and during my lifetime I have seen that change completely. The gender imbalance amongst mathematicians has changed more slowly, but there is no reason in principle that the pace couldn’t pick up substantially. I hope to live to see that happen.

370 Responses to “Has an uncomfortable truth been suppressed?”

  1. Darij Grinberg Says:

    The paper makes a conscious choice to treat the variability itself as heritable, rather than assuming that the upper end of the distribution will bequest their upper-endness (upper-endianness?) onto their offstring while the lower end will bequest their lower-endness. I am not a biologist, but I feel that a model like that isn’t a bad idea; I can certainly imagine variability in *phenotypes* being inherited. For example, consider risk acceptance (famously higher in men): It produces both very successful and very unsuccessful individuals, but the offspring of the successful ones will likely inherit the risk acceptance (both genetically and by nurture), not the success (since risk acceptance doesn’t deterministically make you better off, or else it wouldn’t be called risk). So you get an inherited variability, not a “race to the top”. I’m not saying that this is the only way evolution works (of course, actually opportune traits also get inherited), but it’s one thing that is likely to happen.

    The fact that males inherit traits from both their fathers and their mothers doesn’t mean that each and every trait is equally realized in both sexes.

    The paper doesn’t look very deep to me, but then again it was written for the Mathematical Intelligencer, which is — sorry — not a very deep journal. It’s more about mathematicians than about mathematics; it has an explicit “Viewpoint column” that says “Disagreement and controversy are welcome”; it publishes poems, philosophy and politics. What it doesn’t seem to publish (or at least not in the few issues I’ve checked) are proofs. I’m a bit surprised that NYJM took the paper, seeing that it is indeed not a strong research paper — maybe someone was trying to make a point here.

    • araybold Says:

      I think you have inadvertently identified a weakness in the argument: it is too general for its own good. If it were a sound argument, it would apply, not just to the specific case addressed in the paper, but to evolution in general. The the idea that evolution optimizes for variability, rather than fitness, is a very different theory than today’s (neo-)darwinism, and one that lacks the very strong empirical evidence that supports Darwin’s version.

      One might argue that there are circumstances when high variability could enhance a lineage’s ability to evolve to adapt to changing circumstances. One might suspect, for example, that it shaped the evolution of sex itself, and might be an explanation for the evidence suggesting that parthenogenic species tend to become extinct faster than their sexually-reproducing cousins. This, however, would necessarily be a second-order effect: it would be beneficial only because there is selection for the fittest, and if one wants to argue that it dominates survival of the fittest in some specific case, you need to make a case-specific argument for overturning the general mechanism of evolution.

    • Darij Grinberg Says:

      @araybold: “the idea that evolution optimizes for variability, rather than fitness” is only part of what I’m suggesting. I think evolution optimizes for fitness *whenever fitness can be achieved* (e.g., when there is an optimization that can be done with no downsides), but when it can’t it can still optimize for variability (which happens, e.g., when there are downsides — such as with risk-seeking behavior). And I’d say most things have downsides at least on an evolutionary scale, even though in the last 500-or-so years we have eliminated some of them (such as artificial food production making energy saving unnecessary).

    • araybold Says:

      Apparently, WordPress will not allow me to reply directly to your last post, so I will have to reply here: if there are situations where fitness cannot be achieved, than variability is moot. The paper is tacitly making the opposite claim than the one you are making here: it claims that the alleged increased variability is a *consequence* of there being a fitness that is being selected for.

      What this argument is missing is specificity to sexual selection. The whole point about sexual selection (an important insight of Darwin, which answered a host of potential objections to his theory) is that there *is* a fitness function that can be optimized for even in these cases – so what is missing *from the paper’s argument* is a reason for thinking that variability trumps fitness *in this case* (regardless of what case might be made with regards to energy use and artificial food production, for example.)

    • Darij Grinberg Says:

      @araybold: Can you go into more detail and perhaps suggest a readable reference? I can’t follow you here, but I don’t know any non-pop evolutionary biology, so it’s probably on my side.

      If Ted Hill is claiming that evolution will favor variability on *every* trait, then he is probably seriously off-base. Variability on lactose tolerance serves no fitness purpose if you live in Northern Europe; clearly, the tolerant will simply win. But variability on things like height, where either direction has its ups and downs, makes perfect sense. Are IQ and mathematical ability of the one or the other variety of traits? I’d assume that until fairly recently (say, 500 years ago at most), they were a mixed blessing, and an egoistic gene wouldn’t want all of its offspring to be high on abstract thinking when that comes with the concomitant disadvantages (poor eyesight, greater likelihood of autism, etc.).

    • araybold Says:

      I suppose the situation you describe could exist in principle, but it seems to be a very special case, and furthermore, it is not the case the paper is considering.

      The unusual thing about your case is that it posits a dimension of variability that manifests in observable consequences for organisms, yet which is precisely neutral with regard to fitness. You suggest that this might be because variation has both positive and negative consequences, but we have examples where this is the case, and selection still finds optima. One well-known example is the recessive allele that provides resistance against malaria, but which causes sickle-cell anemia in those with two copies of that allele. It is clearly understood that natural selection selects for this allele where malaria is endemic, and against it otherwise.

      Now, suppose there is a sub-population without the allele in an area infested with malaria. If malaria is suddenly wiped out, this sub-population now has an advantage over the sub-population with the allele. If the selective pressure were strong enough, however (e.g. if both malaria and sickle-cell anemia always caused death in childhood), there would be no allele-free subpopulation to speak of in this area, only the few individuals born without the allele and doomed to die without reproducing, were it not for the sudden disappearance of malaria.

      The paper, however, is explicitly not considering the sort of neutral variability that you propose – it is predicated on selection (for fitness) occurring. As the author of this blog points out, it claims that *higher* selection pressures favor *increased* variation in the trait subject to selection. Furthermore, while the paper is nominally only considering sexual selection, the argument used, if sound, would apply to variation and selection in general – and, if it did, then (neo-)darwinian evolution simply would not work.

      The blog author has pointed out some highly dubious aspects of the paper, but really, one can see there are problems in the first case of its first example, where the paper’s author tacitly contrasts a gaussian subpopulation with a bimodal one. Here, he is, in a sense, gerrymandering his subpopulations to achieve his results, and if we were to consider the population as a whole, we would get the unsurprising result that selection favored subpopulations scoring more highly in desirability.

    • Darij Grinberg Says:

      @araybold (3rd comment on this branch): Thank you, this is actually concrete and useful. I am still not fully convinced. You seem to be discarding the usefulness of mixed strategies (in game-theoretic terms). If you don’t know if your next generation will be living in times of (relative) plenty or hunger, it makes sense for your offspring to be of varying heights, rather than all as tall as possible or all small and slim. Here the variance itself is the optimum, rather than one of the extremes. Has evolutionary biology shown that mixed strategies don’t actually get used?

      Also, Hill doesn’t really talk about fitness, but rather about desirability. So the analysis should apply to peacock’s tails and lyrebird’s songs, whether or not these traits have any effects other than sexual attraction. Or does that too get counted into “fitness”?

      I also don’t see where bimodality occurs in the paper — there’s merely a comparison between distributions with fatter and thinner tails. I’m sure those can occur in nature.

    • araybold Says:

      @Darij: I mentioned the emergence and persistence of sexual reproduction in my first post because it has been suggested that its fitness is precisely that it enhances variability, though that is but one of many hypotheses. I think the biggest problem for variability-is-a-fitness in general is that evolution does not prepare for the future: given two individuals, one of whose offspring display greater variability while the other’s are more fit for the current environment, the latter is likely to be more reproductively successful unless the environment changes enough to overturn the prevailing notion of fitness. Unless the selective pressures are slight, the high-variability, lower fitness trait is unlikely to persist, waiting for the rules to change.

      In your lean-vs-fat years example, if things are highly variable year-to-year, there probably will not be any large organisms – they only thrive when there is relative stability.

      The key insight of Darwin’s, with regard to sexual selection, is precisely that desirability is a fitness. That, combined with natural selection’s inability to prepare for the future, solves the paradox of species evolving gender traits, such as the male peacock’s tail, that would seem to set them up for extinction if the environment becomes more hostile.

      I think Hill has bimodality in the example I mention, where one of his subpopulations consists only of highly desirable and undesirable individuals. This may not have made it into his final analysis, but the fact that he presents this example, demonstrating a sort of gerrymandering of subpopulations, raises doubts about the whole paper.

      As you have not objected to Gowers’ point that Hill’s analysis implies that increased selection pressure leads to increased variation, I assume that you recognize that it is a valid concern.

    • Darij Grinberg Says:

      @araybold: Interesting. The idea that “evolution does not prepare for the future” doesn’t seem to fully square with the selfish gene theory, though, or at least with my (outsider) concept of it. But I indeed don’t remember any proven examples in which a species deliberately plays mixed strategies with some trait instead of just converging on the optimum. I thought height would have a reasonable random component, but apparently it’s extremely heritable ( https://www.scientificamerican.com/article/how-much-of-human-height/ ). This makes intelligence my go-to example, but its heritability is also significant and it suffers from a wealth of non-equivalent definitions. So maybe variance-as-fitness isn’t that common in nature.

      I agree, Example 1 is exaggerated, but I don’t see this as a serious flaw. In mathematics, an example is expected to be intrinsically correct and to illustrate something about the model; it doesn’t have to be realistic, representative or useful. If it exaggerates some effect to raise attention to that effect, that’s for the better. If this is different in biology literature, then a certain amount of misunderstanding should be taken for granted.

    • araybold Says:

      @Darij: The selfish gene hypothesis is about something very different – essentially, that genes are the ‘units of selection’. Dawkins is under no illusion about what natural selection can and cannot adapt for.

      While one poor example is certainly not fatal, it raises the questions of why the author included it and what sort of review the paper received. With regard to the former, one hypothesis is that he is not aware that it is a poor example, or why.

      This is far from the only criticism of the paper, and to me, the conclusion that stronger selection leads to greater variance, and from an analysis that would appear, if valid, to apply quite generally to evolution, is one of the bigger red flags.

  2. Darij Grinberg Says:

    PS. As to this:

    “But in this case, instead of throwing up our hands and saying that we can’t fight against biology, we will say that we should do everything we can to compensate for and eventually get rid of the disadvantages experienced by women.”

    This is hardly a problem with the paper, which merely tries to give a model that describes(!) what is going on. It’s not even talking policy. If we are to follow your suggestion — that we should compensate for disadvantages that may be natural (how?) — then to do this requires understanding and measuring these disadvantages in the first place. Not to mention that this suggestion isn’t everyone’s idea of fairness: It’s one thing to want women to have access to physically demanding jobs like a fireman’s if they measure up to it; it’s another thing to lower the bar because you don’t like small percentages. In professional mathematics, of course, you won’t get small percentages, but more like 30-50% representation depending on what you measure (my subject is one of the better off), but the idea is the same.

    • Xys Says:

      In the case of Basketball, instead of throwing up our hands and saying that we can’t fight against biology, we will say that we should do everything we can to compensate for and eventually get rid of the disadvantages experienced by short people.

    • gowers Says:

      I carefully didn’t present it as a problem with the paper. To repeat the context of that sentence, if an environmental explanation is correct — and there certainly are reasons to believe that the way society is organized puts women at a disadvantage when it comes to mathematics — then it makes sense to try to bring about change. (Xys you seem to have missed this point completely with your analogy, which works only if you assume that the underrepresentation of women in mathematics reflects a biological disadvantage, which is precisely the case that was not under discussion here.)

      Note also that there are many ways of compensating for disadvantage — it doesn’t have to mean giving jobs to people in the disadvantaged group who wouldn’t otherwise have got them. For example, one can make more of an effort to support and encourage women who are on the mathematical ladder than one would make for men. I don’t think one needs to wait for careful measurements of the level of disadvantage before doing things like that.

  3. ziggurism Says:

    Ok the paper is not very good.

    But can you make a comment about the heavy-handed deletion process? Surely once a journal has refereed and accepted and published a paper, they shouldn’t just delete it from existence? There should be a retraction notice. Not lobbying from friends of the board of the journal to pretend it never existed?

  4. Peter Says:

    It seems to me that to debate or even refute the technical basis of the paper after the fact is to completely miss the point here. If we accept the author’s account as given in the Quillette piece, the paper was enthusiastically accepted for publication in two journals, only to be rejected later on the back of a lobbying effort that was motivated by ideology rather than the technical merits of the paper. This corruption of the academic process is the story here. The correct and fair outcome for a paper that has passed the refereeing process is for it to be published, not censored. If its claims are indeed as flimsy as you suggest, surely they can be thoroughly debunked in a reply, and then we have all learned something and the sum total of knowledge advances.

  5. Yemon Choi Says:

    (test message – I tried to leave a reply to one of Darij’s comments, but it seems to have disappeared into thin air)

    • Darij Grinberg Says:

      Well, at least I can see this test post… Sorry for the loss; I should have learnt many times over to write my comments in a text editor, but I still keep forgetting.

  6. Pierre Menard (@pierremenard128) Says:

    > When applied to humans, this model is ludicrously implausible. While it is true that some males have trouble finding a mate, the idea that some huge percentage of males are simply not desirable enough (as we shall see, the paper requires this percentage to be over 50) to have a chance of reproducing bears no relation to the world as we know it.

    Polygamy can lead the precisely the situation in the model. Imagine a society with equal number of males and females but where every male has two female wives. Then one half of the men do not reproduce.

    The technical term for this is effective population size: the number of individuals who contribute offspring to the next generation. See https://en.wikipedia.org/wiki/Effective_population_size

    There is actually some research on a closely related question: the ratio of effective population size between men and women. For example see Table S3 of this paper:


    ..where it is claimed that, over a range of populations, the ratio of female to male population size ranges from 1.8 to 14. I also found this recent paper
    which re-analyzes a dataset of several hominid linkages and finds it “…consistent with a female effective population size roughly twice that of males.”

    None of this settles whether over half of males were unable to find a mate in prehistoric times — but it does lend a lot of plausibility to that hypothesis. In particular, I’d guess that your incredulity is really an over-extrapolation from the modern world.

    • Jim the Curmudgeon (@curmudgeon_jim) Says:

      Good point. I was going to raise the issue of the female/male ratio over time, but I neglected to consider the issue of polygamy.

      In addition, there is some evidence in modern times that women do tend to compete for the top 20% of men, while men in the lower quantiles have a hard time finding mates.

  7. Pierre Menard (@pierremenard128) Says:

    …actually, I take it back: the links I cited more or less settle it. If p is the proportion of males who contribute offspring, and the ratio of female-to-male population size is 2, that means that a 2p proportion of females contribute offspring — and since 2p<1, this gives an upper bound of p<1/2.

    Given that 2 is actually at the low end of estimates of female/male effective population size, it seems that the model used in this paper is quite plausible.

    • Victor Says:

      I think the original post should be edited to reflect this. Particularly since, after reading the relevant critical paragraph, I also found this same evidence with a 30 second google search.

      The criticism mainly pertains to model plausibility, but the model appears to be plausible. Thus, the post is misleading as it stands.

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  12. valuevar Says:

    … we will say that we should do everything we can to *compensate for* and eventually get rid of the disadvantages experienced by women. [my highlight]

    Well, that is a key issue, isn’t it. Obviously getting rid of disadvantages is a good goal in itself (though whether it justifies suppressing research (bad or not) that can be used to support possibly harmful views is another matter). The idea of *compensating* for alleged inequalities, by means of “positive discrimination” of various sorts — and, in particular, justifying and fine-tuing such positive discrimination by saying that a skewed distribution must be caused primarily by discrimination — is what is really at stake.

  13. mk270 Says:

    Tim, have you anything to say from an open access perspective about this remark in the Quillette article?

    “I [i.e., the paper author] pointed out that if the deletion were permanent, it would leave me in an impossible position. I would not be able to republish anywhere else because I would be unable to sign a copyright form declaring that it had not already been published elsewhere.”

    • gowers Says:

      That sounds to me like a small problem that could easily be solved with some ad hoc arrangement. It is quite common, for example, to erase part of a copyright form before signing it: for example, I never agree to hand over copyright to the publisher, and my erasing of that part of the form doesn’t stop journals agreeing to publish my articles.

  14. valuevar Says:

    I am more than willing to believe that the paper is not very good or very deep. It is also the case that it could be misused or misinterpreted. Still, that has no bearing on whether the procedure followed was correct. Besides, would a better paper (still about an abstract model, with no necessary direct bearing on reality) have been treated differently? Part of me wishes for such a better paper, if only to show that the problem with the position it purports to support does not lie at the stage of producing a valuable model.

    • gowers Says:

      It’s worth having a look at the first comment on this page, which suggests that there was more to the story of the “unpublishing” of the paper by NYJM than you would guess from reading the Quillette article.

    • valuevar Says:

      I don’t doubt that the story at NYJM had complicated angles to it – to begin with, Igor Rivin *is* an extreme, uncollegial troll, to put it bluntly. (It’s hard to say that about a colleague, but there it is.) The main issues remain, particularly regarding what happened at Math. Intelligencer.

    • Darij Grinberg Says:

      @gowers: The top post at HN (by tptacek, whom I generally trust) is claiming:

      > Here’s where the plot thickens: apparently, Hill’s paper didn’t undergo normal peer review at either journal, and, in particular, was fast-tracked in (papers apparently appear in NYJM as they’re submitted, not in annual editions) by an editor that vocally shares Hill’s politics.

      Are we sure it didn’t undergo normal peer review at the Intelligencer? Same question about the NYJM (but here it looks more plausible).

      Also, how typical is it that a paper is bumped from a journal to another one without a new round of peer review? I have my suspicions that this happens, but this would be the first time I see a paper bumped from an expository journal into a research one.

      The icing on the cake: If I try to download the Kumar-Sahni-Singh paper from one of the official NYJM mirror servers — say, the AMS one:
      I get the abstract of the Kumar-Sahni-Singh paper, but the PDF files of Hill’s variability paper. I am really fascinated by how this affair is making everyone look like an idiot.

    • Igor Rivin (@igriv) Says:

      Firstly, I would like to thank Harald, known as the most charming of humans, for besmirching my character in a public forum. Secondly, the comments pointed to by Tim are just false. The paper was properly refereed at NYJM, and went through MORE than the usual vetting (NYJM requires one report, we got two; no approval for the full board is required, or ever obtained. The approval of the Editor in Chief is not required (but was obtained in this instance). Abuse of the form “I would not have accepted this paper” is entertaining but off the point – you were not the editor nor the editor in chief nor a referee. Modesty prevents me from speaking on the mathematical merits of the editors, but the referees were excellent mathematicians who had both published extensively in both pure and applied mathematics.

      So, the procedure was followed. Tim Gowers is an excellent mathematician, as we all know, and if Ted Hill’s paper caused him to think about the problem, the mission of the paper was accomplished – it was the first paper in what was hoped for to be a lively scientific exchange. However, the usual format for a scientific exchange is:
      Paper A appears
      Paper B appears enhancing (or questioning) the methods of paper A
      Paper C appears improving on A&B

      And so on.

      By contrast, Gowers seems to suggest that no one should publish anything until “the proof from the book” is found. That does not work even in pure mathematics, and has no hope of success in applied areas.

    • valuevar Says:

      You are more than welcome. I would not feel comfortable besmirching people’s characters behind their backs.

    • Jim the Curmudgeon (@curmudgeon_jim) Says:

      For any of Mr Rivin’s alleged flaws, I agree with him completely. The proper response to the publication of a poor model is a critique of that model.

      Mob outrage is the sort of thing that we would expect in a theocratic society. I am merely surprised that the author of this piece was not asked to drink hemlock.

    • valuevar Says:

      It should be clear (from the remark I originally made, to which all of this is a reply) that I am also troubled by questions of procedure. The only effective rebuttal (if you do have a rebuttal) is a rebuttal, and not what will come through as a necessarily unsuccessful attempt at suppression.

      At the same time, there may be more to this story. Amie Wilkinson states that she was indeed asking for rebuttals to be published, and not for the article to be unaccepted: https://math.uchicago.edu/~wilkinso/Statement.html It would be more common for such replies to be included in a later issue, but still.

    • Anonymous Says:

      According to Hill, Farb specifically asked for the paper to be deleted:

      “Professor Farb had written a furious email to Steinberger demanding that it be deleted at once.”

  15. 17c Says:

    Historically, males WERE 50% less likely to reproduce than females. That’s why we have 2x as many female ancestors as males. The ratio until very recently—likely the population explosion of the Industrial Revolution—was closer to 4:1, and at times has been measured as high as 17:1. That 17:1 ratio wasn’t in caveman days, it was after the invention of agriculture.

    If anything, then, the study underestimates the selection pressure of female choosiness.

    • Jim the Curmudgeon (@curmudgeon_jim) Says:

      Quite right, this is something that the author of this post is apparently unaware of. The male/female ratio that we see in modern times is not representative of the past. I recall seeing a study on relatively contemporary Greenland where the ratio was quite high, and that wasn’t in the dim past.

  16. Josue Ortega Says:

    Nice post. My humble opinion is that this is a controversial model that should be discussed by the scientific community and not just deleted from journals. We may agree or not with the findings but this requires an exchange of ideas, not the suppression of them.

    • Jim the Curmudgeon (@curmudgeon_jim) Says:

      As a non-mathematician but someone with a PhD in an area of applied science that is quite mathematical, I am rather surprised at the apparent consensus that a paper explicating a model of dubious quality should be unpublished.

      I haven’t had a chance to read the paper, and I assume for the sake of argument that the model is a poor model. My concern is rather with the attitude that a poor model can be consigned to oblivion on account of its flaws.

      If we applied this to other areas of research, we would have to jettison half the previously published work in geography, regional science, climate science, evolutionary biology, etc.

      (Let alone the crap that is published in the social sciences using such ‘methods’ as auto-ethnography).

      Is the perceptron an adequate model of neural behavior? Is Arrhenius’ original climate model a realistic model given what we know from the natural sciences? What about Von Thunen, or any model of regional growth in cities? Models from economics that elide temporality and assume instantaneous feedbacks? Transport engineering and transport mode choice?

      I have seen plenty of papers in my own field with outright mistakes in the proofs or in the software implementations. Thomas Herndon found an outright bone-headed error in a major paper by Reinhart and Rogoff that was used as the basis for policy affecting millions of people.

      I have never seen a paper unceremoniously unpublished in this manner. If a model makes unrealistic assumptions or has flaws in its formulation, simply publish a rebuttal. There is something questionable here about the way in which this particular paper is being treated, and the default hypothesis seems to be that the implications about gender are behind the rather idiosyncratic treatment. In short, we all know what happened to Larry Summers, and it appears that the same thing is happening here.

    • gowers Says:

      This is a reply to JimTheCurmudgeon. I think what you suggest would be fine for a science journal. But a paper with virtually no mathematical content is not a good fit for a mathematical journal such as NYJM (if you look at the other papers in the journal, you will see that they are of a completely different character), and if in addition the model is not realistic then it is hard to see why one would make an exception for it.

      Of course, unpublishing a paper is a drastic step, and one that I would not advocate unless proper editorial procedures have not been followed, as happened in an unfortunate case recently with a journal for which I am an editor, though in that case it was eventually decided to keep the paper published but to add an official statement saying that the decision had been a mistake and had been taken by one of the managing editors without the knowledge of the editorial board. There has been a suggestion that the decision by NYJM to publish Hill’s paper was a similar case, and also a strenuous denial of that suggestion.

      I don’t think there is a consensus at all that a paper of dubious merit should be unpublished. If editors make a judgment that they then regret, most people, including me, would say that that’s just too bad. It now seems that even the people who, according to Hill, campaigned to have his paper consigned to the memory hole did not in fact advocate this. See this statement, for example.

  17. Anonymous Says:

    Dear Prof. Gowers, do you have such a long (or any) post about Sergeev’s paper accepted by your journal?

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  20. Pratap Raychaudhuri Says:

    The criticism starts correctly by pointing out technical flaws but soon veers into the domains of sermon and rhetoric.

    For example, “But in this case, instead of throwing up our hands and saying that we can’t fight against biology, we will say that we should do everything we can to compensate for and eventually get rid of the disadvantages experienced by women.” has nothing to do with the paper.

    • gowers Says:

      You are right that it has nothing to do with the paper, as I made clear in the post. Note also the context of the sentence you quote, and in particular the words “in this case”. I was saying that an environmental explanation also fits the facts well, and would have different consequences if correct.

  21. 17c Says:

    By the way, your secondary argument (“But why aren’t these high-variance traits simply bred out of existence over time?”) is eliminated by the existence of peacocks, birds of paradise, and other such creatures.

  22. Krzysztof Says:

    Choosing to engage this elaborate troll on whatever merit it might had (notice the differences between versions, introducing more and more opinion info what was firstly just about badly recasting outdated evolutionary biology) is a mistake, but I’d also point out that males are selective as well and there is no data to justify thesis who is more selective (the genome data is about what percentage of population contributed to subsequent generations, quite a different thing not exclusively related to what percentage of population were mating).

    The more interesting part and what the story and outrage (bipartisan I might say) hinges on is the conduct of the journal involved (let’s leave Mathematical Intelligencer aside as not quite serious as evidenced by its editor first inviting to “stir up controversy”, which was already unprofessional, and then receding on fear of receiving it because of “a possibility of being hyped internationally”).

    With NYJM, a similar case happened at EMS Surveys in Mathematical Sciences where the “grossone” paper of Yaroslav Sergeyev was accepted behind backs of the Editorial Board (of which prof. Gowers is a member). One would expect a commentary on practices allowing such papers to be sneaked in and also subsequent handling. NYJM Board apparently decided publication didn’t really happen at all and didn’t even bother retracting, while EMSS Board while “unanimously
    dissociates itself from this” stopped short of issuing a retraction notice http://www.ems-ph.org/journals/notice/emss/ed_note.pdf

    • Darij Grinberg Says:

      This is not like Sergeev’s “grossones”. Sergeev built an ill-defined theory on shaky ground, defending himself by questioning the need for rigor, while at the same time claiming to have solved some of Hilbert’s problems. Hill’s paper does what little it wants to do — it studies an unsophisticated but plausible toy model that demonstrates why variability can arise — and never claims more.

    • Sergei Yakovenko Says:

      In contrast with NYJM, the ill-famed really pseudoscientific paper by Sergeev remains on the EMSS site exactly as it was “published”. It is accompanied by the Editors statement, but did not disappear in the memory hole.

      Besides, in that case the two Editors-en-Chief took the personal responsibility and resigned. Still waiting for similar measures taken by NYJM editors?

    • Krzysztof Says:

      I do not especially care about controversies and their (dis)contents, but editorial failure modes that allowed these cases to occur.

      In cases of various misconduct we usually meet with incompetence breed by specialization, breach of referee integrity, rogue journals &c. But here we have something kept from the editors in unusual ways.

      Other than that the two cases are entirely different. EMSS paper could be argued is still on-topic. Even as garbage, it is a mathematical one.

      NYJM on the other hand allegedly (Editorial Broad might have come to a different conclusion) published a wall of text culminating in a trivial statement that variances on input give output variance. The entirety of “modeling” here is contained in assumptions about the input, whose justification is a work of social science or evolutionary biology at best, and entirely off-topic.

      As for what you call “plausible” assumptions, Prof. Gowers or I readily came up with unhandled cases. There are entire fields dedicated to study of relevant assumptions, no members of were consulted. The last point should be a wider concern with modeling in general.

    • Krzysztof Says:

      Further it is not a “toy model”. Toys are interesting and behave in interesting ways. Here nothing interesting can be said, that’s perhaps why usually done sensitivity analysis of the model was forfeited, since it is obvious.

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  24. Bogdan Grechuk Says:

    When I studied at school, there was several students having maximal mark in math in our class – 2 boys (including me), and 5-6 girls. We had internal math Olympiad in school, and there were significantly more girls there than boys participating in it. Students with minimal mark where mostly boys.

    Few winners were promoted to town Olympiad, where there were already a bit more boys than girls. Winners of that were promoted to region Olympiad, winners of that – to country Olympiad, and finally – to the international Olympiad (IMO). The percentage of girls significantly decreased at every stage. At IMO, we had 6-boys team, many other countries had the same. Some others – 5-boys-1-girl team. The overall percentage of girls was tiny.

    I strongly disagree that Olympiad rules were unfair, at least in my country. I was a boy from small town, from family with no money or power – in case of unfairness I would never win. In our region team for country Olympiad we had some preparation, joint problem solving activities, etc., and really see who is stronger. The stronger students eventually won.

    After becoming a lecturer, I have marked Olympiads several times. The marking was fully fair and blind, no advantage for boys.

    Do you have any explanation why (i) there are so few girls at IMO overall, and (ii) there are fewer girls than boys at IMO even from any SPECIFIC country (like USA or UK), where we can witness the fairness of selection process.

  25. davidmfisher Says:

    I think the whole thing stinks even worse. Tim has the decency to point to his lack of expertise as an evolutionary biologist. The authors don’t and first send their “article” to popular mathematics journal and when that doesn’t work, to a journal in (mostly) pure mathematics. This clearly marks them as unwilling to deal with the potentially rigorous critiques of their model coming from people with actual expertise on it’s subject matter. Trying to describe the article as just about mathematics is really quite absurd and it should never have been published in a venue without the expertise to evaluate the clearly not entirely mathematical claims. The scandal is not the failure to publish in the end, but the decision to publish in the first place.

    • Darij Grinberg Says:

      Ted Hill in the NYJM version of the paper (here’s it on one of the official NYJM mirrors, which seemingly forgot to replace it: https://ftp.gwdg.de/pub/misc/EMIS/journals/NYJM/j/2017/23-72p.pdf )

      “The goal here has been neither to challenge nor to confirm the VH, but rather to propose an elementary mathematical theory based on biological/evolutionary mechanisms that might help explain how one gender of a species might tend to evolve with greater variability than the other gender.
      Bear in mind that the precise formal definitions and assumptions made here are clearly not applicable in real-life scenarios, and that the contribution here is thus also merely a general theory based on unproved and unprovable hypotheses. This theory is independent of species, and although it may raise red flags for some when applied to homo sapiens, we share the viewpoint of Eriksson et al that the “variability hypothesis is not only of mere historical
      interest but also has current relevance for clinical practice” [EMTA12, p. 329].”

      In other words, it is a toy model, which aims to explain why the greater-variability hypothesis is *plausible*, rather than actually model it to today’s quantitative standards. It’s meant to start a discussion, not to end it. It was written for the Intelligencer, not for NYJM, and it is well within the range of Intelligencer articles; it’s actually on the deeper side of them.

    • davidmfisher Says:

      I don’t see why calling it a “toy model” makes it less obviously garbage from the point of view of biological or social science. Or why that justifies publishing fake social or biological science in a math journal. They claim their mathematical theory is based on “biological/evolutionary mechanisms” but appear to only have a rudimentary understanding of those mechanisms. If they were serious, they would learn something and interact with people who understand those mechanisms before making public claims of any kind based about them. I don’t follow the Intelligencer, but if even if they are in the business of publishing pseudo-science, I think it not terribly controversial if they chose to retract some of the worst pseudo-science they publish. NYJM publishing it was simply and entirely unforgivable.

    • Yemon Choi Says:

      Seconded. As I tried to write in a comment to Darij earlier (perhaps it got blocked by the spam filter?) the paper really doesn’t fit NYJM’s scope and level, as judged by the volumes to date. I think the parallels with the EMS Surveys case, while they shouldn’t be exaggerated, are very real (in terms of editorial process and its apparent failure).

    • Yemon Choi Says:

      Let me try again with a lightly edited version of the comment I originally wrote in response to Darij’s first comment on the post.

      Darij said: “I’m a bit surprised that NYJM took the paper, seeing that it is indeed not a strong research paper – maybe someone was trying to make a point here.”

      Given the NYJM’s usual output, I think this is a massive understatement. (Also, as pointed out at https://www.reddit.com/r/math/comments/9e34xh/read_the_paper_so_hateful_it_had_to_be/e5o0fbo/ the version the Intelligencer received may have included other content wich they were not keen on.)

      I am circumspect about various details mentioned in Hill’s Quillette piece, since the provenance of various quotes is not really clear, and 1st-hand acccounts seem to be being mixed with hearsay. That said, it doesn’t seem like NYJM went about dealing with this the right way: a retraction, if that was the consensus of the editorial board, seems more fitting.

    • Yemon Choi Says:

      FWIW, Hill has done some interesting mathematical stuff even after the so-called main part of his career: see the stuff on Benford’s Law, and cake-division problems. But the level of mathematical detail and care in those works seems rather higher than in the article under discussion here.

    • Darij Grinberg Says:

      @davidmfisher: Do you have some readable introductory sources on modern evolutionary biology that clarify what is wrong about the Hill approach? At this point, your comment is a rather vague “trust me, I’m an expert”.

      @Yemon Choi: I think Hill gets the facts right (yep, that paper did get replaced, as you can check by looking at the official AMS mirror: http://www.emis.ams.org/journals/NYJM/j/2017/23-72v.pdf ) but some of his interpretations look off to me. In particular, I’m not buying his claim that he cannot republish it any more due to the copyright agreement (NYJM is an OA journal and the copyright agreement has probably been mooted anyway by the editors), and I think this claim by Steinberger:

      > Half his board, he explained unhappily, had told him that unless he pulled the article, they would all resign and “harass the journal” he had founded 25 years earlier “until it died.”

      looks like a poetic overstatement (he must have had a surprisingly responsive editorial board, if “half his board” has answered his mail). But the gist of the issue, I’m afraid, is exactly as Ted Hill has been explaining it.

    • Jim the Curmudgeon (@curmudgeon_jim) Says:

      “But the level of mathematical detail and care in those works seems rather higher than in the article under discussion here.”

      That has to be one of the most staggeringly inept observations on this entire post.

      Why should someone developing a model intended to explain purported phenomena meet the same standards for density of proofs as in a pure mathematics paper?

      Half of the sciences are like this. I daresay you haven’t read much in the way of mathematical modeling in natural science or engineering, because you seem to be unaware that the typical process is to publish a simple model first, critique it, refine it, and work from there. Simple models are used as baselines for more complex models. In climate science, major research centers run ensembles of different models simultaneously as sanity checks.

      Assuming that the applied science community is too stupid to figure out that this is a first cut model is somewhat strange. Apparently we are more aware of the iterative and tentative nature of mathematical models than pure mathematicians are.

      Yes, definitely useful to have the actual statement of phenomena reviewed by people in the field. No, a paper providing a simple mathematical model does not have to look like a paper in pure mathematics. Von Thunen, Schelling, or a host of other widely respected researchers were not in the habit of writing pure mathematics papers either.

    • Igor Rivin (@igriv) Says:

      David, I have been very civil here, but you are not being so. You have 0 competence in applied mathematics of any kind (as per your publications list), so your calling the paper “garbage” and maligning the editorial process at NYJM is completely out of bounds and insulting the the NYJM editors and referees.

  26. domotorp Says:

    I guess the only part of this blog post that will make it to popular journals is that according to Sir Gowers “men were prepared to shag pretty well anybody, but only some small percentage of particularly hunky men got their way with women…”

  27. M Says:

    Apparently the paper had a very positive referee’s report. The only explanation I can think of for that is that it was written by somebody who worked in evolutionary biology, didn’t really understand mathematics, and was simply pleased to have what looked like a rigorous mathematical backing for their theories. But that is pure speculation on my part and could be wrong.

    The paper was published and depublished in two different math journals, so it seems likely that the reviewers were mathematicians. The problem, I believe, is rather that both the author(s) and the editors/reviewers are mathematicians with a tenuous grasp of evolutionary biology. For example, the argument of the paper seems to rely on some strange kind of group selectionism which no biologist would subscribe to. Restating the argument in terms of allele and genotype frequencies as biologists would do would probably make its implications much more transparent.

    • deaneyangDeane Says:

      The *real* question is, if the paper is really about evolutionary biology, why was the author trying to publish in in math publications, where it would be refereed by people who have, as you say, “a tenuous grasp of evolutionary biology”?

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  29. Gerard Harbison Says:

    That’s it in a nutshell.

    But a more basic issue is: can you even select for ‘variability’ without group selection? How do you define variability without a group?

    • Pat Says:

      Gerard, I could see ‘variability’ itself being a heritable trait *if* it acted by reducing the buffering against, or increasing the sensitivity to, developmental noise or similar (i.e. if some genes on the Y were able to mediate such processes).

      So, I think this *could* manifest at the gene level without having to resort to explicit group selection, at least in theory. No?

    • Gerard Harbison Says:

      That would be a reasonable mechanism to explain why men might be heritably more variable than women. The question is then why sensitivity to developmental noise might be an adaptive trait and therefore be positively selected.

      A somewhat similar idea that has been considered is whether an ability to tune mutation rates might itself be an adaptive trait. This paper considers it

      (apologies if you’re paywalled)


      But needless to say, that’s not the model Hill used.

  30. Gerard Harbison Says:

    By the way, parenthetically, there is genetic evidence that at some points in our past, the vast majority of males did not leave offspring. One point was about the time we transitioned from hunter-gatherers to agriculturalists. You can even follow this geographically as agriculture spread.

  31. Jason Says:

    “still wouldn’t imply that it is pointless to try to correct the underrepresentation of women amongst the higher ranks of mathematicians. ”

    I agree that it can be good to remove unfair barriers, but I think trying to reach equal proportions of men and women in every field is misguided. See this blog post:

    I think most people who believe that sex differences are the result of biological factors would argue that they are the result of differences in interests, not differences in intelligence. Here is a review article on this:

  32. Alexander Barvinok Says:

    I’d like to share the letter I sent to the American Math Society:

    Dear Colleagues,

    I’d like to draw your attention to the article


    I suggest that the AMS check on the facts in this article. If the allegations of intimidation of the authors, bullying the editors and expunging an already published paper from the archive are true, a serious injury has been inflicted on the profession and we should all try to repair the damage.


    -Alexander Barvinok

    University of Michigan, Ann Arbor

  33. Tarun Deep Saini Says:

    I think you may have missed something important in your argument. Somebody may have pointed it out above, but let me state it again for your consideration.

    If the mate selection is based on a single physical trait, for example height of a male, then quite obviously only tall guys get to propagate their genes, and then obviously the male population becomes taller with time, which is somewhat similar to the ever more cumbersome peacock’s tail. Thus, obviously, it produces less variation in height rather than more. This part is reasonable.

    However, in humans (and other species), females may select based on many independently or jointly desirable traits. If we consider a certain number of such desirable traits, then starting with an N-dimensional Gaussian distribution, selection happens primarily outside an hyper-ellipsoid (in a percentile sense), which keeps on moving outwards due to evolutionary pressures as extremes of independent traits are selected. It is then obvious that selection based on any one trait may not select on the basis of other traits, which will thus survive even though they are quite weak.

    This is, in fact, quite obviously true for humans. For example, consider how many male body shapes and sizes, and levels of fitness are selected by females who are looking ONLY for mental acuity; and on the other hand, females who select ONLY for beauty usually don’t care care how dumb or smart their partners are.

  34. Daniel Says:

    Here’s my attempt at reconstructing the sequence of events:

    1. Hill and co-author write semi-serious pop-sci article with toy model explaining variability hypothesis. They send it to Math Intelligencer’s Viewpoint column, a quite appropriate channel for it.

    2. Feminists torpedo the publication. I assume there’s no traditional peer review at Viewpoint, both the acceptance and the pressured rejection were decisions by the editor-in-chief.

    3. Hill is outraged. Igor Rivin NYJM editor shares his outrage, and as a gesture, he decides to right the wrong by publishing the paper even though it’s completely inappropriate for NYJM.

    4. Rivin rushes the paper through peer review, possibly with a combination of A. enlisting reviewers who share his outrage, and B. not informing the rest of the editorial board.

    5. The editorial board finally becomes aware of the decision, now they are outraged, threaten Rivin and the editor-in-chief (who was largely absent during this for health reasons) of everything if the paper gets published in their journal.

    6. The feminists from Step 2 jump into this fight, too.

    7. The editor-in-chief is finally pressured into making the paper disappear, and decides that “memory-holing” it is better than a retraction that’s humiliating for all involved.

    8. Hill disagrees about the memory-holing being a good solution.

    • Gerard Harbison Says:

      Except it really hasn’t been memory-holed. I can find the preprint easily online. At this point, we’re talking more about the indignity, because it’s gotten far more publicity than publication in NYJM would ever have gotten it.

    • ziggurism Says:

      The feminists in question being allegedly Amie Wilkinson and her husband Benson Farb of the University of Chicago math dept. (Father and father-in-law too?)

    • gowers Says:

      According to Anonymous Participant, your point 2 is wrong. (It’s a fair summary of what Hill says, so it’s Hill who is being misleading. The most charitable explanation is that he didn’t set out to mislead but merely gave what seemed to him to be a reasonable interpretation of the partial evidence he had. But in that case, since he was publicly accusing certain people of behaving very badly, he should have made sure of his facts.)

    • deaneyangDeane Says:

      Could you provide a factual basis for items 2 and 6?

    • Marcus Says:

      Please define what you mean by feminist. Its generally accepted sense (Merriam-Webster): “the belief that men and women should have equal rights and opportunities”. You deployed the word as if it is something faintly pejorative. Do you believe that women should go back to not having property too?

  35. Leo Says:

    Professor Gowers,

    “When applied to humans, this model is ludicrously implausible. While it is true that some males have trouble finding a mate, the idea that some huge percentage of males are simply not desirable enough (as we shall see, the paper requires this percentage to be over 50) to have a chance of reproducing bears no relation to the world as we know it.”

    Wouldn’t the exact same argument apply to a model where the probability of mating was a function of where an individual is in the ranked set of individuals for a much larger set of functions than the one in the paper

    0% if below a threshold percentile x
    100% if above the threshold percentile x.

    It would just as well apply to functions like
    10% if below a threshold percentile x
    20% if above the threshold percentile x.

    and variability would still be selected for depending on whether x was greater than or less than the 50th percentile.

  36. P Says:

    > While it is true that some males have trouble finding a mate, the idea that some huge percentage of males are simply not desirable enough (as we shall see, the paper requires this percentage to be over 50) to have a chance of reproducing bears no relation to the world as we know it.

    Starting from birth, the modern figure seems to be around 25%, but historically it could have been higher (I see claims ranging from 60 to 90%). Anyone associated to a university is already surrounded by more-fortunate-than-average men, so it’s easy to get a misleading impression.

  37. Richard Says:

    This is an interesting analysis, but it seems rather to miss the point. His paper wasn’t rejected because of the subtleties of statistical reasoning. It was rejected (if his account is to be believed) because it failed to comport with the dominant feminist narrative. The majority of those who blocked it were arguing on ideological grounds, not mathematical ones. The proper place for your criticism surely was after publication, not after discovery of suppression of the publication. And, given the shear tonnage of nonsense feminist pseudo-research that gets published annually without the slightest objection, we would have to wonder why alternate viewpoints were held to such different standards.

    • Daniel Says:

      > This is an interesting analysis, but it seems rather to miss the point. His paper wasn’t rejected because of the subtleties of statistical reasoning. It was rejected (if his account is to be believed) because it failed to comport with the dominant feminist narrative. The majority of those who blocked it were arguing on ideological grounds, not mathematical ones.

      This was my starting point as well, but the reality is more nuanced. Please read my attempt at a summary slightly above your comment. It was rejected as a non-peer reviewed magazine column, apparently because “it failed to comport with the dominant feminist narrative”. Then people attempted to push it into a peer reviewed journal for ideological reasons. (I don’t mean right-wing conservatism, I mean free speech advocacy.) The people who blocked that second attempt had very good mathematical reasons.

    • Richard Says:

      Well I’m no mathematician, but a governance process that encompasses threatening your friends with being unfriended on Facebook seems an odd way to go about enforcing academic rigour and rolling back the frontiers of human knowledge. It does, on the other hand, seem entirely consistent with generally understood tactics of feminist coersion.

    • Jim the Curmudgeon (@curmudgeon_jim) Says:

      The paper seems publishable in a journal on mathematical or evolutionary biology, or perhaps even in the journal of artificial systems and societies. Complex systems science journals might have an interest.

      The reasonable approach would have been to reject it from a math journal and for the author to publish it in one of the alternative venues above. I suspect, however, that the level of vitriol and emotion that accompany this story indicate that the various actors were doing more than expressing discontent with the level of mathematical rigor.

  38. Lennie Friedlander Says:

    I also read the paper, and I also think that the model is probably oversimplified, though I am not an expert in population dynamics. However, in my view this is completely irrelevant. What is relevant is that a paper was being suppressed for the only reason that one can derive from it ideologically undesirable conclusions. I do not see what is the difference between this type of behavior and attempts to forbid teaching evolution in some parts of the world (no comparison made between Hill and Darwin). By the way, I am also on more liberal side of political spectrum.

    • gowers Says:

      “What is relevant is that a paper was being suppressed for the only reason that one can derive from it ideologically undesirable conclusions.”

      That’s what Hill says, but that’s what he would say. At least in the case of the NYJM a much more likely explanation is that it was a completely inappropriate paper for that journal, as it contains virtually no mathematics.

      Also, I find it weirdly old-fashioned to talk of the paper being “suppressed”, of of its “disappearing”, when it’s there on the arXiv for anyone to see, and the arXiv is the main way that mathematics is disseminated these days. Declining to give a stamp of approval to a paper is not at all the same as suppressing it.

    • Gerard Harbison Says:

      Igor Rivin, the editor of NYJM, actually invited Hill to submit it to the journal. And while we’re considering the influence feminist politics might have had on its retraction, we might as well consider how Rivin’s politics might have influenced his invitation.

      Or is that suddenly no fair?

    • Richard Says:

      I’m not sure if it’s fair or not. I am fairly sure, however, that there are far more feminists seeking to influence mathematicians than there are mathematicians seeking to influence feminists, so at the risk of invoking probability in a maths forum …

    • Jim the Curmudgeon (@curmudgeon_jim) Says:

      “I find it weirdly old-fashioned to talk of the paper being “suppressed””

      Who owns the copyright for the paper, exactly?

      Is the author able to have it published elsewhere?

      Someone mentioned above that there could be an ‘agreement’ for the author to be able to publish it in another venue. However, that’s not the whole picture. If the author transferred copyright to the journal, they control the publication and distribution of the work. The author is then at the mercy of the journal to be able to find an alternative venue for publication.

      Yes, it is available as a pre-print, but we all know that pre-prints don’t have the same prestige as an actual journal article. It’s a bit like putting down a deposit at a car dealership on a porsche, and then being told that you can’t have the porsche and your deposit will be returned to you as an equivalently valued Hyundai.

    • Igor Rivin (@igriv) Says:

      Gerard Harbison: I have been (and am) editor of many journals and have invited people to submit papers to all of them, viewing this as one of my primary roles as editor, to make great matches between authors/papers and journals. In the case of NYJM (which is not quite the Annals), this is a major role of the editor (people will submit to the Annals because of the name). What exactly is your objection?

  39. Stan Says:

    Excellent. Obviously no reason to publish this.
    Memory Hole, please. Along with papers on female- perpetrated domestic violence and false rape accusations.

  40. Academic publishing is a mess and it makes culture wars dumber | Give Info Says:

    […] This year, mathematician Theodore P. Hill co-wrote a paper about how the variability of traits differ between men and women. Uh-oh! It was accepted for publication by the respected academic journal The New York Journal of Mathematics. But within days it was gone, leading to accusations that scientific ideas were being suppressed. Upon close reading, though, the paper turned out to be, as Fields Medalist Tim Gowers put it, “a bad mistake.” […]

  41. Darij Grinberg Says:

    What’s with the sudden flood of “the paper hasn’t been properly memory-holed; it’s still on the arXiv” comments? That’s not the point. The point is that a journal to which the paper was submitted — and in which it wouldn’t have been out of place — has first approved it but then dropped it due to political meddling. And then another journal, which actually did have good reasons *not* to publish it, has first published it to prove a point, and then silently retracted it (“the commissar vanishes”-style), again due to political meddling. This is not about availability of the file — by that criterion, almost nothing is ever memory-holed these days, since you can find everything if you look hard enough on the internet.

    • Krzysztof Says:

      You omitted the part where it was published due to political meddling in highly unusual speedy fashion.

      Or that Theodore Hill, the author, turns out having a website called MotherFunctor where he calls for more activism in academia. I find his accusations of activism, while playing himself shocked in naive disbelief, insincere in that light. This is another circumstance that reinforces my belief of this being an engineered troll.

    • Darij Grinberg Says:

      @Krzysztof: I wasn’t aware of the MotherFunctor website. But from what I am seeing, it has gotten its anti-PC slant as late as 2017 (here is its 2016 version: https://web.archive.org/web/20161104091610/http://motherfunctor.org/ focusing mostly on FOIA requests), which looks more like an effect than like a cause of his experience with the Mathematical Intelligencer.

      If “free speech activist” translates to “troll” to you, then good luck when you actually need people to stand for your free speech.

    • Krzysztof Says:

      The troll part is my evaluation of the general setup of the paper and its many subsequent variations. I haven’t dwelved into his activism beyond seeing his repeated calls for it upon googling his name. As I said I find naming people for it insincere.

      I have zero appetite for further qualifications of his or anyone else’s activism, and judging individual rationale and morale thereof, beyond observation it involves mostly political action you seemed to decry (before addressing snarky political remark at me).

    • Darij Grinberg Says:


      > beyond observation it involves mostly political action you seemed to decry (before addressing snarky political remark at me).

      Political action comes in various forms. One is pushing provocative (and possibly ill-researched) papers into journals in the hope of triggering a debate. Another is threatening retaliation and secondary boycotts at editors for publishing an idea that doesn’t fit into your worldview. There is no symmetry here. If Wilkinson and Farb behaved as the Quillette article described (which I can’t be sure of, since it’s a second-hand quote in that article), they don’t belong into any editorial board of a journal, period. As for Rivin, if he has foregone the refereeing process, I think he’s fucked up but it’s a lighter shade of black.

    • Krzysztof Says:

      I’m feeling I have nothing more to contribute to the political debate you persistently wish to have other than bad grammar and misspellings.

      I will not discuss the supposed asymmetry you’re referring to as I expressed my complete disinterest in such deliberations.

      I have to however express my astonishment at your weighting of Rivin’s conduct against some other shades you don’t specify.

      I find this downplaying and insinuation at some “real black” distasteful. It appears he bypassed normal procedure altogether, rushed the thing and published in unusually short order, leaving doubt proper review took place. To that Editorial Board reacted in a nervous or whatever bad way you want to call it. Then an activist called them activists in a conspiracy.

      The rest of the background allegations in the story colourfully told by the author doesn’t add to these concrete events and actions.

      I would like to know what editorial procedures and setups are prone to this kind of attack on integrity. Surely not editorial board members having Facebook (the supposed threat of defriending mentioned upthread).

    • Igor Rivin (@igriv) Says:

      If you look at my response to another thread by Harald, you will see that procedures were followed and exceeded. Please don’t accuse me of nefarious behavior before acquainting yourself with the facts (this is to Krzysztof )

    • Krzysztof Says:

      Thank you for supplying the details not spelled out before.

      Despite the unfortunate occasion I’d like to thank you for your many works I benefited from over the years immensely, starting with my freshman year (if I recall correctly I used your toroidal chessboard idea for n-queen problem to overdo a programming assignment). In contrast to the other commenter I never heard or saw a thing tainting your character up to yesterday (there were rumors of your politics I was oblivious to and intend to stay that way).

      I don’t however understand how the paper was thoroughly reviewed within three weeks. I have never had any kind of work, including for lay press, accepted in such time frame.

      Should “we” in “NYJM requires one report, we got two” be interpreted as “we the Journal” you are apparently in conflict with, or you and the editor who gathered referee reports (i.e. were the roles of inviting editor and that person separated)?

    • Igor Rivin (@igriv) Says:

      Thanks for the rapid (and kind) response. To answer your questions: “We” refers to NYJM in reference to the paper. With better typesetting capabilities, I would have highlighted “requires” and “got”.

      Three weeks: I assume you have read the paper, if so, you will have found that it is quite short and does not require a huge amount of background. The referees have had no trouble verifying correctness, and primarily need to assess importance and novelty (which both passed muster). I have been editor on many journals, and refereed hundreds, if not thousands, of papers, and a three-week refereeing process is more the rule than the exception (the six month refereeing periods are mostly due to referees being busy with other things, or very technically difficult papers – usually, the fact that people procrastinate is a sign that they find the result not THAT interesting. In this case, this was clearly not an issue.

  42. james c (@james1071) Says:


    may be relevant to the discussion

  43. Kerth Gersen Says:

    The things is, both publications have procedures to dispute the inclusion of a particular paper. These involve pointing out factual or methodological errors in the paper. They do NOT involve threats of political outrage mobs, statements about how “harmful” the conclusions might be (to certain ideological/political positions), or replacing the published paper with another EXACTLY the same size.

    That the paper can still be found on arxiv does not mean no attempt was made to “memory hole” it, just that the attempt did not perfectly succeed.

    As an outsider to academic matters, it sure as hell seems that you are bending over backwards to provide some semblance of cover for a blatant abuse of power.

    ALSO, to pretend that the only “reproductive selection” going on among hunter-gatherers was how good-looking the males were, or what nice furs they wore, is to (deliberately?) ignore survival pressures on males that included exposure, accident and reverse predation (and yes, I can hear the saber tooths saying “There’s no such thing as ‘reverse predation’, it’s all just predation.”). Arguably there was much greater reproductive selection going on for males, besides whether or not they were “chosen” by females. To pretend otherwise is just an unsubtle variation of the increasingly popular straw man argument: “So…what you’re saying is…” Yuck.

  44. Reshef Meir Says:

    The correct title should have been “Has an uncomfortable *viewpoint* been suppressed?”

    The unfortunate and obvious answer is “yes, it has, and in a shameful way”
    whether this viewpoint is “truth” is irrelevant. A post like this one, exposing the faults in the model, is welcome, but cannot justify removing an article after publication.

    Many articles have problems in the model or even in the technical proofs (hell, many published theorems have counter examples!)
    I have never heard of retraction due to these reasons, let alone deleting an article without notice.

    • Camila Says:

      Perhaps, but dont you also find the author’s positioning himself as a martyr for free speech and academic freedom irritating, given the crapiness of the article? If it were me, and I had gotten such a crappy idea accepted into a journal, only to have the community point out that it is completely wrong, I would show somw contrition and humility.
      What the author of this post is saying is 100% true. The ideas of this paper, like 99% of all ideas, belongs in the trash, not in the academic literature.

    • Jim the Curmudgeon (@curmudgeon_jim) Says:

      “dont you also find the author’s positioning himself as a martyr for free speech and academic freedom irritating, given the crapiness of the article?”

      No. Apparently you don’t read much constitutional law, because many court cases have dealt with the protection of free speech in cases where the speech was obscene, degrading, or even hateful.

      A crappy article should be rejected, or it should be published and subjected to critique. It shouldn’t be hounded out of publication and banished.

      All of the sciences have dodgy work involving manipulated data, faulty proofs, errors in computer programs, etc. As Reshef says, those papers are never expurgated in the manner that this one was.

  45. Eric Rasmusen Says:

    I have to admit I’m creeped out that the eminent author of the post and so many commenters see nothing wrong with the argument,
    “The Hill paper doesn’t have any mistakes in it, but it looks like a pretty mediocre paper, so there’s nothing wrong with two journals retracting their acceptances under pressure from feminists who don’t like the paper’s subject matter.”
    In the US we’re seeing a lot more educated people than 20 years ago who don’t really see any point in free speech. This seems related.

    • c young Says:

      Spot on. There seems to be an appeal to the principle that it is OK to pull mediocre papers for political reasons (if that is what happened).

    • gowers Says:

      I merely claimed that the paper was mediocre and made no statement about whether it was OK to pull it. To my mind, as I said in another comment, if proper editorial procedures are followed and the editors later regret their decision, then that’s too bad and they should not pull a paper. If proper editorial procedures are not followed, then the issue becomes more complex. In this case there is a dispute about whether proper editorial procedures were followed, which makes the issue more complex still. This complexity is reflected in the fact that the vote by the editorial board of NYJM to pull the paper was passed by a two-to-one ratio and not unanimously. (I think that last fact is not in dispute.)

    • Anonymous Says:

      Mr. Gowers, you are a great mathematician in a different area but you are not expert on this kind of mathematical modeling of evolution. How many other papers in this area have you read? Were they much better, or is the whole area mediocre?

      My impression is that in this area (and in some others, like economics for example) depth of actual math part is not necessary to be a good paper. Some of the best papers in economics have mathematics on undergraduate level.

      Your attack on the paper was not warranted, and it detracted from the question of whether this paper was censored on political grounds.

      P.S. I would appreciate an explicit literal answer to the question “How many other papers in this area have you read before deciding to call this paper mediocre?”

    • gowers Says:

      I was not judging the paper relative to other papers in the field of evolutionary biology, and would have had no issue with its appearing in a biology journal if the experts in that field thought it was up to their standards. So I have no idea whether the general level of papers in the field is comparable to the level of this one, but I can say that if the paper is not of mathematical interest then it doesn’t belong in a mathematics journal.

    • Anonymous Says:

      There is a subject called mathematical biology. Many math departments, including the one I work in, have faculty working in this area. Are you saying their work does not belong in mathematical journals?

      You did not dignify my question with an answer, from which I conclude that the correct answer to “How many other papers in this area have you read before deciding to call this paper mediocre?” is 0.

    • deaneyangDeane Says:

      The NYJM does not publish mathematical biology papers. There are much more suitable journals. What you really should be asking is why the author chose to submit it to a pure math journal, instead a more suitable one. The fact is that if you submit a math paper to a biology journal, it will be quickly rejected. Why is the converse unacceptable?

  46. TheBulldogWrinkle Says:

    Tim, your point about change in the gender balance among doctors and lawyers raises an interesting question regarding the gender disparity in math. If women’s past under-representation in medicine and law was the result of cultural barriers within these communities(which it most certainly was), then doesn’t women’s current under-representation in math require the mathematics community to be somehow more sexist than today’s doctors and lawyers? Is there any evidence of this? I say this an an outsider, but I find it hard to imagine

    All of the barriers you enumerated(lack of role models, belief in inferiority of women, time demands that clash with family responsibilities) once applied to women who wanted to enter law and medicine(probably a lot more so than they apply in women in academia today). The time demands have never disappeared and likely never will. And yet, here we are with women having achieved parity in these fields among the younger cohorts in many western countries.

    • Krzysztof Says:

      Women were becoming about 5% of the lawyers long after they were legally permitted to join the bar and judiciary at the turn of the century. There were several class-action suits in the 1970’s https://scholarship.law.cornell.edu/facpub/12/

      In the 1980’s the whole profession determined the problem needs to be adressed directly because it is self-perpetuating, integrating past discrimination over time. The anwser decided was to just hire more women, i.e. not being gender blind. That started with quotas at top law firms and included affirmative action and active marketing in schools (reversing the previous “affirmative action” suppressing women and its residual effects). Deliberate efforts evaporated from existence (and memory apparently) by the late 1990’s as balance naturally occured when there were lots of women role models in the profession and new ratios became self-perpetuating.

      As to the relevance of this to academic mathematics. I don’t know the numbers, but David Bressoud has lots of graphs in various posts on https://launchings.blogspot.com I don’t have time to go through them or point to specifics, but they seem to be pretty high in levels of education attained and degrees earned (as is also my personal experience), albeit with a minuscule drop recently. Hiring women for faculty positions on the other hand stays low.

      Law schools and med schools don’t have to consciously try to hire women today, their pool of qualified applicants just breaks down evenly after making for the new equilibrium (which didn’t came about by itself for half a century since removing barriers).


      Perhaps relevant to the whole open-ended discussion that ensued here is an article from the Notices of the AMS concerned with higher male variability hypothesis in mathematics specifically http://www.ams.org/notices/201201/rtx120100010p.pdf

    • Krzysztof Says:

      The story I saw comes from a contributor to a rather low quality noisy forum I used to frequent. I’m leaving a link below, but also see his other variations on this theme by searching for his handle supplanted by “law” and “women” in the bottom text field and selecting comments on a resulting page. My previous attempt at summarizing the basic point got stuck, apparently triggering the SPAM/moderation feature of this blog with one too many link. Sadly my scholarship in history is too weak to find a better source.


    • Jim the Curmudgeon (@curmudgeon_jim) Says:

      Indeed, there is almost no chance that mathematics is more heavily infused with sexist males throwing up barriers than law. The old boys club still predominates in law firms, and women have a much more difficult time making partner.

      Despite that, law schools are now majority female. Medicine, biology, veterinary science, speech/language pathology, education… there are many fields were women are dominant. Oddly enough, in countries with low levels of sexual discrimination (e.g., Sweden) there are less women in computing and engineering than in countries with misogynistic and repressive governments (e.g., Iran).

      I’d love to see evidence of actual discrimination against women in North American mathematics faculties. The Chinese didn’t have very many role models at Harvard or Georgia Tech, yet they aren’t sitting back and complaining.

    • Krzysztof Says:

      Chinese employ a highly contentious points system which is essentially quotas.

    • Krzysztof Says:

      Sorry, I misunderstood, I meant Chinese in China. You seem to be making an ethnic point. I don’t really know about these things, but gender and ethnicity seem to be different subjects to evaluate affirmative action on. I’ve seen argued it shouldn’t be compared because economic status, a strong confounding factor, is heritable with one but not the other.

    • gowers Says:

      Replying to Jim the Curmudgeon here. You appear to be suggesting (though I think you probably aren’t really suggesting) that the only environmental factor that could explain underrepresentation of women in mathematics faculties is straightforward discrimination. But there are many other possible causes. I would guess that one of the most important is that the message is sent in various ways to young girls that mathematics is more of a boy’s pursuit: there seems to be plenty of evidence that from a certain age (about 6 if I remember correctly) girls who up to that point were just as keen as boys on subjects like mathematics and physics suddenly stop perceiving themselves that way. I have a seven-year-old daughter who says that mathematics is her favourite subject and my wife and I are trying very hard to make sure that she will not get some subliminal message that that is not what young girls should be like.

      It seems, from the link Krzysztof provides, that in order to get to the point where women outnumbered men in law schools, there first had to be a campaign of positive discrimination, which then led to law becoming a much more popular choice for women, which in turn led to the point where positive discrimination was no longer necessary. It is at least imaginable that the same thing would happen if a similar campaign were to take place in mathematics. (I’m not saying that such a campaign should happen, but it isn’t obvious to me that the advantages would be outweighed by the disadvantages.)

    • valuevar Says:

      I find it odd to discuss positive discrimination for women in mathematics as if it were some sort of hypothetical possibility. It is an acknowledged policy at quite a few institutions and finding institutions, both for hiring and for conference invitations and the like. Of course (a) it is much more common in some institutions than in others, (b) good luck guessing the extent (none, slight, substantial or overwhelming) from the wording of the job announcement/special-program description/etc. (Obvious corollary to (b): someone who benefitted from it very little or not at all can easily be perceived as having benefitted from it a great deal, and vice versa.)

    • gowers Says:

      I think there is an important red line that the lawyers, if I understand the story, crossed, but I would guess that few mathematical institutions are comfortable crossing, and that is whether one is prepared to hire a female candidate when one judges that a male candidate is clearly better. However, I think many institutions are ready to go as far as they can without crossing that line. For example, if, as is often the case, it isn’t clear which of two candidates (who may well be in quite different fields) is better, and if one of them is female, they will go for the woman. And that at least seems to me to be a good policy: it improves the gender balance without risking the perception that “she wouldn’t have got the job if she hadn’t been a woman”.

    • valuevar Says:

      Well, there’s the ambiguity of “a woman will be preferred given equal qualifications”: people with equal qualifications are essentially non-existent, and so the condition can be construed as void; at the same time, pairs of candidates where neither is better than the other in every possible way are very common, so, if a woman is to be preferred in every such situation, you have got a very strong preference indeed. Both interpretations exist in practice (and so does everything in between).

      It may be that one cannot often say (truthfully) that a candidate definitely would not have got permanent job X had she not been a woman. (In the case of some temporary positions, invitations, etc., that is more often the case.) Still, there are cases where the probability has been affected greatly, and deliberately so. There are certainly jobs where everybody knows beforehand that a woman will be offered the job first (assuming that any woman above a certain level applies). Matters become more stark when you integrate over someone’s career (assuming of course that he or she was born at just the right time). In the end, we do have that there are things we know about someone’s career that we would not like to express – and it is also the case that the scales can be tilted enough that someone can and will tend to rise quickly above people who are clearly at a better level, to the extent that a comparison is possible. So, in the end, there doesn’t seem to be much of a difference between two kinds of positive discrimination.

    • valuevar Says:

      I should add that we are still lacking a good source on what happened in law and medicine. The posted link just leads to a remark in a forum, made without citing sources.

  47. erasmuse Says:

    I haven’t checked, but I look in at evolutionary biology now and then (it actually has a lot of links with game theory, which I work on), and I thought a model along the lines of the Hill one had been broadly accepted as valid for many years. Or, put differently, given the evolutionary pressures, it would be strange NOT to see greater variability in males than in females in humans and in polygamous animals. In addition, the fact that we see greater male variability in animals cuts against the environmental/cultural explanation. This is why progressives hate sociobiology: it shows that lots of things can be explained without resorting to culture as the cause.
    We have a lot of models like this in economics, where greater variability is useful to overcome thresholds. An example is my “Managerial Conservatism and Rational Information Acquisition, ” Journal of Economics and Management Strategy (Spring 1992), 1(1): 175-202. http://rasmusen.org/published/Rasmusen_92JEMS.conservatism.pdf Towards the end is a cute application: we should expect men and women alike to be disappointed on average in their spouses, while happy that they married them. Hint: It’s just Bayes’s Rule and regression to the mean.

  48. gowers Says:

    It has been pointed out to me privately (and also in one or two of the comments above) that Hill’s paper has had nine versions and that earlier versions, including the one submitted to the Mathematical Intelligencer, are significantly different from the latest one.

    In some of the earlier versions, Hill actually addresses one of the points that I discussed above, suggesting that female selectivity in humans could well have decreased, and that this should in time lead to less variability amongst males. Then, very curiously, he refers to a paper in the published literature that observes that the difference in variability between males and females in mathematics test scores in the US is decreasing and tentatively suggests that that would support his theory. Does he really think that the effect would show up in two or three generations? Perhaps he did then but changed his mind.

    Even odder is the fact that the paper he refers to is one that casts doubt on the applicability of the variability hypothesis to mathematical ability. The abstract reads as follows.

    “Using contemporary data from the U.S. and other nations, we address 3 questions: Do gender differences in mathematics performance exist in the general population? Do gender differences exist among the mathematically talented? Do females exist who possess profound mathematical talent? In regard to the first question, contemporary data indicate that girls in the U.S. have reached parity with boys in mathematics performance, a pattern that is found in some other nations as well. Focusing on the second question, studies find more males than females scoring above the 95th or 99th percentile, but this gender gap has significantly narrowed over time in the U.S. and is not found among some ethnic groups and in some nations. Furthermore, data from several studies indicate that greater male variability with respect to mathematics is not ubiquitous. Rather, its presence correlates with several measures of gender inequality. Thus, it is largely an artifact of changeable sociocultural factors, not immutable, innate biological differences between the sexes. Responding to the third question, we document the existence of females who possess profound mathematical talent. Finally, we review mounting evidence that both the magnitude of mean math gender differences and the frequency of identification of gifted and profoundly gifted females significantly correlate with sociocultural factors, including measures of gender equality across nations.”

    I’m not making any statement here about the correctness of the above paper, but just that its use by Hill was rather … what shall we call it? … selective.

    • gowers Says:

      The paper Hill refers to is this one. (I’m on my university computer so I’m not sure whether it’s freely available to read — apologies if not.)

    • Jim the Curmudgeon (@curmudgeon_jim) Says:

      Quickly scanned that paper and I was somewhat underwhelmed. The methodology section is scanty, and they spend most of the paper describing results from other researchers. No one claimed that there are no females who lack superior mathematical abilities, so that part of the paper seems superfluous.

      You appear to be right that there are claims made in the paper that raise questions about whether it was cited properly.

      At any rate, he could still write a research paper that says: IF there is such a thing as variability between sexes, and there is evidence both for an against that claim, can we come up with a mathematical model to explain such variation.

      That situation would be no different from early climate change research, where there was no general agreement about the actual warming of the climate. The early climate models were made as theoretical tools to explore a possible issue, well before we had reliable sensors and large datasets to work with.

    • gowers Says:

      I agree that such a research paper could indeed be interesting and worthwhile. But while I now understand that some of my criticisms in the post were misplaced (in particular, the selectivity hypothesis is more reasonable than I thought), I still think that the paper fails to address an issue that really should have been addressed before one can claim that it is a serious contribution to the discussion. Hill makes the critical assumption that the the distributions of desirability within the two populations remain constant when their sizes change. While this is not logically impossible if the genes involved do not directly cause the desirability but cause something else that results in more variable desirability, arguing that such side effects are more important than what one would think was the more normal situation — that if some feature increases desirability then that feature will be selected for. To apply it to intelligence, the claim would be that if women decide they will have children only with men of well above average intelligence, the children won’t be any more intelligent on average than they would have been otherwise, since what causes the intelligence is some other feature that leads not to intelligence itself but to a greater variability in intelligence.

      My guess is that the same people who claim to demonstrate the variability hypothesis also subscribe to the view that more intelligent parents tend to have more intelligent children, which would mean, unless I’ve made a mistake, that Hill’s model wouldn’t apply to intelligence. And I think that a similar argument probably applies to most of the properties where men are supposed to show greater variability.

    • Darij Grinberg Says:

      @gowers: I don’t consider intelligence to be monolithic (yes, you can define “g”, but that’s more or less explicitly focusing on whatever happens to be the main principal part and ignoring the rest). Even so, I don’t think intelligence is the ultimate deciding factor for success in mathematics — there seems to be at least a combination of intelligence, self-control and motivation in play, and I can personally attest that some kind of risk-taking behavior (which rarely manifested for me on the physical level) has been crucial in my perseverance on certain mathematical problems (the risk here is studying a question that doesn’t appear interesting to the mainstream, in the hope that once it is solved the community will suddenly find the answer interesting). And risk-taking behavior, while [in itself heritable](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3077362/), manifests in wildly varying outcomes.

    • Jim the Curmudgeon (@curmudgeon_jim) Says:

      I haven’t had a chance to read more than a page or two of the paper, but your analysis here strikes me as exactly the sort of feedback that is useful for critiquing the model.

      I think your guess in the last paragraph is reasonable, albeit most people are aware of reversion to the mean.

    • Pierre Menard (@pierremenard128) Says:

      @gowers — It seems to me you are discussing a variation on the model that would make no difference to the results. Suppose females select the top X% of males according to trait A; and suppose now that the distribution of trait A changes with time, perhaps increasing as a result of this selection process. As long X% is small, if there is a lever to crank up the variability of trait A, evolution will pull it.

  49. anonymous participant Says:

    I would like to urge everyone to please not take Ted Hill’s narrative at face value. Most of the “feminist activists” he suggests were trying to “censor” his paper did no such thing, and were merely calling for a same-issue rebuttal in the Mathematical Intelligencer.

    These are mathematicians as committed to free speech as anyone here. It is not the fault of someone who wanted to write a rebuttal (with scientific criticisms and all) that the journal freaked out and made the wrong call of pulling the paper.

    This story is *way* more complicated than how he presents it.

    And, I should add, in his piece he is sharing quotes from private emails, addressed to his co-author, without permission and out of context, and removing critical pieces from those quotes. Ever wonder what was removed in the “…” pieces? You should.

    I hope as a community we can be a little more rigorous about what we accept as “truth” in the context of such storytelling. We are supposed to value truth and transparency above all, but this story falls far short from the standards we should all have.

    The true asymmetry here is that none of us who have been attacked by this narrative can, at this point, defend ourselves publicly. Amie is getting non-stop hate mail. I am dying to jump in, but do not want to reveal my name for fear of the same. Unfortunately, only men involved are able to have this open, public, lively debate right now.

    The reason is that Hill’s post has activated, in addition to interested colleagues an mathematicians, a thoroughly frightening and misogynistic mob. You have no idea how frustrating it is to watch this and not be able to join in the debate because of these extra-mathematical elements.

    • Anonymous Says:

      According to seminal feminist thinker Mary Belenky, logic is “a tool of domination”, and quantitive reasoning is “incompatible with a humanistic appreciation of the qualitative aspects of the phenomenological world”. The methods of logic, analysis, and abstraction are “alien territory belonging to men” and “intuition is a safer and more fruitful approach to truth”.

      Many who are not ready to abandon reason interpret this to mean: it’s OK to make stuff up, and if you don’t understand it, it’s because you lack “a woman’s way of knowing”.

      On the basis of this postmodern flexibility, feminism has yielded claims about reality, many now widely accepted as axiomatic, which, when tested against the standards of quantitive reasoning and processional academic standards of proof, have every appearance of having been based on evidence and observation which has simply been fabricated.

      It is against this profoundly anti-intellectual background that this scrupulously nuanced evaluation of a perhaps less than perfect paper is being conducted.

      “anonymous participant” suggests that, as a consequence of it, a “thoroughly frightening and misogynistioc mob” has been activated. Yet feminism’s anti-intellectual research methodology is being used to justify horrors, including for example retrospective non-consent (legitimately criminalising sex for which consent is later withdrawn), and denial to men of the principle in law of innocence until proven guilty.

      It’s swallowing that monstrosity, while straining on the gnat of a less than perfect math paper, that is *truly* frightening, and why many from outside the math community are interested in it.

    • anonymous participant Says:

      I have no idea what this reply to my post is saying. I am a mathematician. When I say “truth” I mean plain old truth. As in, what actually happened. There is nothing anti-intellectual about wanting to voice criticisms of a (seriously-flawed) paper in a same-issue rebuttal.

    • Yemon Choi Says:

      Delurking to thank “anonymous participant” for their contribution – I am glad that someone else has pointed out that the selective and unsourced quotation that Hill employs is problematic. (This is the kind of thing that many academic historians learn to critique in their training; I often wish scientists got similra formal training.)

      Rather carefully, I didn’t venture any opinion on the article’s handling by the Intelligencer. I am rather dismayed to see that the handling by NYJM is being portrayed as “a perfectly reasonable paper was deleted from a journal after being accepted”, rather than “clearly there was a failure of editorial process in the article being effectively commissioned and then accepted without the board’s consent”. As a couple of people have vaiantly attempted to point out upthread, the paper simply isn’t in the scope or domain of a journal such as NYJM, and I would have said the same if Hill’s article was attempting to draw the opposite conclusions (i.e. attempting to *rebut* the GMVH with toy maths).

    • M Says:

      Why don’t Wilkinson and others publish their take on the controversy? If Hill’s account is inaccurate, it’s irresponsible for people who know what happened to keep quiet. Wilkinson has reportedly said that Hill’s account is false while refusing to justify that claim in any way. If true, that’s strange behavior.

    • erasmuse Says:

      Commenter M is right: Wilkinson and others named owe it to us to present their side of the story, if they deny Hill’s. I very much like it that Hill names names. That is the way to stop bad behavior. Of course, it is good to hear from both sides too, and often one discovers that the first story was “fake news”. That’s the idea of “fisking”: going through a web post or news story line by line and refuting it. When I read Hill’s story, my first reaction was to google to see if I could find someone contradicting him, so I could weigh the evidence. Nothing showed up.

      Generally the people who say they want secrecy and who use back channels to get at people rather than publicly making their case are in the wrong, though. “The best disinfectant is sunlight.”

    • anon Says:

      M and erasmuse: Wilkinson and others owe absolutely nothing to anonymous commenters on the internet, and anyway recent history has shown that no response will do anything to stop hundreds or thousands of ignorant people from deluging them with hate mail and threats. Hill’s naming names is not the way to stop bad behavior, it in fact explicitly encourages it from anonymous online mobs, especially when the accused is a woman.

      In fact, assuming the other side of the story is anything even close to what anonymous participant says (and anyone familiar with the people supporting this paper will have zero reason to accept Hill’s version of events), they have a serious case for defamation and any responsible lawyer will specifically tell them not to comment publicly.

    • Jim the Curmudgeon (@curmudgeon_jim) Says:

      “This story is *way* more complicated than how he presents it.”

      Right, so instead of putting some effort into it and publishing the other side of the story, you will show up on a blog post as an anonymous oracle and tell us all there is nothing to worry about.

      If you thought his piece was flawed, you can publish a critique in another journal. There are plenty of flawed if not fraudulent papers out there that have never been unpublished in this manner.

      (At one of my universities an asian female grad student employed in a major bio-med lab turned out to have been faking her data collection. Their work was cited by hundreds of other researchers, leading to a major scandal. Her degree was revoked but none of the papers were unpublished).

      “Hill’s post has activated, in addition to interested colleagues an mathematicians, a thoroughly frightening and misogynistic mob”

      Frightening how? If you are worried about misogyny and violence I would be far more concerned about immigration patterns than a few academics who don’t agree with you.

  50. james c (@james1071) Says:

    Tim, leaving the issues of publication and retraction aside, I have some comments to make about what you have written.

    I have just a general reader, so this could be a gross simplifiication or wrong.

    1 The way to think of natural selection is that it acts on genes, not individual members of the species.

    2 What might make no sense from the perspective of an individual – say altruism, does make sense from the perspective of the gene.
    Altrustic person A seemingly gains nothing from helping person B , but the shared altruitsic gene is helped (in the sense of increaing chances of spreading by reprodcution).

    3 Thirdly, genes come in packages – i.e. rather like a car, there are lots of added features.

    4 Genes interact with other genes in the package – and how they express themselves thus can vary. In particular a gene may be expressed in men and not in women.

    5 Mating for men was much more competitive than it is now.
    Our ancestors are mostly female.

    Finally I am getting to the point.

    Some people,men and women, might carry genes that encourage high risk, reckless behaviour.

    The effect of these genes is different in men and women – expressed more in men.

    The genes encourage high variation behaviour – which makes breeding success more variable. So, some men with these expressed genes fail to reproduce. Others hit the jackpot.

    So,the gene is transmitted by the winners who carry it.

    • gowers Says:

      This is an interesting point, which I think was also made in a comment by someone else earlier. My problem with it is that for many of the qualities A where men are supposed to be more variable than women, it is hard to think of a different quality B that would have as a consequence increased variability in quality A. For instance, something like an increased willingness to take risks might well lead to more varied life outcomes, but I don’t see why it, or any other vaguely plausible attribute, would lead to more variability in a quality such as mathematical ability.

      I’m not saying that you’re wrong, but just that I need more convincing.

      Maybe a more plausible candidate is obsessiveness. Perhaps if you have a gene that inclines you to become obsessed with things, then for a quality such as mathematical ability it could lead to a significant advantage — if you get obsessed with mathematics — or a significant disadvantage — if you get obsessed with your stamp collection.

      A general point I might make here is that several of the comments on this post have been interesting and have made me realize that my grasp of the issues was far from perfect. But surely it was the job of the author, and of the editors who accepted the paper, to ensure that these clarifications were there in the paper, given that it was aimed at an audience of mathematicians most of whom, like me, will be unaware of many of the subtleties of evolutionary biology. For instance, this point about attributes that have the effect of increasing the variability of other attributes is crucial to Hill’s argument, so instead of giving us huge numbers of citations to papers that claim to observe increased variability (which, if he means what he says about not making any claims about the consequences for the real world, are not all that relevant), why not give us citations to literature that demonstrates that attributes of that variability-increasing kind exist?

    • P Says:

      w.r.t. “obsesssiveness,” check out simon baron-cohen’s work and his “extreme male brain” theory of ASD.

  51. erasmuse Says:

    It could be that genes that express extreme traits more often “make mistakes”, so even a gene for something good like strength or IQ could be risky. Males have more birth defects than females, and presumably there’s some corresponding advantage to that. See
    https://www.ncbi.nlm.nih.gov/pubmed/11745830 . Interestingly, that article says about half the extra birth defects are in the sex organs, though, which is a separate reason entirely.

  52. Javier Says:

    What’s at issue here is the professionalism of the editing of mathematical journals. Anyone with much experience with mathematics journals might question whether many of them, including some of the most well known and prestigious of them, fall short of what are generally regarded as professional editorial standards.

    What’s at issue here is not the quality of the article, rather the quality of the process whereby its quality was determined. That the atricle that was published before being retracted in an unprofessional manner has low quality would be only another indictment of the professionalism of the editorial process (provided this is indeed what happened). To compound an editorial error in the acceptance with an unethical not-retraction retraction amounts to putting the fire out with manure.

  53. james c (@james1071) Says:

    Thank you for responding to my comment. I would be interested in a biologist’s opinion. My comment was very much from a layman’s perspective, and would be interested in what a biologist would have to say. I don’t have an opinion of how this all fits in with women and maths.


  54. Academic Activists Send a Published Paper Down the Memory Hole | 3 Quarks Daily Says:

    […] More here. […]

  55. Observer Says:

    Statement from Amie Wilkinson here:


    • gowers Says:

      Thank you for that. I hope a lot of people who have been quick to criticize her will see it and that it will give them pause.

    • Andy P. Says:

      Tim: I suggest adding a link to Amie’s statement at the top of your post so that causal readers don’t miss it. I understand that Benson Farb will also be issuing a statement soon.

    • gowers Says:


    • hailongdao Says:

      May be I missed something, but Wilkinson’s statement does not seem to refute what described in the Quillette piece regarding the process at Intelligencer. “Amie Wilkinson, a senior professor of mathematics at the University of Chicago, had become aware of our paper and written to the journal to complain. A back-and-forth had ensued. Wilkinson then enlisted the support of her father—a psychometrician and statistician—who wrote to the Intelligencer at his daughter’s request to express his own misgivings…” Nowhere did Hill write that Wilkinson asked the journal to rescind his accepted paper.

  56. c young Says:

    Many of the leading mathematical minds here don’t seem to be able to deal with basic propositional logic.

    The proposition ‘No paper that has been accepted for publication should be dropped for political reasons’ applies to *all papers*.

    ‘All papers’ includes papers later found to be of questionable quality.

    Hence if it has been determined that a paper has been dropped for political reasons, questioning its quality is a nonsensical diversion from the matter at hand.

    You come across as extreme conformists. Thank goodness you have the ‘moral luck’ to live in a generally benign political climate.

  57. Darij Grinberg Says:

    Hats off to everyone involved — which includes both Igor Rivin and Amie Wilkinson and hopefully Benson Farb soon enough — for making open and specific statements about multiple points of disagreement.

    We now have seen a lot of discussion on the paper itself, in which several scientists have argued both in favor of and against the model presented in the paper. My conclusion from this discussion is that if the model is false, then at least not trivially so, and in that case the community will profit from a public debate involving evolutionary biologists. Papers about “frequently made mistakes” are a thing in the mathematical literature, and this should not be an exception. Is the Intelligencer up to this challenge? Barring that, what about other expository journals that take up socially relevant subjects?

    • Andy P. Says:

      I have not seen a single post here or anywhere else on the internet arguing in favor of this model from someone who is 1. a researcher in a field remotely related to the topic of the paper, and 2. posting under their own name so we can evaluate their credentials. Perhaps I’ve missed something, but your claim that “if the model is false, then at least not trivially so” sounds completely unsupported to me.

      Just because internet trolls find this model compelling does not make it so.

    • Jim the Curmudgeon (@curmudgeon_jim) Says:

      Ah, the local gatekeeper of the academy shows up.

      So here we have credentalism in action. (Could have sworn that Ramanujan didn’t have a degree, and that a hell of a lot of work in the foundations of mathematics was done by philosophers).

      “your claim that “if the model is false, then at least not trivially so” sounds completely unsupported ”

      How interesting. Someone talking about models who doesn’t understand modeling. Allow me quote someone far wiser than myself:

      “For such a model there is no need to ask the question “Is the model true?”. If “truth” is to be the “whole truth” the answer must be “No”. The only question of interest is “Is the model illuminating and useful?”.”

      In short, all models are false. They are all approximations to the real world, and they are developed through iteration and successive refinement.

      You don’t even have a passing familiarity with modeling. Even a second year computer science student has a better grasp on model development and iterative development.

    • Andy P. Says:

      Jim: Your “argument” against my claim consists entirely of a series of unsupported assertions concerning what I do and do not understand. I see no reason to respond to it.

    • Darij Grinberg Says:

      @Andy P.: The biologists have been mostly silent on this thread in general. Maybe they don’t generally read this blog too much (can’t blame them, maths isn’t all that outsider-friendly).

      Journals like the Intelligencer should be interested in dispelling common prejudices even (and particularly) when they are common among non-domain experts. But you don’t dispel a prejudice with the Delete button.

  58. Gil Kalai Says:

    My main problem with the paper is the huge leap between the model and the interpretation.

    There are some mirror sites with the removed Journal version of the paper http://www.emis.ams.org/journals/NYJM/j/2017/23-72v.pdf and surprisingly the removed journal version seems more contentious than the arxived version (e.g. in mentioning Summers and Damore).

    • Jim the Curmudgeon (@curmudgeon_jim) Says:

      Because no other ever published in a conference paper or journal ever has a big leap between the model and interpretation.

      I mean, let’s look at economics, which elides detail from the real world by assuming rationality, instantaneous updates, etc etc. Donella Meadows (yes, a woman) savaged these models years ago, showing that by adding temporality to a simple model one suddenly introduces a range of complex behaviours that are a better approximation to the real world.

      “(e.g. in mentioning Summers and Damore).”

      Let’s look at that:

      “A resurgence of controversy came after the VH was linked to the forced resignation of Harvard President Larry Summers and the firing of Google engineer James Damore [SH17a].”

      Is there something amiss about providing evidence that the variability hypothesis is politically controversial? This provides context for the work. (I personally would have omitted it in a modeling paper, but in a law or policy paper this sort of reference would be expected).

      If anything I would reject that paper for terrible use of the passive voice (e.g., “after the VH was linked to the forced resignation”). Linked? By who? How can a hypothesis be linked to anything?

      I don’t even care about the variability aspect or the gender aspect, by the way. Women equally as talented as men, great. I have a daughter, so that is fine with me.

    • Gil Kalai Says:

      Jim, This is not a law and policy journal or even an economics journal. This is a mathematical journal.

      Referees and editors in economics journal are well aware that the refereeing applies not only to the mathematical model but also to the interpretation and rhetoric. Here the (implied) bold interpretation and reference to human and to mathematical talents of humans is strange, unnecessary, and weaken further the quality of the paper.

    • Gil Kalai Says:

      Regarding the context of the work, the paper (and also Igor) claim that the problem is a central issue in evolution biology for more than a hundred years. If one can find convincing (or even just nice) mathematical modeling, what context do we gain by the reference to an inappropriate (perhaps even sexist) statement by Summers? And if this give prediction for say the variance (or full tail behavior) of the length of tails of male and female squirrels isn’t it artificial and strange to look for context for the proposed mathematical models, from all things in mathematical talents of human?

    • Gabriel Nivasch Says:

      Gil, the reason the paper talks about humans, I think, is because human male variability was the starting motivation for Hill’s model, given that humans seem to be the main focus of the previous empirical studies. 

      Perhaps indeed, as you say, the model is only appropriate for simpler animals and not for humans. And perhaps it would have been more appropriate for the paper to emphasize that.

      On the other hand, perhaps male variability  can only subside after a very long time period, so we are “stuck” with it.

      I guess this is part of the controversy that, to Hill’s own admission, he and Senechal were expecting to stir.

      But instead of a healthy, civilized discussion (like in this forum), what they got was an ugly campaign of threats to ruin the reputation and careers of all those involved.

    • gowers Says:

      Responding to Gabriel Nivasch: Have you read this statement? There is a big difference between asking for a rebuttal to be published and threatening to ruin careers. I don’t know of any evidence that the latter occurred, apart from an unsubstantiated suggestion in Hill’s article that his coauthors withdrew their names from the paper after intimidation by Penn State. Before calling that a campaign, one would need to know a lot more about what form that intimidation took and who was behind it.

    • hailongdao Says:

      To Tim Gowers: many people would find emails from NSF asking acknowledgement of funding to be removed and tense conversations with the chair/colleagues about how their research do not fit in quite threatening. Especially in this day and age. Similar stories have happened at a few universities lately, with rather unhappy outcomes (typically not involving mathematicians, but this is perhaps a sign that the culture wars might be moving to our field). It might not be a orchestrated campaign, but the effects are the same.

    • Gabriel Nivasch Says:

      Tim, yes I saw. As others pointed out, Amie’s statement does not seem to contradict Hill’s article at all. (Nor do the different NYJM accounts seem to contradict each other: It’s possible that the article was off-topic and most editors were unhappy about it, *and yet* its acceptance followed all the rules regarding # of editors etc.)

      It’s ironic that two of the co-authors decided to drop out because of the threats of a so-called “diversity committee”. Happily, your forum does accommodate diverse points of view regarding the “greater male variability”, as well as regarding the merits and flaws of the paper.

      It’s also ironic that what causes so much controversy is not humans having descended from apes, which since Darwin people sort-of managed to swallow, but rather the relatively minor issue of differences between the sexes.

    • Gil Kalai Says:

      Dear Gabriel, sorry for not responding to your comments in “real time”. Your last paragraph poses a very interesting question. You wrote “It’s also ironic that what causes so much controversy is not humans having descended from apes, which since Darwin people sort-of managed to swallow, but rather the relatively minor issue of differences between the sexes”.

      The distinction between Darwin’s theory of evolution and the Greater Male Variability Hypothesis (GMVH) is simple. Darwin’s theory of evolution, that gives vastly-applicable, and vastly-important scientific insights, including the fact that human evolved from (ancient) apes, is now a solid undeniable part of our scientific understanding of the world. In contrast, GMVH is a vague statement whose scope is unclear and its scientific significance (if any) is unclear.

    • richardjlyon Says:

      > GMVH is a vague statement whose scope is unclear and its scientific significance (if any) is unclear.

      This is not accurate. Not only are differences measurable between genders, but differences are proportional to the degree of gender equality in society. When barriers to women are removed, women are free to exercise personal choice, and those choices reveal personal preference.

      Moreover, to quote a recent paper[1]: “It seems that as gender equality increases, as countries become more progressive, men and women gravitate towards traditional gender norms.”

      Quite the paradox, and an inconvenience to feminism’s dominant narratice that sex difference is socially constructed and therefore susceptable to political ‘correction’.

      [1] “Mac Giolla, Erik & J. Kajonius, Petri. (2018). Sex differences in personality are larger in gender equal countries. International Journal of Psychology. 10.1002/ijop.12529.”

    • Peter Kriens Says:

      @ richardjlyon
      Something is only a paradox when it is derived from sound reasoning. In this case I’ve not been able to find any good scientific paper with sound logic reasoning that makes the cases for the thesis that gender is 100% social construct and 0% innate. Informal arguments for the defense of this thesis invariably cannot discriminate between innate or cultured differences. For example, giving girls dolls can be explained with culture (push) but also biology (pull). Not even talking about the possible interaction over time.

      So I am not seeing a paradox at all, I see that the central thesis that gender is 100% culture is shown extremely unlikely by these studies. I always felt it was defended more as a dogma than a proper thesis.

  59. Alexander Barvinok Says:

    Here is one detail: Sergei Tabachnikov was an author of the original version of paper. The article implies that a “persuasion” of some sort was applied to him and he withdrew his name. I still think that the AMS will do good, if it tries to find out the facts of the matter. As some commenters concluded, a damage to the profession has been done, but an honest and complete description of what happened may stop further damage.

    • Anonymous Says:

      The “persuasion” was applied after certain employees of Penn State contacted the NSF. In all this story, the action of those employees is the only truly immoral action, and they are the only ones who (if confirmed) should suffer serious consequences.

      Its one thing to have a disagreement and maybe get too emotional about an issue one cares about, its another thing to try to actually destroy somebody’s life and livelihood.

  60. Edwin Steiner Says:

    Re “Its argument can be summarized as follows. […] 2. If one sex is more selective than the other, then the less selective sex will tend to become more variable.”

    This is false. The paper explicitly states that the argument does not require any comparison of the selectivity of the sexes. The argument is rather that the more selective sex A is, the more evolution will favour subpopulations of sex B with higher variability in the properties selected on.

    Re “[…], this model is ludicrously implausible. […] the idea that some huge percentage of males are simply not desirable enough […] bears no relation to the world as we know it.”

    I am not equally sure about this, but you might be wrong about how well you know the world. See for example: https://www.lesswrong.com/posts/cHEQSEPz4eipGHFy9/differential-reproduction-for-men-and-women

    • Edwin Steiner Says:

      P.S.: To be fair about the first point, the difference in selectivity could be inferred from the outcome after applying the argument of the paper all other factors being assumed to be equal. But still this is not part of the actual main claim, which is that selectivity above a certain threshold will favor higher variability in the other sex while selectivity below that threshold will favor lower variability.

    • Krzysztof Says:

      That’s one of my gripes with presentation in that paper (other than confusing the reader with all sorts of irrelevant remarks). Analysis of various parameters and model’s sensitivity to them is left as an exercise to the reader. Perhaps understandably because of triviality of the model, but that doesn’t make for a convincing analysis especially when all sorts of other content is infused instead.

    • Edwin Steiner Says:

      @Krzysztof, Re “That’s one of my gripes with presentation in that paper”:

      Fair enough, I’d say. One may criticize many points and that’s fine. None of this, however, justifies the way the paper has been suppressed and deleted from the journal.

      After the paper had been accepted for publication, the right thing to do for the critics would have been to insist on the publication of a response to / rebuttal of the paper, if possible back-to-back with the paper in the same issue of the journal.

  61. Andy P. Says:

    Benson Farb has now also replied. I recommend also linking to this in the body the post.


    ps: Since is the kind of thing that trolls might highlight and try to insinuate that I am trying to hide, I should point out that I am a former PhD student (and coauthor, and friend) of Benson Farb.

    • Andy P. Says:

      (the word “former” is meant to modify PhD student [and I guess coauthor, though I suspect that we’ll collaborate again in the future], not friend)

    • Igor Rivin (@igriv) Says:

      Firstly, if you are trying to hide, you are not doing a very good job, since hovering the mouse over your name reveals your identity. I will just assume you had intended this.

      Secondly, I had read Benson’s letter, and it is factually inaccurate. I am very disappointed, but am hoping this was an honest mistake, and that he will fix it shortly.

    • Andy P. Says:

      Igor: As a matter of principle, I never comment anywhere anonymously and don’t make any attempt to disguise my identity. However, I am not sure that the non-mathematicians who are suddenly very interested in this (say, the neo-nazi anti-semites over at 4chan who are raging at Amie and posting the most vile possible stuff; I hope you are happy with this outcome) automatically understand the web of academic relationships underlying these exchanges.

      If Benson said something inaccurate, then the right thing to do is not to make vague insinuations that he is wrong, but rather to say what precisely in his statements is incorrect. He cited precise dates and detailed descriptions of the process. Anything less than that from you convinces no one.

    • Igor Rivin (@igriv) Says:

      Andy: Unlike you, I don’t read 4chan, thanks for letting me know. As for Benson, his comment that the editor did not supply the referees’ reports until 2/17/18 is just false. The Editor in Chief was kept scrupulously in the loop in the fall of 2017, which is where the reports were received. Benson is (not very) indirectly accusing me of something – I am very, very disappointed.

    • Andy P. Says:

      Igor: I don’t read 4chan, but links to the various discussions have been passed around. But I guess you don’t get enraged by anti-semitism unless it supports your political positions.

      As far as your statement, it sure sounds to me like you are dissembling. He is saying that you took three months to provide the referee reports to the rest of the editorial board during a discussion of the paper. No claim is made about you providing the reports to the editor in chief during the process that led to the original acceptance (and given how ill Steinberger is, I rather doubt that he was super-engaged with the process; however, this is purely speculation on my part, and I have no inside information).

    • Igor Rivin (@igriv) Says:

      Andy: I resent the innuendo both about anti-Semitism and about “dissembling”. Mark became very ill after the events. Since say yourself that you don’t actually know what you are talking about, you should maybe not be slandering those involved?!

    • Andy P. Says:

      Igor: I will simply note that you didn’t respond to the main substance of what I said regarding the dates that you supplied the referee reports to the editorial board.

    • Igor Rivin (@igriv) Says:

      I do not have any interest in responding to the substance of what you said, since you are not treating me with any semblance of respect. I am sad and disappointed that someone who has broken bread with me in my house would act this way over ideological differences, but I suppose these are the times we live in.

    • Anonymous Says:

      Dear Professor Rivin,

      You say “As for Benson, his comment that the editor did not supply the referees’ reports until 2/17/18 is just false.”

      Below is the exact text of the comment:

      “At the request of several editors, the editor-in-chief pulled the paper temporarily on 11/9/17 so that the entire editorial board could discuss these concerns. A crucial component of such a discussion are the reports by experts judging the novelty and quality of the mathematics in Hill’s paper. The editor who handled the paper was asked to share these reports with the entire board. My doubts about the paper – and the process – grew when repeated requests for the reports went unanswered. Nearly 3 months passed until the two reports were finally shared with the entire board on 2/7/18.”

      Which part of it is false?

  62. On the recently removed paper from the New York Journal of Mathematics | What's new Says:

    […] time was on that board, for more details.  Some further discussion of this incident may be found on Tim Gowers’ blog; the most recent version of the paper, as well as a number of prior revisions, are still available […]

  63. Darij Grinberg Says:

    Let me go back to the question of what happened at the Intelligencer — as it is, to me, the one where actual suppression has definitely occurred. (As many have commented here, there were other issues at stake at NYJM, muddying up the issue, and there is also some factual disagreement ongoing between Igor Rivin and others.)

    The Farb and Wilkinson statements ( https://www.math.uchicago.edu/~farb/statement and https://math.uchicago.edu/~wilkinso/Statement.html ), taken together, seem to imply that neither of the couple was pressuring the Intelligencer to remove the article (I’m not talking about the NYJM here).

    Hill’s Quillette testimonial, on the other hand, writes the following:

    > But, that same day, the Mathematical Intelligencer’s editor-in-chief Marjorie Senechal notified us that, with “deep regret,” she was rescinding her previous acceptance of our paper. “Several colleagues,” she wrote, had warned her that publication would provoke “extremely strong reactions” and there existed a “very real possibility that the right-wing media may pick this up and hype it internationally.”

    This leaves several options:

    1. One of the turtles is lying ( http://poj.org/problem?id=2168 ). I don’t have any priors in favor of this option (and, in the case of Hill, I have reasons to believe that all *factual* claims in his Quillette article are true, exaggerations left aside), so I don’t find it particularly likely.

    2. Wilkinson indeed, as she claimed, “never made the suggestion that the decision to publish it be reversed”, but she implied it so heavily that it was essentially taken for granted.

    3. Someone else (not Farb or Wilkinson) was harassing the Intelligencer editorial board after the article came out. (Wilkinson’s claim that the “unpublication” happened one day after her mail suggests that she was being the last straw, providing scientific cover to a decision that was already desired.) In the interest of science to be free from political scheming, I would love to know the names.

    4. The Intelligencer editors found the “playing into the hands of the alt-right” issue so convincing that they themselves chose to unpublish the paper. (Which would bely their own conception of a section for controversial content!)

    Who can offer insights on which of these (if any) happened?

    • Mark C. Wilson Says:

      Has anyone asked Marjorie Senechal? I too would like to know about the Intelligencer. The NYJM issues are interesting, but there may be a reasonable explanation. It is not easy to see how the Intelligencer’s decisions can be justified. And the claims by Hill about NSF intervention have not been discussed much, but seem really important too.

    • samuelfhopkins Says:

      It seems to me that the publicly available account of what happened at the Intelligencer is totally coherent. Wilkinson sent an email to the EiC saying something to the effect of “this paper is bad” (it is!), “it’s junk science” (it is!), “I’d like to request it be printed alongside a rebuttal by experts in the field” (which the authors certainly were not). The EiC got spooked because, reasonably enough, she did not want her magazine to become a battleground for the culture wars. Now, the actions the took at this point may have been incorrect, but I think it behooves anyone really looking for a complete account of this saga to get Majorie Senechal’s account of what happened.

      On the other hand, I don’t see how anyone can downplay what happened at the NYJM. The Intelligencer is a culture magazine; the NYJM is a serious journal of theoretical mathematics. Put aside the issue of whether referee procedures were technically followed as they should be: does it make any sense that this article was published in the NYJM? Can anyone say with a straight face that that is a reasonable outcome? It’s like seeing numerology, or “A Mathematical Analysis of the Best Rock Songs from the ’60s” be published in a serious pure math journal. The referee process had to have broken down, in spirit if not in fact, for this to occur, and I think it’s something academic mathematicians have to be very concerned about. (Of course it is not the unique example in math of political control of a journal leading to an unfair outcome.)

    • richardjlyon Says:

      > she did not want her magazine to become a battleground for the culture wars.

      What “battle ground for the culture wars”, exactly, in the context of academic publishing? That implies some notionally matched set of opposing forces. In this instance, there is a feminist pseudo-research publishing industry measured in hundreds of millions of dollars per year in funding and generating uncountable quantities of barely scrutinsed, weaponiseable material. And there are events like these, apparently so rare that they can be individually scruinised. Aren’t you saying by other means that feminism’s supression tactics have in fact, on this occasion, worked?

    • Igor Rivin (@igriv) Says:

      Samuel F Hopkins: What is your competence in this? How dare you insult the editors and the referees? You know absolutely nothing about the subject matter, all you have is your ideology and your arrogance.

    • Andy P. Says:

      Igor: Hearing you describe someone’s qualifications to evaluate this paper as including only “ideology” and “arrogance” is pretty amusing.

      Assuming that I have identified Samuel F Hopkins correctly, he is a mathematician, and thus perfectly qualified to judge the difference between mathematics and non-mathematics. Whatever Hill’s paper is, it is not a mathematics paper in the sense that the other papers in the NYJM are.

      Though I know you view yourself as some kind of universal genius (in your own rather pompous words on your website, you describe yourself as a “Mathematical universalist”), your own educational and professional record (the one that qualified you to be an editor of a journal) also have nothing to do with the purported topics of this paper (i.e. biology, evolution, and mathematical modeling).

      Even if this paper was of an appropriate genre for the NYJM, I’m not sure why you felt qualified to choose referees for it and evaluate their reports.

    • Igor Rivin (@igriv) Says:

      Andy, are you inhabiting my mind now? If not, how do you know what I think of myself? As for your factual comments, you are making yourself look like a fool (for example, the second most cited paper (and several others) on my Google Scholar profile is on mathematical modelling; the paper on Harmonic mean, etc, with N. Komarova is actually on evolutionary biology (and the subject matter is not that far from Hill’s paper), and I have various other papers in related fields. Please stop, and let Mr Hopkins speak for himself, if he so wishes.

    • Andy P. Says:

      Igor: I was aware of both of those papers when I wrote my comment. Politics aside, I actually like your serious research quite a bit and have read a fair amount of it. For instance, Justin Malestein is a long-term collaborator of mine, and back when he was a postdoc conversations with him inspired me to check out your work on zeolites, including the first paper you cite. If you were a hack, I would not be nearly as disturbed by your growing radicalization and decreasing professionalism.

      Rather than engage in a lengthy exchange about this, I’ll just say the following: both papers you cite are easily found online, and I recommend that other interested readers check them out and form their own opinion of how accurate your characterization of their intellectual content is (and thus how accurate my account of what kind of research you are known for is).

    • Andy P. Says:

      ps: I’m done with this exchange, and have no plans to respond further.

    • samuelfhopkins Says:

      I am a mathematician; you can for instance see my academic webpage here: http://www-users.math.umn.edu/~hopki319/. I’m a close colleague/friend of Darij’s: we had the same PhD advisor and are now both postdocs in the same group at the same university. Anyways I don’t have much to add beyond what I (and many others) have said: it is evidently embarasssing and disturbing that this article was published by the NYJM, and any academic mathematician should be able to see that immediately.

    • Igor Rivin (@igriv) Says:

      I am relieved that Andy is done, and certainly encourage whoever is interested to look up my publication (and preprint) record, and form their own opinion. As for Samuel F Hopkins, I had figured out that you were a mathematician, what galls me is that you think you know better than two referees, myself, and the EIC of NYJM. All of these individuals are quite accomplished, so I repeat, your statements come across as arrogant and ideological.

    • Pyrrho Says:

      Igor, your last comments directed at Samuel are nothing more than an appeal to authority. Expecting automatic deference to your authority (even when added to that of a few others) from other mathematicians seems as if it would likely lead to feeling galled a lot of the time.

    • Igor Rivin (@igriv) Says:

      Pyrrho: A journal publication is a form of “appeal to authority”, the editors and the referees have the authority to accept or reject a paper. Everyone else gets to have an opinion (God knows that not all Annals papers are Gowers level), bust saying that your opinion trumps that of the people who are charged with making the decision is arrogant.

    • Pyrrho Says:

      Igor, you’re right that editors have the authority to accept or reject a paper, or require a retraction. (I don’t see that referees have the same authority; they recommend, but they don’t have the final say.) But that’s where editorial authority ends; the fact that an editor has made a decision about a paper doesn’t extend into some kind of authority to determine who is being arrogant about their opinions and who is not. Again, your apparent expectation of automatic deference seems to lead you astray. If I take what you’ve just said seriously, no one except an editor or referee for a paper could find a reason for a retraction without being arrogant. No one (except an editor or referee) could opine that “Journal X has really gone downhill lately” without being arrogant.

  64. crew Says:

    Women have two X chromosomes, and many of the genes on the X chromosome are expressed in the brain. Men have only one.

    However, something like 60% of the genes on one of those X chromosome are silenced in Barr bodies. Which one is silenced is essentially randomly selected.

    This means that dosage dependent genes affect women at the average of the alleles on their X chromosomes, while for men whatever they get from their singleton X is what they get.

    (What happens if you have too many alleles generating proteins. Think Trisomy 21.)

    Thus, women have a lower variance, but they pass their X on to men, for good or bad.

  65. Anonymous Says:

    I do not want to comment on the contents of the paper but the purported lack of “variability” in a population could also be a social phenomenon. Take for example the early humans who lived in a setting which does not offer the kind of opportunity that modern humans have. Any particular individual would be “professionally” a hunter irrespective of whether they were actually good at it. It is not due to the “inherent” lack of capability that they are not mathematicians or singers or any of the other professions of modern humans.

    So even if there is truth in there being less variability in a community it could be due to the social circumstances. And so
    jumping into the conclusion that “it is all in the genes” is bad science. If we were to do what we are inherently good at, we should all be hunting in the Savanah because that is what is
    “in our genes”.

  66. Javier Says:

    The statements by Wilkinson and Farb are disingenuous because they omit the plainly relevant fact that Amie Wilkinson and Benson Farb are married to one another.

    Both agree that they pushed for the paper to be “rescinded”, but in neither case was the paper formally rescinded. Rather it was removed, post publication, from the web. Professionally speaking, the difference is huge.

    Both statements attest to a lack of professionalism in the editorial processes of the two journals, which is really what is at issue here (rather than the quality of the article that was badly processed).

    • Javier Says:

      Addendum: It seems safe to conclude that neither of these journals should be considered “serious” as the editorial processes of both are clearly substandard.

    • michaelgreinecker Says:

      That they are married was already mentioned in the Quilette article. Why should corrections mention the things that need not be corrected?

  67. Social Justice Extremism Comes To Mathematics • Rejecting Rationality Says:

    […] mathematical blogs critisize the argument in the paper (see back and forth in comments) but don’t allege […]

  68. ciyer Says:

    Thanks for composing this cogent and incisive response.

    What’s frustrating to me about the pro-GMVH side is how unscientific the argument is. It’s simply based on insinuation. “More men have won the Nobel Prize in Physics than women; GMV exists. *nudge, nudge*.”

    Phases of the moon also exist. If I wanted to show that phases of the moon partially cause the discrepancy in the number of Nobel Physics Prizes awarded to men vs. women, I’d build a model that would estimate the effect of phases of the moon on the difference in the number of prizes awarded to quantify how big the effect is.

    You think GMVH partially explains the fact that of the 206 Physics Nobel Laureates only two have been women? Fine, build a model and tell me how many female laureates your model predicts? Is it more or less than two? And while you are at it, build a model that estimates how many potential Nobel Laureates choose to pursue a different career because of perception that women cannot succeed in physics.

    Once that is quantified, we can start talking about whether it is helpful or detrimental to discuss the GMVH.

  69. Anonymous Says:

    Farb writes that he is an editor at NYJM but he is not listed as one of the editors on their website: http://nyjm.albany.edu/edboard.htm Could anyone explain what is going on?

    • Anon375 Says:

      Benson Farb was listed as editor on the webpage of NYJM on 30 December 2017 according to the waybackmachine. So he was an editor at the time that the article was pulled (11/9/17). The next entry on the waybackmachine is from 26 February 2018 and there Farb is no longer listed. So possibly he was no longer an editor at the time he says the handling editor produced the reports (2/7/18).

  70. c young Says:

    > I merely claimed that the paper was mediocre and made no statement about whether it was OK to pull it.

    Fair enough, in your case. Yet the main reason that the quality of the paper is being debated above and elsewhere is that many see mediocrity as legitimating political interference.

    Many years ago I visited the USSR on holiday. Part of the deal was a session with a soviet sociologist with whom we could raise any issue (it was the Gorbachev era).

    So we challenged him about the suppression of free speech in the Soviet Union – particularly that of his fellow academics.

    He was an urbane and apparently reasonable person – an academic of a type quite recognizable from the West. Of course, he didn’t claim that the dissenters work threatened soviet power and should be suppressed on that basis. He didn’t even claim that their views were wrong. Instead, he raised a plethora of doubts about their motivation, and their personalities. There were plenty of avenues for making their points. They were old news. Tiresome people. The awkward squad. No concession would ever make them happy.

    (Early feminists in the West received exactly the same treatment.)

    For this reason, I am extremely skeptical when ‘special circumstances’, ‘complex issues’ or other pettifogging reasons seem to rationalise the suppression of ideas that are coincidentally viewed as ‘beyond the pale’ by those in power.

  71. av Says:

    Some thoughts on the two statements posted by Amie Wilkinson and Benson Farb, as they relate to Hill’s article.

    Both statements appear to omit aspects of the affair discussed in the original Quilette article by Hill, without contradicting them. I take it as weak evidence that these aspects are true.

    Amie Wilkinson’s statement makes no mention of the involvement of her father, the eminent statistician, and his criticism of the paper. On the other hand, Hill makes no allegation (on careful rereading) that Wilkinson or her father demanded that the paper not be accepted at the Intelligencer, which makes Wilkinson’s claim that she never did at least plausible.

    Farb’s statement minimizes his personal role (he’s one of 24 editors, etc.). It never mentions the “furious email” (Hill) that Farb wrote to the editor-in-chief and which is quoted by Hill. Farb disclaims that his wife never played any role in any deliberation at NYJM, but of course Hill never alleged that Wilkinson actually injected herself into the editorial process at NYJM, just that she got her husband to fight the battle. Farb’s email, as quoted by Hill, mentions that his father-in-law had already criticized the paper; that criticism was in a private letter to the Intelligencer’s editor, so Farb must have learned of it from junior or senior Wilkinson.

    The timeline also looks a little strange. The “disappearance down the memory hole” of the paper at NYJM happened in November and that seems like the most scandalous part of the whole affair to many (you don’t “disappear” an already-published paper and replace it by another, you add an editorial note of comment or disavowal or even rescindence, etc.). But Farb merely presents it as “temporarily pulled”, at the request of “several editors”, and focuses on a later decision, in February, by the entire editorial board. Hill, however, quotes from the editor-in-chief (Steinberger)’s letter already in November telling him that unless Steinberger pulled the article, half the board would resign and harass him, etc. I’d hazard to guess is that Farb was leading the charge to pull the paper in November and that “the several editors” are mostly him or were led by him, and that the quotes from Farb’s letter by Hill are true. It’s possible that Hill was told in November that the decision to pull was temporary, pending the discussion by the full board (as Farb claims) and withheld that detail from his timeline; it’s also possible that Hill wasn’t told that, or that it was a mere technicality anyway, and Farb misleads by focusing on it.

    Finally, I would note that (1) Farb’s statement doesn’t include, like Wilkinson’s does, an avowal that the “discussion of scientific merits of research should never be stifled” or anything like that. (2) Farb starts by saying he’ll set the record straight on Hill’s “unfounded accusations”, but never mentions what specific accusations he’s refuting; I don’t see any single point of factual disagreement between Farb’s statement and Hill’s article.

  72. Alex Jones Says:

    Thanks for the great post Tim. I just wanted to respond to the point raised in the last paragraph and ask you a question.

    I don’t think it is the case that the variability theory “depends on the idea that how good one is at mathematics is a question of raw brainpower”. I’ve seen many people propose that the extreme traits males possess include a lot of the traits that make a mathematician successful, such as enormous dedication, work ethic, passion, etc. Also, I think competitive nature is a nontrivial factor in motivating a mathematician to do his or her work, and do think (some versions of) the variability theory applied to humans do suggest increased competitive nature in males (which certainly does have its roots in biology).

    My question to you is why you very much want to see the gender imbalance in mathematics rid of, or at least quickly diminished, in your life time. It appears to be an irrational desire that I think is making you make illogical conclusions. I think you would agree that raw mathematical brainpower, however you want to (reasonably) interpret it, would no doubt be a help to becoming a mathematician. So, if one part of the population has more individuals with very high raw mathematical brainpower, then it is a natural conclusion that that part of the population will have more individuals as mathematicians. [Note: I am not saying raw mathematical brainpower is sufficient or necessary to becoming a mathematician, but it no doubt should have a positive correlation.] I therefore am confused why, if we accept the variability hypothesis and its implication on discrepancies in raw mathematical brainpower, the gender imbalance in math needs to be “corrected”. Thanks.

  73. Easy Says:

    I didn’t read ALL of the replies – but upon reading the premise of the article’s authors (females being more selective about partners, etc…) I instantly knew that the fallacy had little to do with good or bad math – but with assumptions about evolutionary forces….. In simple language – my understanding is that stressors cause either failure or success…. challenges force pressures related to survival and overcoming them results in increased skills and abilities. Female worlds until recently have been restricted in terms of exposure (for safety or to rule – women tended to stay more at home…. have less exposure to risk or novelty…. and women’s worlds required greater cooperation skills (being weaker – more submissive and likely to cooperate)… so females likely developed earlier communication skills related to social involvement. Male challenges drove testosterone and were life threatening – required cooperation to the degree it required completing a task… function oriented… and their travels required earlier orientation to geography – hence coordinates and spatial orientation….. Males also were the physical leaders…made more of the life decisions – determined routes – their stressors were higher – their challenges more “outward-oriented” as in away from home – they travelled more and further – they had to learn on the run…. and since the forces in their lives were different in these and other ways…. the males had both more drive and need to be at the top intellectually (they had more power to make decisions and had to make more decisions) – with greater repercussions – being successful was more rewarded throughout evolution – ie. smarter females with leadership could be killed more easily or raped and sidelined… males had greater rewards for success… females had greater risk…. their cooperative, weaker capacity left them cooperating with more male decisions than vice-versa…. men ruled. The life threatening challenges also resulted in more “falling down”…as in even today more males commit crimes or drop out of school etc… more risk more reward…. upside and downside…. programmed to take greater risks…. another analogy – in societies where being male requires greater and greater machismo…higher homosexuality rates – being macho-male is too difficult… evolution created the norms of body chemistry in males and females….. hence, also the drives and potentials….. In order for females to be at the same or similar levels – they must first create societies where sexuality is unlinked from hunter-survival or nurturing-family roles…. orientation and preferences must become arbitrary…and THAT is what is being done in this epoch…. FYI – females for the reasons above – likely developed speech and other social skills – perhaps more complexity of them and sooner – than males (females socialize in the community earlier and more)… while males developed for evolutionary pressure reasons better decision-making skills…. more unitary focus (the troop’s life depended on it)…. hence – women talk more in general…discuss things more – but have greater difficulty and are more easily derailed from decisions…. while males tend to have less interest or ability to converse just to do so (we have chatty Kathys…. not chatty Kens) – while males make swift decisions (and keep trying to solve women’s problems while women just want to be listened to – hence misery in relationships)….

  74. Easy Says:

    another thought – until recently – most females had little choice and often reproduced via rape…. or simply whatever male was local enough and could provide for survival….

  75. Henry Wilton Says:

    There seem to be quite a few comments that misunderstand the relationship of a mathematics journal (like NYJM) to its editorial board. The bottom line is that the reputation of the journal *is* the reputation of the editorial board. The editors are expected to be willing to vouch for the mathematical merit of every paper published in the journal. Conversely, the reputation of the editors is what encourages authors to submit their papers to the journal.

    Some commenters seem to have interpreted the protests from members of the NYJM editorial board as politically motivated, “left-wing” or “feminist hysteria” etc. For instance, see the poster Eric Rasmussen’s characterisation of Tim’s argument.

    >“The Hill paper doesn’t have any mistakes in it, but it looks like a pretty mediocre paper, so there’s nothing wrong with two journals retracting their acceptances under pressure from feminists who don’t like the paper’s subject matter.”

    These comments are wide of the mark. It’s clear that Ted Hill’s paper is not remotely appropriate for a serious pure mathematics journal like NYJM. This is not a statement about the merits of Hill’s paper as putative biological model, nor about the politics of its argument. It’s just that it’s not a mathematics paper of even slight interest. If a paper like this were published in a journal that I edited, I would contact the managing editor and tell them that if the paper were not retracted then I would resign; not because of politics, but because editing a journal that published papers of such low mathematical quality would violate my professional integrity.

    Benson Farb’s statement makes clear that this is more-or-less exactly what happened. This would have left NYJM with two options: retract the paper, or lost some fraction of their editorial board. And deciding to retract the paper under these circumstances seems like a good decision.

    Having said that, that NYJM decided to “disappear” the paper in this strange way does badly damage the journal’s reputation. It would also make me very uncomfortable about sitting on the editorial board, or submitting a paper there. One can only guess as to how this decision was taken. An obvious guess is that it’s a fudge, because there was no consensus among the editors. Mathematicians that I attribute this apparent chaos behind the scenes at NYJM to the fact that the managing editor is known to be in hospital; this seems reasonable.

    In conclusion, NYJM appears to have made two grave mistakes: accepting Hill’s paper in the first place, and then failing to properly retract it. I hope this comment makes clear that neither of these should be attributed to the left-wing or feminist politics of any of the editorial board (Benson Farb or anyone else). On the contrary, the first mistake, can be directly attributed to the right-wing politics of the handling editor, Igor Rivin, and perhaps the second mistake should be too.

    • c young Says:

      Thanks, helpful perspective.

    • nieuwezijde Says:

      Thank you for your perspective.

      I hope this comment makes clear that neither of these should be attributed to the left-wing or feminist politics of any of the editorial board (Benson Farb or anyone else)

      Your comment makes it clear that you are trying the best you can to
      obfuscate the issue of what you delicately call “retraction”. Which, in my view, strengthens the suggestion that the deletion of the paper can be directly attributed to feminist politics of Benson Farb and Amie Wilkinson.

    • Igor Rivin (@igriv) Says:

      Since your politics is extremely LEFT wing, it is disingenuous to pretend to be a dispassionate observer. In fact, had you bothered to read my various comments on Tim’s post, you will see that the decision to solicit (and then publish) the paper was not political, unless you consider the desire to publish interesting papers an expression of politics. As for your claims that the paper was not remotely appropriate – the very qualified referees and the editors of the journal thought it was. Your opinion is of no consequence whatever, sorry. The insistence on a full editorial board review of the decision was unprecedent and not at all in accordance with the journal’s practice. By the way, I am editor of several journals, and while some are run dictatorially (the Editor in Chief approves all papers, the other editors are advisory), and some give the editor full authority to accept and reject papers, none require editorial board approval. The number of journals that do is quite small (Annals, JAMS, G&T are the only ones I know of).

    • Winston Says:

      As a mathematician, I found this paper of extremely high interest. A paper does not have to have very difficult mathematics for it to be interesting. In this case the paper would be highly interesting to most mathematicians who have an interest in evolutionary biology. Hill gives a very nice toy model and provides a starting point for explaining one of the most widely observed (and generally accepted) phenomena in evolutionary biology, the greater male variability hypothesis.

      For mathematicians interested in various proposed causes of the gender gap, I highly recommend as a starting point reading the transcript of this 2005 debate between Steven Pinker (Professor of psychology at Harvard and author of several books on evolutionary psychology) and Elizabeth Spelke (Professor of Psychology at Harvard University, where she is Co-Director of the Mind, Brain, and Behavior Initiative).


      I am not at all sure how Rivin’s politics are relevant here.

    • Peter Kriens Says:

      @Henry Wilton Your explanation sounds very reasonable and I would be inclined to believe it if that was all we knew. However, there was also the earlier retraction by the Intelligencer that involved the same family as well as the letter from the NSF.

      I wish some good investigative journalists (the Atlantic anyone?) would make a serious article about this. After all, the stakes are pretty high.

    • Pyrrho Says:

      From the (partial) set of facts available to me, Henry Wilton’s account looks very close to the mark. In a situation like this, it is very likely that at least some of the editors would have felt strongly that the reputations of both the journal and its editors were at stake. At the point when this paper was published, a good number of editors had put years of effort into the journal; I can easily imagine people in that position feeling that they had been betrayed. As Henry says, they might have had reasons for that which were entirely independent of political considerations.

      One aspect of this which I haven’t seen anyone mention is the fact that Hill’s article contains quotes from what he describes as an email from an editor to an editor-in-chief. That’s the kind of information which wouldn’t ordinarily make its way to an author, and it suggests there was a serious problem with maintaining confidentiality of editorial deliberations. Yet another reason why some of the editors might be feeling a deep sense of betrayal.

      I’m struck by the fact that people’s views on the relevance (or not) of politics in this situation often seem unevenly applied. This article went viral because it supported a “left-wing activists suppressing science for political reasons” narrative. And yet, as far as I can see, it points to no evidence that the person it paints as the main villain was motivated by politics at all, much less that her motivation was exclusively political. It seems to rely heavily on guilt by association to achieve that effect. And yet, in this very thread, we have someone claiming that she was motivated exclusively by “feminist politics.” Under the circumstances, I have trouble taking seriously Winston questioning of the relevance of Igor’s politics if he can’t also bring himself to question the relevance of Wilkinson’s politics.

      The article does attribute quotes to Farb which suggest he raised political considerations, but among those considerations was the concern that the acceptance of the paper was itself driven by political considerations. Igor says that’s not true but, of course, that’s what he would say. I find myself wishing that people who are worrying about the influence of politics on the decision to unpublish this paper (which, to be clear, I think is an entirely legitimate concern) were also at least a bit worried about the possibility that politics played a role in the decision to accept it.

      There are some questions about the editorial process floating around that Igor has chosen not to address. Those are:

      1. Why were referee reports not provided to members of the editorial board who had requested to see them until almost 3 months after the paper had been unpublished?

      2. Was an opinion from a mathematical biologist (or someone with similar expertise) requested?

      Let me add a few to the list:

      3. Did Igor have both referee reports in hand at the point when he made the decision to accept the paper? (Hill mentions only one referee report.)

      4. Did the first referee express any opinion as to whether the paper was in his or her field of research? (Farb asserts that neither referee was an expert on the topic of the paper.)

      5. Did the first referee express any opinion as to whether an opinion from a mathematical biologist should be obtained?

      6. Does Igor have any knowledge about how Hill (apparently) got information about confidential board deliberations?

      7. Was information about confidential board deliberations also shared with referees? (This is also a no-no, but someone seems to hinting that he is one of the referees, and knows more than one would expect: https://posttenuretourettes.wordpress.com/2018/09/12/lysenko-is-smiling/)

  76. Lysenko is smiling – posttenuretourettes Says:

    […] but I happen to have corroborating first-hand knowledge) in this Quillette piece. The fields medalists are on it, but I humbly posit that a crucial angle is still missing. Has anybody tried to discover […]

  77. A nonny mouse Says:

    To the people saying that since the paper was mathematics, and NYJM is a generalist math journal the paper was appropriate: the Duke Mathematical Journal for instance is in principle a generalist journal, but in reality it has a strong preference for certain subfields of pure mathematics. Many other generalist journals are like this. I disagree that the paper should have been disappeared, but no one can pretend it is on-topic for NYJM, given the usual coverage of topics. Perhaps, though, individual editors can choose what they feel is appropriate? This seems like it would need checks and balances, especially given the present ill-health of the EiC.

    (Disclosure: I have a pure mathematics paper published in NYJM, and generally have had a good opinion of the journal.)

    • A nonny mouse Says:

      Also: I think it would be helpful if the referee reports were made public, to verify or otherwise the standard of critique that has been said to have occurred. No one’s names need be forcibly attached, but that would certainly be a useful data point if they were comfortable in standing publicly by their assessment.

  78. Gil Kalai Says:

    As an aside, let me mention that in my view it is important to have a large women representation in the editorial boards of mathematical journals. NYJM can (and in my opinion should) do much better in this respect.

    • richardjlyon Says:

      May I ask why? I imagine that might be a consideration for so-called Social ‘Science’ Journals. But math is abstract. Isn’t it important (imperative) to have the people who are most qualified to fulfil the duties of the editorial board? In what way is their gender relevant to that objective?

    • Gil Kalai Says:

      This is a good question! Perhaps you noticed that Igor Rivin described in a comment above the mode of operation of NYJM and many similar journals where editors solicit good mathematical papers for the Journal. This is quite welcome but naturally it may create bias based on personal contacts and relations and, in fact, a similar bias in the editorial board selection process may be the reason why the number of women in NYJM is low even compared to the number of women in top departments of mathematics.

      So the small representation of women in NYJM most likely mean that the team is not the most qualified to fulfill the duties of the editorial board, and also it may create (unintentional) bias against good papers written by women.

    • richardjlyon Says:

      Isn’t this a slippery slope? If that were a valid proposition, then there must also be the possibility of unintentional bias against good papers written by African American mathematicians (e.g. “Modelling the underlying dynamics of crime by ethnicity”), Jewish mathematicians (e.g. “Modelling the underlying dynamics of intelligence by religion”), gay mathematicians, immigrant mathematicians, Republican mathematicians, etc.

      Could your instinctive consideration of this particular grouping in any way reflect the extraordinarily successful campaign by women to be accorded special privileges in our society?

      Far better, surely, to hire ‘the best’ and submit their selection to regular scrutiny.

    • Gil Kalai Says:

      Richard, this is again a good point. I agree with you that the “friend bring a friend” method is problematic not only regarding women, but I think that paying attention to the very clear issue of women representation may bring change also for other biases that in my view harm mathematics and the community of mathematicians.

      (And for those who subscribe to the Darwin-Summers-Damore-Hill theory of idiots/geniuses dichotomy for men, I note that for serving in editorial boards and other forms of academic service, geniuses give little advantage while idiots may cause a lot of damage. 🙂 )

    • richardjlyon Says:

      Gil – thank you for the thoughtful response. I don’t want to labour the point, but in the US, the average African American family has $5 for every $100 that the average white family has accumulated, and inequality remains roughly as it was at the time of Reconstruction (Stanley. 2018. “How fascism works”, p.94). There are many grievances that compete for resources (I’m simply selecting one at random – I am not making an argument for privileged treatment of any particular racial grouping), but the success of feminism to promote gender-based grievances to the top of everyone’s lists has been remarkable.

    • Gil Kalai Says:

      Thanks for the discussion, Richard. (Sorry, folks, we move further away from mathematics.)

      “Could your instinctive consideration of this particular grouping in any way reflect the extraordinarily successful campaign by women to be accorded special privileges in our society?”

      Richard, one of the “special privileges” you may refer to is the privilege not to be sexually harassed and not to be victim to more serious sex crimes. Indeed the campaign against sexual harassment and other sexual crimes is leaded by women. Men form the vast majority of sex offenders, and while women are the majority of victims there are also many men victims.

      Now, if we find ways (for example, via education) to reduce sexual offences (and I do not pretend to know how) this will be beneficial for saving both women and men from being victims, and also for saving (mainly) men from being offenders. This will be beneficial for women and the “slippery slope” would be that it will also be beneficial for men.

      “The success of feminism to promote gender-based grievances to the top of everyone’s lists has been remarkable”

      It is on top of my list because, like in the example above regarding sex offences, I regard the justice for and participation of women important on its own and also as a potential key for other problems in the society both in my country Israel and in other places. To a large extent other “special privileges” that women and other groups struggle for is “equality” and mechanism for equality and against bias would be beneficial not only for women. I should emphasis, perhaps that my view is based on my common sense and ideology. I don’t try to support it with mathematical models and proofs. And here and elsewhere I may well be wrong.

      Another more mundane reason it is on top of my list, is that I am just one person, and I don’t feel I need to have a long or comprehensive list. This was my choice long time ago and other people can make other choices.

    • richardjlyon Says:

      (All – I also apologise for the departure from the central theme of the thread, and promise that this will be my last post).

      Gil – interestingly, the claims that sexual harrassment is widespread (or an ‘epidemic’, to use the language of moral panic), that women form the majority of victims, that false allegation is rare, etc. – which you appear to regard as axiomatic – are all coming under scrutiny from a growing number of respected (and worried) feminist academics (e.g. Sommers, Williams).

      Three common observations are often made by them: (i) a surprising quantity of evidence supporting such claims appears to be fabricated (ii) the methodology followed is often unrecognisable by normal academic standards, and manipulated to confirm rather than test hypotheses (iii) efforts to examine these methodological irregularities invariably provokes extreme resistance.

      While it is undoubtedly true that women experience sexual harrassment and men perpetrate it, the reverse is also true and widespread. For a topical example, a prominent spokeswoman for feminism’s current instrument for sensitising society to their grievance about sexual harassment (‘#MeToo’) is an alleged pederast and rapist of boys. Indeed, the phenomenon of male victimisation is largely unexamined – and unexaminable – in academic literature, for precisely the reasons that are arguably within the scope of this thread’s topic.

      There is therefore, in my view, sufficient grounds not to abandon conventional skepticism about such claims, and no basis for a priori arguments about Board composition based on factors other than mathematical competence.

      This is one context to this thread’s discussion about the behaviour and motives that may have led to the rejection of a paper that potentially challenges (effectively or otherwise) feminist claims that gender difference is a political issue (and therefore mutable) rather than a scientific one.

      With that, I will thank you for your thoughts (which I find sincere), and Mr. Gowers for his latitude in permitting this aspect of the debate to be examined, and rest my case [any further debate unavoidably requiring enquiry about the testability of claims in the absence of examinability.]

    • Gil Kalai Says:

      Richard, I hope we agree that both women and men have the right not to be sexually harassed and not to be victims of more serious sex crimes.

      I cannot thank you for your last comments but I think they do shed some light on the situation we are in.

    • Richard Says:

      Your doubt may spring from an affirmation of the consequent fallacy (vis. “If you are a misogynist, then you question feminist claims; you question feminist claims; therefore you are a misogynist”). The feminist paradigm, of necessity, is riddled with it (e.g. if you are powerful, then you are a man [T]; you are man [T]; therefore you are powerful [F] i.e. “Patriarchy”).

      No, I am not a misogynist and, yes, we both agree that women have the right not to be sexually harassed and not to be victims of more serious sex crimes. I’m sorry that seemed to you like a reasonable doubt to have of me. Now I really will leave this debate to allow it to return to its original topic.

    • Javier Says:

      Editorial boards ought to be filled with good mathematicians who are decent people (the latter requirement is far too often neglected) irrespective of gender, race, ethnicity, or what have you.

  79. Winston Says:

    I would like to thank Igor Rivin for giving his point of view in the form discussion which helps clarify matters greatly for me.

    Having read now the account of Hill, the statements by Wilkinson and Farb, and the statements by Rivin in this forum, I believe that the way these two journals conducted themselves was a disgrace. If they have any semblance of honour, they should now publish the article as originally accepted, apologize to Hill, and also allow other mathematicians and biologists to respond in a subsequent issue.

    For the mathematicians here who know little about evolutionary psychology, I strongly recommend the book “The Blank Slate” by Steven Pinker as a starting point.

    Full disclosure: I am a permanent mathematics faculty at a top University with a strong interest in evolutionary biology and neuroscience. I am writing this comment pseudonymously because I fear professional repurcussions if I use my real name. I can confidently state that if I had taken a different point of view (similar to Gowers’s) I could freely express myself in my real name and fear no such repurcussions.

    • Pyrrho Says:

      It sounds like you might have been a good candidate to referee this paper. I wonder if Igor would be willing to say whether a mathematical biologist was involved in the review process, or if that possibility was considered at any point prior to publication.

      I agree that the outcome at NYJM was very bad. I can’t see any way to justify removing a published paper without comment, much less replacing it with another. That in itself seems like a good reason for members of the editorial board to consider resigning. One can only hope that the leadership of NYJM is working towards a more satisfactory resolution. Their current silence on the subject is painful, but the fact that the editor-in-chief is seriously ill may be contributing to the fact that the journal seems stuck where it is now.

      I’m not particularly bothered by the outcome at the Intelligencer. In that case, we’re talking about an opinion piece in a publication which isn’t by any stretch of the imagination a research journal. The norms for publishing research don’t seem particularly relevant here. My instincts would lead me to give an editor free rein to reverse a decision to publish such a piece, for any reason they consider compelling. Unless, of course, the piece expresses a point of view I strongly feel should be expressed; then I’d be up in arms about it.

    • Igor Rivin (@igriv) Says:

      Thank you very much for your kind words. You mentioned before that you did not think my political views had anything to do with the matter. I very much agree, but what does matter is my (somewhat collective) experience from the USSR where truth was in the service of ideology and where mathematics was essentially the only way to escape the ideological oppression. . It saddens me greatly that we now find ourselves in this Lysenko-ist bad dream (ironically, my family lived on Vavilov street in Moscow …). Hopefully, if enough people try to do the right thing, we shall overcome.

  80. Aloysius Miller (@aloysiusmiller) Says:

    Wouldn’t it have been better to refute the article publicly? Doesn’t that happen all the time in real science? I am in no position to comment on the merits of anyone’s arguments but science is a dialog not an ideology. Or that is what I thought.

  81. tommydontplaythat Says:

    At the end of the article: “…there is no reason, in principle, that the pace would not pick up substantially. ” In principle – which begs the question- what principle? That women are just as qualified and intetested in math as men? Isn’t that measurable – or is it too problematic to question noble principles – like religious tenents? When science apes religion – with apologies to Darwin – we all lose.

  82. Centrocercus urophasianus Says:

    Regarding the following comment…

    “While it is true that some males have trouble finding a mate, the idea that some huge percentage of males are simply not desirable enough (as we shall see, the paper requires this percentage to be over 50) to have a chance of reproducing bears no relation to the world as we know it. I suppose it is just about possible that an assumption like this could be true of some species….”

    The situation where the majority of males fail to reproduce is actually seen in many species – it’s quite common. There are the well-known extreme examples – e.g. elephant seals or various lekking bird species – where just a few males may monopolize reproductive access to dozens of females. But there are plenty of less extreme examples – e.g. in lions on average prides have something like 2 adult (breeding) males and 5 adult females.

    So perhaps “bears no relation to the world as we know it” is a bit strong!!

  83. another math anon Says:

    The NYJM calls itself “The First Electronic Journal of General Mathematics”. Benson Farb called the de-published Hill paper topically “inappropriate” for NYJM because no previous papers had been published on that subject (i.e., with the same AMS classification) in the previous issues of NYJM. This appears to be a new standard he invented, and not the stance of the journal.

    If the NYJM does now want to adopt Farb’s new standard as a requirement for publication, and limit submissions to the areas in which the journal has already published papers, it should update the instructions for authors on their site. Currently the instruction is to submit to the editorial board member whose listed interests are closest to the contents of the paper.

    • Anonymous Says:

      It has also historically called itself a venue of “rapid publication”, which in this case meant months rather than years, but does give a chuckle in the present single case of weeks.

      However as a math anon you surely know that journals are never general in the sense of everything goes and are limited by expertise of people making up the editorial board. General just means not specialized, and mathematics in this case means exclusively pure mathematics as can be seen from the self-described remits of particular editors http://nyjm.albany.edu/EditorialAreas.html if not general makeup of the published work.

    • another math anon Says:

      1. The mathematics in this paper is pretty simple, therefore in in the intersection of the expertise of all editors. I’m guessing that most of them would have hit on the idea of asking a mathematical biologist, biology-biologist, or evolutionary theorist to read the paper and comment on novelty and interest. Given the simplicity of the paper one would expect it to be refereed faster than some highly technical work.

      2. They do publish applied math papers, including papers without any theorems. http://nyjm.albany.edu/j/2001/7-18.html

    • Pyrrho Says:

      The mathematics is indeed simple, and almost any research mathematician of reasonable caliber could check it in a day. The more interesting issue is evaluating its significance as a model for the kinds of phenomena it is attempting to explain, however tentatively. I agree that asking a mathematical biologist, biology biologist or evolutionary theorist would have been a natural step. The question is: was that step taken?

    • Pyrrho Says:

      The paper by Rosar and Peskin you point to was published at a time when there were people like Jerry Bona on the editorial board. It’s not surprising they were publishing applied papers on fluid mechanics back then. http://web.archive.org/web/20010209134201/http://nyjm.albany.edu:8000/Edboard.html

    • Igor Rivin (@igriv) Says:

      Pyrrho: so are you saying that at least for the last 17 years, a sufficient condition for publication in NYJM was that one (1) editor was interested in the paper? Asking for a friend.

    • Pyrrho Says:

      I said nothing of the kind. Read more carefully.

    • Darij Grinberg Says:

      Who in this comment thread (independently of your opinions on NYJM, the Intelligencer and the merits of the study) thinks that

      1. the NSF’s insistence on removing the grant acknowledgment from the paper was off-track and partisan;

      2. diversity bureaucrats have no business deciding what the “values of the NSF” are;

      3. the possibility of hype by the wrong crowd should never be a criterion against publishing science? (Already for the reason that it’ll likely blow up and then the hype will be even larger.)

      If these are as mainstream as I would expect, maybe we should send our own letter to the NSF. With no presumptions about the “values of the NSF”, but merely as a collective statement of opinion. Science doesn’t gain much by taking the backseat to politics.

    • Pyrrho Says:

      1. It depends. In the old days, when you acknowledged NSF support in a paper no matter how tenuously it was connected to the grant proposal, I would have found it disturbing. But I’ve heard comments to the effect that NSF has become more stringent about requiring research papers which acknowledge support to fall within the scope of the project. If that’s true, and it was the reason the NSF insisted on the removal, then I don’t have a problem with it.

      2. I don’t think describing a faculty member in a math department who holds a departmental position related to diversity as a diversity bureaucrat is a fair description. That makes it hard for me to get to the point of agreeing or disagreeing with this.

      3. I wouldn’t go so far as to say never; I can imagine situations (mostly in societies unlike the one in which I live) where I think it would be quite justified. In the particular case at hand, I don’t think the possibility of hype by the wrong crowd was a good reason not to publish the paper.

    • Darij Grinberg Says:


      > But I’ve heard comments to the effect that NSF has become more stringent about requiring research papers which acknowledge support to fall within the scope of the project. If that’s true, and it was the reason the NSF insisted on the removal, then I don’t have a problem with it.

      If that’s true, then I think it indeed changes the calculus. I guess I should ask Tabachnikov.

      > 2. I don’t think describing a faculty member in a math department who holds a departmental position related to diversity as a diversity bureaucrat is a fair description. That makes it hard for me to get to the point of agreeing or disagreeing with this.

      OK; you’re right, these are actual mathematicians.

      > 3. I wouldn’t go so far as to say never; I can imagine situations (mostly in societies unlike the one in which I live) where I think it would be quite justified. In the particular case at hand, I don’t think the possibility of hype by the wrong crowd was a good reason not to publish the paper.

      Here’s, I think, a rather symptomatic case: https://www.nytimes.com/2018/08/04/opinion/sunday/anti-vaccine-activists-have-taken-vaccine-science-hostage.html

    • Igor Rivin (@igriv) Says:

      Pyrrho: what the discussion says is that there were applied papers because a single editor (Jerry Bona) was interested in the subject matter. I had assumed you were a mathematician, so I did not feel the need to elaborate on this reasoning.

    • Pyrrho Says:

      Igor, “necessary” would have been a better word than “sufficient” in your first attempt to rephrase my meaning. This second version makes a weaker claim than the first version, but still seems to lean in the “sufficient” rather than “necessary” direction.

    • Pyrrho Says:

      Darij, I agree that the issues related to vaccine science are disturbing. I’m guessing we’d agree that we want high quality research on both the benefits and dangers of vaccines to be done, and that we want the public perception of the implications of that research to be as accurate as possible. Part of the reason vaccine science has reached this point is because of shoddy research which went viral. I’m wondering: suppose you were an editor of a journal like NYJM, and a paper somewhat in the spirit of Hill’s were submitted which described a toy model which “is proposed to help explain how” vaccines “might tend to” be dangerous. (Quotes from Hill’s abstract.) How would you handle it?

    • Yemon Choi Says:

      This is a comment on Darij’s comments, but the threading doesn’t go to that level. Darij, while I recognise that you have walked back slightly on the phrase “diversity bureaucrats”, I just want to record my opinion for anyone else reading that this is *way* off base as a description of at least one of the two people you mention, probably both. (I’ve seen this come up on some reddit thread, which is the main reason I bring it up here, not to pick a fight with you personally.)

      I don’t expect many let alone all mathematicians to share my own interests and valuations of researchers, but if you were referring to https://mathscinet.ams.org/mathscinet/search/author.html?mrauthid=341913 then I think the reflexive labelling of someone active in “promoting diversity” who you probably wouldn’t see eye to eye with as a “diversity bureaucrat” is not just unfortunate but a touch lazy, in the same way it would have been lazy for me to label Hill as a grudge-holding crank without first checking his actual previous output and approach to mathematics. (As I said before, I was quite interested in both the Benford and the fair division work some years ago.)

      (If we are playing disclosure games: erm, I sat through a nice plenary talk by Brown, and I am a fan of his book with Ozawa, and that is pretty much my only interaction with him.)

    • Darij Grinberg Says:

      @Yemon Choi: I appreciate you digging into the details and adding nuance. I mischaracterized Henderson and Brown on the basis of their behavior that Hill attested to in his Quillette article (and I consider Hill to be truthful on fact), while I should have characterized *their behavior in this case* instead. On these narrow grounds I apologize to Henderson and Brown.

      I believe the correct version of point 2 would be “The NSF’s behavior should not be affected by drive-by critics making political arguments”. The letter from Henderson and Brown *might* have included non-political arguments as well, but for now I suspect that even if it did, the politics is what did the damage.

      If you are on good terms with either Henderson or Brown, I would be happy to read a statement by them, as well as the letter in its original wording. For now, my belief is still that the point where the biggest harm to science was done is either their letter to the NSF, or the NSF’s reaction to that letter (depending on what the letter said). Researchers are rightfully expected to be able to deal with criticism, but backlash from a funding institution is a much different story.

      I also think it is worth asking Tabachnikov what exactly the NSF told him.

      (I am not commenting on the whole Facebook secondary-boycott and harrassment narrative, because the things I have heard are not very concrete; I am decidedly *not* saying that nothing wrong was going on there.)

  84. Mark Sapir Says:

    1. What Intelligencer did with the article is beyond good and evil and should be condemned by all mathematicians. I guess Tim should start a new boycott movement. Or is he is going only after “millionaires and billionaires (C: Berny Sanders)”? .

    2. I would think that the paper is weak for NMJ. It is just not deep enough.

    3. The problem is not with the model. My long ago extensive experience with applied math showed that if you smooth it up, you get exactly the same result but with considerably more efforts. Nobody knows – why, but as an applied mathematician used to tell me back in Russia: your sophisticated models are perhaps better but our simple models fly and shoot with great precision which was a truth.

    4. Being a brother, a husband and a father of female PhDs in mathematics, I can tell that the conclusions of the paper is wrong, but that just says that a better model is needed or that biology is not the only factor and perhaps not the main factor at all.

    • Alexander Barvinok Says:

      Dear Prof. Sapir,

      This is regarding your point 4). If I understand correctly, the paper discusses the variance (or some other anti-concentration measure) of a distribution. As such, it does not really have any bearing on any particular members of the population. For example, the statement that the suicide rate in the United States is twice (say) high as the homicide rate, does not imply that I am twice as likely to kill myself than to be killed by somebody else. Please accept my apologies if I misconstrued your remark.

    • Gil Kalai Says:

      Dear Sasha, if we put the threshold at “the ability to have Ph. D. in math” and ask “Is the percentage of of men equipped with the intellectual power to reach this level higher than the percentage of women?” then Mark Sapir’s example give anecdotal small positive support that the answer is NO. On the other hand, Hill’s paper gives ZERO support (0) that the answer is YES.

    • Mark Sapir Says:

      @GilKalai: “Mark Sapir’s example give anecdotal small positive support that the answer is NO” In fact if you look at other East Euriopean countries, then you should conclude that

      1. There is absolutely no bias toward men going into STEM fields (large math departments in these countries have 50-80% of women students).

      2. There is little/no bias in women getting a PhD in math at these departments: about 50% of faculty at the large East European math department are women.

      So a men bias in 1 and 2 is a purely Western phenomenon, and biology has nothing to do with it. Politics, traditions, etc. are dominant factors.

      3. There is a strong bias toward men at the very top of the “food chain” of strongest mathematicians. But that has nothing to do with lack of intelligence for women.It has everything to do with the specific of the profession. Imagine Gregory Perelman. Suppose, for the sake of argument, that everything you heard about him is correct. In particular, the guy (when active) is an ultimate “math machine”, thinking and actively working in math 24/7/365. Can you imagine a female with family being like that? In order to be a woman highly successful in math, you need to be a math Mozart, like Mirzakhani. A genius with a light touch. That is extremely rare. There are many more Perelmans than Mirzakhanis.

    • Igor Rivin (@igriv) Says:

      Mozart’s “light touch” (by which, i assume, you mean that he could write great music effortlessly) is a myth. The guy worked all the time. Read “Peak” by Pool and Ericsson.

    • Math machine? Says:

      However even Perelman was unable to put up with the mobbing, also antisemitism at his institution. Other examples abound. As David Ruelle opines in “Mathematician’s brain”, treatment of Grothendieck was shameful. Physics had that macho problem too, but that’s changing already while mathematics lags behind.

    • Anonymous Says:

      “On the other hand, Hill’s paper gives ZERO support (0) that the answer is YES.”
      Why? The paper contains a model.

    • another math anon Says:

      @Mark Sapir,

      I’d love to know what large East European math departments those are. Ukraine had high numbers of females in their IMO teams and their most famous current young mathematician is female (Viazovska). Further west, Italy has a high number of woman undergraduate and PhD students, maybe a female majority. Iran has a high number of female math students. As a general statistical correlation, the less feminist the society the more women study math (reasons are not clear, but Sweden for example has very low female numbers in math).

      However, some of this has to do with economic incentives and different allocation of “math people” to math vs physics vs CS vs engineering. Women are almost everywhere higher-represented in programs that train teachers, and in some countries the requirement for being a math or physics teacher is to get a degree in those subjects (or math and math-pedagogy are not distinguished in the statistics). Where the job market for teachers is competitive, it makes sense for the person with a math degree to continue for a PhD. In poorer countries the men who would have done math might switch to engineering and computer science (to earn more money) instead of math or physics. So it would be interesting to compare the enrollments in engineering and applied math and other mathematical subjects beyond pure math. If there is any European country where, summing all the different variations of “math subjects”, women study these things at the same rate as men that would be very interesting.

    • Igor Rivin (@igriv) Says:

      According to the data in this document (with some inferences made), there is no country in Europe (Eastern or otherwise) where what Professor Sapir describes holds: https://ec.europa.eu/eurostat/statistics-explained/index.php/Tertiary_education_statistics#Fields_of_study

  85. donald j. tingle Says:

    “And even if we were to accept that something like that had been the case, it would be a huge further leap to assume that what made somebody desirable hundreds of thousands of years ago was significantly related to what makes somebody good at, say, mathematical research today.”

    Are you suggesting that it is really such a leap to conclude that general intelligence exists, and that women might find it attractive?

    I so, I find it personally offenseive. To me and my wife.

  86. Anonymous Says:

    Mr. Gowers in this blog post and in his comments seems to be making a rather broad statement, which can be summarized as follows:

    “If a paper in math biology has mathematical part which is not particularly deep, the paper does not belong to a mathematical journal.”

    Does Mr. Gowers realize this applies to a much wider group of authors than Mr. Hill and Mr. Tabachnikov? For example, has Mr. Gowers tried to apply it to some of the works of Mr. Bernd Sturmfels?

    Applying the above proposition selectively to the work of Mr. Hill and Mr. Tabachnikov seems rather unprincipled. Perhaps Mr. Gowers’ parents should have taught him to pick on kids of his own size.

    • Anonymous Says:

      Sorry but I am very familiar with the work of Prof. Sturmfels and can’t make anything of your point. What do you have in mind?

    • Anonymous Says:

      I would rather not go into details. Everybody can look and judge for themselves. The point is that Mr. Gowers rushed to attack his colleagues’ work without making even a minimal effort to check what comparable works look like and where they get published.

    • Anonymous Says:

      I am not awaiting eagerly for details on how anything Sturmfels did has in any way been incompatible with Gowers principles for judgement. I may as well wait to win a lottery.

    • Anonymous Says:

      Also citing Sturmfels as work comparable to Hill is insulting, I am very much in doubt you are capable of going into details here as algebraic statistics has been, I may say quite confidently, the most sophisticated theory statistics has ever saw.

    • Alexander Barvinok Says:

      “Also citing Sturmfels as work comparable to Hill is insulting…”

      I suggest we all refrain from such double-edged remarks…

    • Anonymous Says:

      I don’t want to live in the same world of your imagination where that is double-edged.

  87. Anonymous Says:

    The power differential in this story is clearly on the side of Ms. Wilkinson and Mr. Farb, not Mr. Hill and Mr. Tabachnikov. The former are quite famous mathematicians, they work in an elite department and enjoy friendship of other famous mathematicians. For example, Mr. Tao rushed to inform us that Ms. Wilkinson “was a recent speaker here at UCLA in our Distinguished Lecture Series”, as if it has any relevance.

    More importantly, while sadly alt right tendencies are on the rise in the greater American society, inside academia rather radical form of political correctness is mainstream. Mr. Tabachnikov has already suffered pressure from NSF, and his future funding from them might be in danger. Furthermore, I am certain that administrators at Penn State are actively looking for legal ways to punish him.

    To speak out against Mr. Hill and Mr. Tabachnikov in this situation without explicitly mentioning that they do not deserve any threat to their livelihood is wrong. Especially if you are as famous as Mr. Gowers or Mr. Tao.

    I also sympathize with Ms. Wilkinson and Mr. Farb. The amount of attention they and Mr. Tabachnikov are receiving is uncomfortable for any human being who is not a professional politician. All three of them I suspect are greatly stressed by the need to protect their good name. What Ms. Wilkinson and Mr. Farb need to realize is that in the current political climate in academia they are not in any serious danger, unlike Mr. Tabachnikov. I am sure they are good people who did not want any harm to come to Mr. Tabachnikov’s livelihood from this story. It would help if they made it clear in some kind of public statement.

    Finally, I want to express my personal opinion that publishing this paper was a pea-brained idea. What was the point? I am particularly upset with Mr. Hill for getting Mr. Tabachnikov in trouble. Unlike the other three participants, I feel like Mr. Hill wanted this kind of attention and is enjoying it.

    • Winston Says:

      If you are expressing in the last paragraph the general idea that one should avoid publishing things that are likely to contententious, divisive, or controversial, then I disagree. The only criteria should be academic quality, which in the view of the editor involved, was met. If we as a community avoid publishing controversial things, on the grounds that people may get upset or reputations might suffer, then we have abandoned the principles of free enquiry.

      Their is a long thread over at the conservative/libertarian legal blog “The Volokh Conspiracy” on this Hill episode: https://reason.com/volokh/2018/09/08/a-mathematics-paper-two-math-journals-w

      One comment, in particular, stood out to me in its poignancy: “Aside from the depressingly numerous Witchfinders, there are some tragic characters in the story – Sergei Tabachnikov, Marjorie Senechal and Mark Steinberger – who seem to be ordinary, good people, but who, when faced with unbearable pressure, found their courage was not enough.”

      I would add that the only people who come out well in the whole episode are Hill and Rivin, based on my understanding of what what happened. (BTW I don’t know either personally, though I know Harald, who clearly has a personal opinion about Rivin, quite well).

      As far as Wilkinson and Farb are concerned, they clearly acted in a cause they felt strongly about. I do not believe they should suffer professional repurcussions, and I do believe that it is their right to unfriend anyone they wish for any reason. Nor do I wish to characterise them as villains. However, if they are now receiving hordes of internet hate mail, I confess that I do not exactly feel sorry about them either.

  88. Скандал вокруг статьи Хиля – Alexa Project Says:

    […] комментарий математика Тимоти Гауэрса с продолжением. Замечу, что Гауэрс, пожалуй, наиболее авторитетный эксперт в данном случае: он явно разбирается и в математике (лауреат Филдсовской премии, “математическая нобелевка”), и в научных статьях. […]

  89. Valentin Ovsienko Says:

    I am sure (or not so sure?) that Tim Gowers will add a link to the following statement:
    at the top of his post, along with the previous two.

  90. another math anon Says:

    In addition to the theorem-free applied math paper previously published in NYJM, there are also several elementary papers (e.g. on Diophantine equations) that would have fit perfectly in the American Mathematical Monthly, Mathematics Magazine, or (if shortened) in the Mathematical Intelligencer. Those elementary articles are perfectly good math research and there is nothing out of the ordinary in publishing them in NYJM, but it is also true that they are “basically undergraduate exercises in pure math”, which was one of the charges levelled against Hill’s paper except with the word “applied” instead of “pure”.

    None of the elementary papers that I found have the intrinsic intellectual interest to a broad audience of the evolutionary problem addressed in Hill’s paper.

    I take this as further evidence that Hill’s article was not out of line for NYJM. The statement on Hill’s website indicates that the version sent to Mathematical Intelligencer was in fact a shorter article without much mathematical detail, so probably more appropriate for Intelligencer than appears from the ArXiv post.

    Hill’s statement also claims that Wilkinson and/or Farb (through Wilkinson’s father) provided NYJM with specific criticisms only of the shorter Intelligencer article, not the longer article that was in question at NYJM.

    This is not looking good for the removers of the paper, and Hill’s point about reputational damage in his letter to NYJM are also valid. He wanted NYJM to make clear that there was nothing wrong or substandard about the mathematics in his (solicited) article and that it was removed for other reasons. I think this becomes outrageous when not only does NYJM not make an official statement addressing Hill’s reasonable concerns as an innocent party to the whole fiasco, but their editor Farb has the chutzpah to publicly cast vague and condescending aspersions on the merits of Hill’s work as though that were the reason for the Intelligencer + NYJM + Facebook + NSF events.

    • Yemon Choi Says:

      Would you care to name these papers, then? I have been aware of NYJM since around 2000 (so well after it started but well before the current events) and I won’t pretend to have an encylopaedic knowledge of what has been published there. Since your stance is that Hill’s paper is equally if not more deserving (due to “the intrinsic intellectual interest to a broad audience of the evolutionary problem “), I can’t see why you would refrain from naming the “elementary papers” that you wish to use as comparison or as a control Gedankenexperiment

    • another math anon Says:



      Some of these papers don’t use any outside theorems at all, building everything from scratch within the paper (with elementary tools).

    • Yemon Choi Says:

      Thanks, AMA – my question was a genuine one, so I appreciate you digging up these samples. On a quick look, some of these papers are very different in scope/depth from the impression I’d formed of NYJM from other articles that I happened to have read. Indeed, looking at volumes 16 and 19, the articles from those volumes which you’ve linked to seem very out of place to me!

      Thanks again for the extra data, which will inform my future views/recommendations concerning the journal — whose original mission I still support, generally speaking.

    • another math anon Says:


      I found those by using the NYJM’s site search for keywords that I thought might appear in low-tech papers, such as “simulation”, “spline” and “Diophantine”. I wouldn’t have guessed in advance that fuzzy logic or triangle geometry (nominally; actually elliptic curves) would be in the journal, but I think it is good for a journal to allow a wide latitude instead of trying to be Annals Lite.

      To me, NYJM is better and more fully a “general mathematics journal” (as it calls itself) if it does publish some low-tech papers. It’s a bit like the English common law on adverse possession, that to protect one’s right to some property one has to “openly and notoriously” utilize it every so often. A journal that in principle publishes work from all over mathematics should stake its territory from time to time and publishing less technical articles is part of that.

    • Igor Rivin (@igriv) Says:

      Precisely. The choice is to find interesting off-the-beaten-track stuff (Hill’s paper being Exhibit A, but they exist in all fields), or to be Annals two tiers down.

  91. What we’ve got here is failure to communicate | Igor Pak's blog Says:

    […] followup discussion on the very unfortunate Hill’s affair, which is much commented by Tim Gowers, Terry Tao and many others (see e.g. links and comments on their blog posts).  While many seem to […]

    • Stir, stir, stir! Says:

      “If you would not be discussing the math in the paper without the pretext of its submission history, you should not be discussing it at all.”

      You know, that’s like your opinion, man. I question you teaching us, who clearly did exactly that, as you have nothing really to teach beyond your own opinion. You offer inventing moral philosophy from (your) first principles ignoring large body of work in actual existing moral philosophy. Do your notions of morality have analogues? What did philosophers say of your twisting the notion? Would Rosseau agree with your pronouncements? Why would you be right by other philosopher’s sound logic? We will not know because depth of your thought ends at having opinion because as you admit at the end, emotionally relating to someone.

  92. Bentley Strange Says:

    Unfortunately you seem to have no understanding of genetics at all and I would have thought that as such, you might have refrained from commenting rather than expose your ignorance.

    The gene in question (or combination, the distinction is unimportant) doesn’t confer greater success but greater variability.

    Get that through your thick head and you might like to re-evaluate the paper.

    It is a shame that you feel so obligated to use such faulty arguments for purely political ends.

    • gowers Says:

      I think it’s pretty obvious from what I have written that this basic point is not lost on me — see also my follow-up post.

      Since the phrase “thick head” is aimed at me I’ll leave your comment, but if it had been aimed at anybody else I would have deleted it.

  93. Just sayin Says:

    How comes nobody mentions that Hill’s erstwhile coauthor, SERGEI TABACHNIKOV, is an associate editor of Mathematical Intelligencer (see https://www.springer.com/mathematics/journal/283). That certainly adds some insight to the initial acceptance of the paper in MI.

  94. Gil Kalai Says:

    Dear all, regarding the issue of removing Hill’s paper from NYJM, I find two things that Ted Hill wrote in his March 15 email to the editorial board not only reasonable, considerate and generous but also the possible key for moving forward. This is what Ted wrote:

    “Please note that I am NOT advocating that NYJM re-publish my article, but merely pointing out the harm to our profession if it remains deleted. ”

    “If some of you had simply written to me directly at the time the controversy started and complained that it did not look like a good fit for NYJM, I might well have agreed (it was solicited, recall), and I might have found some compromise to revise it substantially or might have requested it be removed for submission elsewhere. ”

    I think that, at this point, removing the paper for submission elsewhere is the most reasonable step. This does not settle all the serious problems raised by this case, and certainly not the academic questions raised by the paper.

    Removing the paper for submission elsewhere does not reflect badly on Hill’s academic reputation and only reflects the fact that the paper caused a strong debate in the editorial board of the journal both regarding the scientific merit and regarding the reviewing and evaluation process.

  95. Igor Rivin (@igriv) Says:

    For everyone’s information:

    I am very sad to inform you that Mark Steinberger passed away this morning. Mark founded the New York Journal of Mathematics almost single-handedly. I think we all greatly appreciate his contributions to the mathematical community by launching the first general purpose, open access, electronic journal in mathematics. Our memories will be with him.

    • Darij Grinberg Says:

      This is the saddest news here. My condolences to family and colleagues. I have only once interacted with Mark, when I was publishing my own paper in NYJM just 2 papers before the controversy; he was friendly and helpful in the process. I also highly appreciate his posting two comprehensive sets of lecture notes on his website https://www.albany.edu/~mark/teach.htm .

    • Yemon Choi Says:

      Regardless of any stance I may have demonstrated above (or may demonstrate in the future) I join with these commiserations, and thank you for informing those following the original issue and this blogpost.

    • David Roberts Says:

      Thank you Igor, my condolences. Starting an electronic journal in the early 90s was an act of necessary rebellion and I applaud it and the journal’s longevity. I hope editorial board take this time to reflect on how they want the journal to run and make some concrete policy documents. In light of the recent troubles with the Hill paper I feel transparency is the best hygiene. I wish the journal all possible success.

      Even though I do not like, in my ignorance of the technical details, the thrust of the paper *as applied to mathematical success*, and a very careful framing the result should be employed to avoid hype over the result by people with a barrow to push, I do believe the paper should in fact be republished with a statement that not all the editorial board supported its publication, and that it was an invited submission by yourself. An editorial laying out the barest timeline of events (and I do mean barest: dates of submission, acceptance, publication, withdrawal and republication) would be useful.

    • Igor Rivin (@igriv) Says:

      David, thank you for your kind words. In fact, the solution you propose was, in broad terms, proposed by me (with support by Mark) when the controversy escalated, but it was rejected by the board.

    • Gil Kalai Says:

      My young colleagues and friends at the time, Oded Schramm and Itai Benjamini were enthusiastic about the pioneering publishing model of Mark Steinberger’s NYJM, they both made very good contributions to the journal over the years, and Oded served as a member of the editorial board until his untimely death.

    • David Roberts Says:

      Igor: In saying “I hope editorial board take this time to reflect on how they want the journal to run and make some concrete policy documents.” I recommend checking out


      and I would hope that that level of transparency and open access structure could be achieved (at present three of the five points are met).

      One more comment on the paper itself: the level of noise introduced by social and environmental factors in the case of mathematical achievement is extremely large, to the point that variations in innate ability are in all likelihood largely swamped. This kind of effect would be very hard to estimate, but we all know people who were very good mathematicians and for whatever reason, and not for lack of trying, never got a continuing academic position.

    • David Roberts Says:

      I should have said “variations in innate ability, *should they exist (and likely they don’t)*, are in all likelihood largely swamped *by such environmental noise*.”

      mea culpa.

      (And just to be crystal clear, as a general principle I very strongly support women in STEM, mathematics in particular, and reject sexist explanations for the small numbers of women mathematicians in the most selective environments. I wouldn’t have accepted the Hill paper in NYJM, were I the responsible editor, to say the least.)

  96. AnotherLover Says:

    Ah, the problem you’re having is you’re unaware that an average woman is perfectly acceptable to most men, but an average man is not perfectly acceptable to most women. We have twice as many female ancestors as male, which means the 50% number you bring up is actually just accurate — on average, one man that successfully breeds does so with 2 women. Yes, this is true historically, and I don’t know at what point in time you expect humankind to have magically switched gears. It makes no sense, that argument.

    So, if that’s your argument against this paper, I’m inclined to believe Yuri Bezmenov is right, and you have been duped so hard by the communists with their critical theory that you’re desperate to avoid ever having to say anything un-PC. You’re afraid of the totalitarian fist of PC culture (that I have been warning people about since I first heard of PC over twenty years ago). You’re afraid of what will happen to you should you personally say that most geniuses are male.

    You’re desperate because of the same fear that kept the paper from publication. Go find out what our friend Yuri has to say about this kind of thing. (Hint: If the KGB’s plan for Soviet subversion of American culture was fully functional today, those prosecuting it would toast with cheers every night after a fresh day of new victories. You can argue the Soviet Union is gone, but it’s plain to see that Yuri’s description of the Soviet’s very most fervent wishes for the destruction of American society have come true. The first two stages, Demoralization and Destabilization, are complete). Maybe more. I’m not an expert. Yuri was:

  97. test Says:


  98. Anonymous Says:

    This episode very much has the feel or airing one’s dirty laundry in public.

    I can’t speculate on the effect of Hill’s article has among the general public, but its effect on the math community is pretty much equivalent to blacklisting NYJM, and surely Hill knew that when he wrote the article. (Personal anecdote: A coauthor once suggested sending a paper there and even though I did not know much about the journal, I had no objection. Now I surely would.)

    This could (and should!) have been resolved between the people involved, possibly with someone or some entity both sides respect enlisted as an arbiter. Escalating it to this level has caused much collateral damage and will probably cause more. Litigating this in the court of mathematical (or more general) public opinion is, I think, a mistake.

    As a general note, math journals are (and should be) like the police. You can try to go around them, but you never argue with them. If every disgruntled author who every got treated badly by a journal wrote about it on their blog or published a newspaper article about it, there would be little else to read about in the corner of the internet populated by mathematicians (and it would be even harder to find people willing to referee).

    I could go on to comment at length on what Hill, Farb, Wilkinson, Rivin, NYJM etc… should have done differently but, as tempting as this might be, I will not.

    • Igor Rivin (@igriv) Says:

      Firstly, I am sorry this controversy has led you to blacklist NYJM, but I do understand.

      Secondly, I am afraid your argument is very similar to the one used by the Soviets to suppress dissent: what are those people doing whining in the West about internal issues. The KGB IS the internal police – you can go around them (ok, you can’t) but you can’t argue with it. Airing their dirty laundry in public is ill-advised, indeed treasonous, since it makes us all look bad. Etc.

      I don’t know what your background is, but for many of the people here (myself included), this argument is all too familiar.

      By the way, this is not to either endorse or condemn Professor Hill’s decision to go public.

    • Anonymous Says:

      I don’t have any personal experience with oppression in the Soviet Union although (not surprisingly) I know plenty of people who do.

      I do think that it is excessive to compare the plight of an emeritus professor at Georgia Tech complaining about a math journal to that of a political refugee from the Soviet Union speaking out about oppression there (which is what it appears to me you were doing.)

      I do have at least some experience dealing with disagreements between mathematicians and, based on that experience, I find that they rarely benefit from being blown up far beyond the people involved. When the people involved have strong (or stubborn, depending on your point of view) personalities then escalating things just makes them dig in and makes the conflict that much harder to resolve. Your experience may differ.

  99. Mathematics matters | Bits of DNA Says:

    […] evolutionary biology (see On the recently removed paper from the New York Journal of Mathematics, Has an uncomfortable truth been suppressed, Additional thoughts on the Ted Hill paper) because some mathematician wrote a paper titled […]

  100. Igor Rivin (@igriv) Says:

    Hill has now posted the information he had promised in his statement: https://www.dropbox.com/s/estihpbvdbiy4qg/Hill_RetractionWatchAppendix_Sep14.pdf?dl=0#

    • Darij Grinberg Says:

      404. Dropbox is not a good place for documents that are meant to be seen by many.

    • longtail Says:

      Try the link from this page: https://retractionwatch.com/2018/09/17/what-really-happened-when-two-mathematicians-tried-to-publish-a-paper-on-gender-differences-the-tale-of-the-emails/. One of the referee reports is included.

    • Darij Grinberg Says:

      @longtail: Thank you!

    • Gil Kalai Says:

      Hill’s file give some more of the gory details, e.g. regarding the three-week refereeing period that was discussed at some length. By my calculations, the actual referee process from submission to acceptance took less than two days.The email from Igor soliciting the paper was from October 13, 10:09 PM. (We dont know when Ted agreed but we can assume it was shortly afterwards.) The acceptance paper (which mentioned only one referee and one referee report) was sent on October 15, 7:30 AM. The file also contains the referee report itself.(I will feel safer if Gowers and Tao will go over my calculations and confirm them.)

    • gowers Says:

      Replying to Gil. Your calculations look correct to me. I suppose one could remark that the mathematical content of the paper is so close to zero that a day is sufficient to referee it.

      Two things stood out from the report itself. The first was a paragraph where the referee admitted that (s)he was not qualified to comment on the reasonableness of the model and suggested consulting a mathematical biologist, which seems not to have been done. The second was the following paragraph, which said that the author should address various questions, which are about more or less exactly the points that have bothered me about the paper’s reasoning. Hill decided not to address them, perhaps because Rivin wrote “It is not necessary to address these for publication, but if you could add a couple of lines, it would be great!”

    • erasmuse Says:

      It is highly significant that Hill has published specifics in names and dates, whereas his enemies have only published two statements that don’t even mention the important fact that they’re married to each other and don’t say exactly what they did, only what they say they *didn’t* do.
      The more airing of dirty laundry like this, the better. It is very easy for an academic field to get corruptly captured by the people at top universities who edit the top journals and advise the smartest future professors, and they can operate entirely behind the scenes via their power network. Economics seems to have a bit of this too. My impression is that climate science is entirely like that— a complete racket, perhaps because grant money is so important there.

    • David Roberts Says:

      Dear Igor, in the interest of transparency, since Hill did not include the second referee report, are you able to release it?

  101. Just sayin Says:

    https://retractionwatch.com/2018/09/17/what-really-happened-when-two-mathematicians-tried-to-publish-a-paper-on-gender-differences-the-tale-of-the-emails/ gives the impression that Hill’s erstwhile coauthor, Sergei T, angered (perhaps legitimately) by what happened at Math Intelligencer (where he is an editor) complained to Igor Rivin, who then solicited the paper from Hill for New York Journal of Mathematics and then sent it to a referee who wrote a report that recommended the paper for publication first and foremost because it is important to not let things like what happened to Larry Summers and Climategate occur, and second because the Math is technically correct. The referee admits to not being a mathematical biologist and suggests that one should perhaps be consulted, which seems never to have been the case.

  102. Just sayin Says:

    It is also strange the solicitation letter from Igor promises quick refereeing and says the editor-in-chief was very positive on it. The whole process was obviously rushed.

  103. Jack ma Says:

    Feminist Amie Wilkinson: You must unfriend him, or I will unfriend you. LOL.

    • Mark Sapir Says:

      @Jack ma Says: Keep the discussion civil! There is nothing wrong in being a feminist. To be uncivil pretty quickly makes you into a monkey. And a patriarchal monkey is usually ugly unless it is a monkey from Rio but those are very small

  104. Mark Sapir Says:

    “When soliciting papers, “a quick decision” is the standard carrot”. IMHO it is a mistake. The time of refereeing cannot be a carrot at all (speaking as the Editor-in-Chief of the Journal of Combinatorial Algebra). I always promise a thorough refereeing,sometimes by many referees, whatever number of them needed. That is the whole purpose of math journals. Otherwise arXiv is enough for everything.

    • Igor Rivin (@igriv) Says:

      This is the carrot I have seen used most. Whether or not it is philosophically the purest approach is a different matter. (a parenthetical comment: the first time this carrot was offered to me, I accepted it, and the refereeing took 4 years).

  105. Mark Sapir Says:

    @IgorRivin: “According to the data in this document (with some inferences made), there is no country in Europe (Eastern or otherwise) where what Professor Sapir describes holds: https://ec.europa.eu/eurostat/statistics-explained/index.php/Tertiary_education_statistics#Fields_of_study

    That is wrong. Country xUSSR. Cities: any “provinvial” city with ~10^6 population. University: any (especially Pedagogical) department: Math. Women/Men ratio > 50%. Same for Yogoslavia and Romania. Moscow SU: ratio about 30%. But for State Pedagogical Inst: about 90%. Same for Leningrad (again including Gercen Institute). The math departments had about 500 of math majors. Physics departments had quite a lot too.

  106. Gil Kalai Says:

    Related to the general theme of this post let me mention a beautiful  NYT article by Amie Wilkinson: With Snowflakes and Unicorns, Marina Ratner and Maryam Mirzakhani Explored a Universe in Motion. I believe that the article can lift our spirit which is something I cannot say in good faith about the overall discussion we have here.

    I don’t know Wilkinson personally (I do know some other “heroes” of this episode), but, loosing my father in 1979, I do envy her for being able to consult with her father. All the comments regarding it negatively, including those in Hill’s complaint,  are, in my view, absurd nonsense.

    While at it, let me also refer to Lior Pachter’s valuable post “mathematics matters“.

  107. What’s good for the goose – posttenuretourettes Says:

    […] joined the fray, siding with Lysenko. He accuses the mathematical commentators on Tao’s and Gowers’s blogs of making illiterate pronouncements on biology. As we’ll shortly see, he’s plenty […]

  108. ClosedRangeTheorem Says:

    I think the important point here is that you’ve been willing to read the paper and think it through for yourself, and look for problems, as is a fair part of the scientific method. The author’s main complaint in his quillette article is that people used threats and intimidation on the editors to have the paper removed. Such shady behaviour is indeed a threat to science, which should concern us all, regardless of political views.

  109. Mark Sapir Says:

    “When soliciting papers, “a quick decision” is the standard carrot.” I would say more: In the whole NYMJ situation it was the only mistake on your and Mark’s part. But a serious one,IMHO. The carrot would be to ensure that the referees do not just stop refereeing (which happens often) but that should be the standard practice for solicited papers or not.

  110. Gil Kalai Says:

    Related to the general theme of this post let me mention a beautiful  NYT article by Amie Wilkinson: With Snowflakes and Unicorns, Marina Ratner and Maryam Mirzakhani Explored a Universe in Motion. I believe that the article can lift our spirit which is something I cannot say in good faith about the overall discussion we have here.

    I don’t know Wilkinson personally (I do know some other “heroes” of this episode), but, loosing my father in 1979, I do envy her for being able to consult with her father. All the comments regarding it negatively, including those in Hill’s complaint,  are, in my view, absurd nonsense.

  111. Gary Says:

    Regarding your last two arguments. Yes, an environmental model can just as easily be shown to explain why we tend to see men at the top, and therefore we should do everything reasonably possible to eliminate those barriers. That doesn’t preclude the evolutionary model though, as both can both be working simultaneously. It also does not explain the bottom end of the tail, ie, why males collect at the bottom of the distribution. I don’t understand why this is so often framed as two competing arguments when it’s very likely both are in play.

    Second, I have trouble understanding why you would want to dispute the argument that the top mathematicians will likely have the highest intelligence. Just because it’s a damaging myth that one must have raw brainpower to be a good mathematician, does not mean those with the highest raw brain power will not tend to become the best mathematicians, physicist, etc. Yes, there are people like Fineman among our most esteemed physicist (with “only” an estimated IQ of 135), but he is an exception to the rule. Most of the top world-changing scientists had genious or near genious level IQs. No doubt this is true among mathematicians as well.

    I can’t help but get the impression you are letting your hopes cloud your judgement.

    • gowers Says:

      The purpose of mentioning the environmental model was merely to make the point that one shouldn’t be tempted by the biological model just on the grounds that it neatly fits the fact that representation of women decreases as you go higher up the hierarchy, since an environmental model fits that fact just as neatly. The relative importance of biological and sociological factors is not at all easy to determine and will no doubt be debated for a long time. But since sociological factors clearly are part of the mix, we don’t have to wait for this debate to be concluded before we take action.

      I don’t deny that there is a link between mathematical ability and raw intelligence, but I do think that the link is not as close as is popularly believed. And the reason I think that is that the correlation I have observed between mathematical success (defined not in career terms but in terms of the quality of mathematics produced) and raw intelligence (harder to define, but things like an unusually good memory and a “magic” ability to see things very quickly) is weaker than I thought before I became a mathematician.

      But I’m interested in your assertions about most of the top scientists having very high IQs. Do you have a reference for that?

    • JK Says:

      Regarding the claim about top scientists having high IQs there is an old study in Nature.

    • JK Says:

      There is an even older study of IQs of eminent scientists:

      I have been looking into the g-factor/IQ tests debate. Though there are several books on the topic, I am unable to find a well-written summary of the evidence and arguments (with data and references) for and against the claim “g-factor is a reasonable measure of what we call intelligence”. It would be really good if some reputed statisticians/mathematicians do an impartial study of the literature and give such a summary.

    • Igor Rivin (@igriv) Says:

      If you read Pool and Ericsson’s “Peak”, they make a case that IQ is NOT the determining factor in areas like Chess and Go (in fact, the average Go master’s IQ is 98(!)), and the real talent is being able to concentrate and work. So, there is that.

  112. erasmuse Says:

    The idea that a high-variability strategy can be a good idea is well-known in economics, particularly in finance and in game theory. Mathematicians might find more to say in this area, and we economists would value more “toolbox” theorems for applied work. We had to develop some things about truncated distributions in Harbaugh and Rasmusen, “Coarse Grades,” AEJ: Micro (2018) http://www.rasmusen.org/papers/coarse-harbaugh-rasmusen.pdf “Properties of Upper and Lower Means” section. Hardy did some inequalities work relevant to this. Which makes me realize: Prof. Rivin, maybe you should ask Ian Jewitt at Oxford (Nuffield College) if you can publish his 2004 “Notes on the `Shape’ of Distributions,” mimeo, http://www.rasmusen.org/special/jewitt%20NotesonShapeofDistributions.pdf, which has 27 cites on Google Scholar but was for reasons unknown to me never published.

  113. Richard Monsurington Says:

    “When applied to humans, this model is ludicrously implausible. …the idea that some huge percentage of males are simply not desirable enough (as we shall see, the paper requires this percentage to be over 50) to have a chance of reproducing bears no relation to the world as we know it.”

    “I am also far from expert in evolutionary biology and may therefore have committed some rookie errors”


  114. c young Says:

    > The purpose of mentioning the environmental model was merely to make the point that one shouldn’t be tempted by the biological model just on the grounds that it neatly fits

    The ‘environmental model’ a.k.a. ‘social constructionism’ has been the subject of a decent amount of quantitative studies by psychologists. We don’t really need to speculate.

    For instance, the idea presented above that Russia presents a model of gender equality because there are many female mathematicians goes against everything we know about human development.

    What do Russia, Iran and Bangladesh have in common? They feature at the bottom on any index of human (and feminine) flourishing but they have high numbers of women working in STEM.

    What do Norway, Sweden, the UK and US have in common ? They feature at the top of those indexes and they have a tiny percentage of women in STEM.

    This is sometimes known as the Nordic Gender Equality Paradox. It appears that the more freedom women get, the less they want to behave like men i.e. men and women get more dissimilar the more freedom they get.

    There is no country in the world in which women and men do not show sharply differing interests. If you want to claim that this is ‘socially constructed’, you have to explain how that can be. ‘Patriarchy’ isn’t an explanation – unless ‘patriarchy’ is a synonym for ‘biology’.

    Anyone here who still thinks Russia represents the future of western gender relations should watch this documentary from Norwegian state TV. It is presented by a comedian, and looks glib, but the scientists it features are leaders in their fields.

  115. Controvertido trabajo matemático sobre variabilidad de los sexos | Coloquio Oleis Says:

    […] devenir editorial y social de este trabajo (para más detalles ver esta entrada del blog de Tao, el blog de Gowers,  este comentario de Wilkinson,  este comentario de Farb,  este comentario de Hill,  o este […]

  116. SEPTEMBER DIARY: Moral Conundrum At the Tire Shop; Sacking Cities; Evergreen Nazis; Etc. [12 ITEMS], by John Derbyshire - open mind news Says:

    […] lengthy debates online: Ted Hill’s Quillette piece now has 559 comments; Sir Timothy Gowers’ original September 9th blog post has 359, and Sir Timothy posted a follow-up on September 13thsomewhat less critical of Ted Hill’s […]

  117. Genetic determinism once more obnubilates French readers | Mathematics without Apologies, by Michael Harris Says:

    […] and here is an article by Gowers analyzing the claims in Hill’s alleged study. https://gowers.wordpress.com/2018/09/09/has-an-uncomfortable-truth-been-suppressed/ There is a second post, in which Gowers goes to extreme lengths to give Hill the benefit of the […]

  118. Un fundamento matemático para la Teoría de la Variabilidad (o no) | La manzana podrida Says:

    […] la Universidad de Chicago que ha sido acusada de ser la instigadora de buena parte del proceso. Un fantástico resumen de todo se puede encontrar en el muy recomendable blog de Gowers que fue el que nos puso sobre la […]

  119. Mathematics: On the recently removed paper from the New York Journal of Mathematics - Levpros Says:

    […] time was on that board, for more details.  Some further discussion of this incident may be found on Tim Gowers’ blog; the most recent version of the paper, as well as a number of prior revisions, are still available […]

  120. Katzenbetreuung Luckenwalde Says:

    Toller Artikel…

  121. Winston Says:

    I urge everyone here to please condemn the recent “open letter” against a young Cambridge scientist described here. It pains me to see that several Cambridge mathematicians have signed this lettter.


    This is McCarthy-ism, and an attack on academic freedom. I urge Professor Gowers to add his name to the petition at the bottom of the article, and I urge others here to do the same.

  122. Anonymous Says:

    The government is lying

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