I have just received an email from Sergey Kitaev, one of the three combinatorialists at Strathclyde. As in many universities, they belong not to the mathematics department but to the computer science department. Kitaev informs me that the administrators of that department, in their infinite wisdom, have decided that the future of the department is best served by axing discrete mathematics. I won’t write a long post about this, but instead refer you to a post by Peter Cameron that says everything I would want to say about the decision, and does so extremely cogently. I recommend that you read it if this kind of decision worries you.

## The fate of combinatorics at Strathclyde

June 19, 2019## Voting tactically in the EU elections

May 21, 2019This post is addressed at anyone who is voting in Great Britain in the forthcoming elections to the European Parliament and whose principal aim is to maximize the number of MEPs from Remain-supporting parties, where those are deemed to be the Liberal Democrats, the Greens, Change UK, Plaid Cymru and the Scottish National Party. If you have other priorities, then the general principles laid out here may be helpful, but the examples of how to apply them will not necessarily be appropriate to your particular concerns.

### What is the voting system?

The system used is called the d’Hondt system. The country is divided into a number of regions, and from each region several MEPs will be elected. You get one vote, and it is for a party rather than a single candidate. Once the votes are in, there are a couple of ways of thinking about how they translate into results. One that I like is to imagine that the parties have the option of assigning their votes to their candidates as they wish, and once the assignments have been made, the candidates with the most votes get seats, where is the number of MEPs representing the given region.

For example, if there are three parties for four places, and their vote shares are 50%, 30% and 20%, then the first party will give 25% to two candidates and both will be elected. If the second party tries a similar trick, it will only get one candidate through because the 20% that goes to the third party is greater than the 15% going to the two candidates from the second party. So the result is two candidates for the first party, one for the second and one for the third.

If the vote shares had been 60%, 25% and 15%, then the first party could afford to split three ways and the result would be three seats for the first party and one for the second.

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## How Craig Barton wishes he’d taught maths

December 22, 2018A couple of months ago, I can’t remember precisely how, I became aware of a book called How I Wish I’d Taught Maths, by Craig Barton, that seemed to be highly thought of. The basic idea was that Craig Barton is an experienced, and by the sound of things very good, maths teacher who used to take a number of aspects of teaching for granted, until he looked into the mathematics-education literature and came to realize that many of his cherished beliefs were completely wrong. Since I’ve always been interested in the question of how best to teach mathematics, both because of my own university teaching and because from time to time I like to pontificate about school-level teaching, I decided to order the book. More surprisingly, given my past history of buying books that I felt I ought to read, I read it from cover to cover, all 450 pages of it.

As it happens, the book is ideally designed for people who *don’t* necessarily want to read it from cover to cover, because it is arranged as follows. At the top level it is divided into chapters. Each chapter starts with a small introduction and thereafter is divided into sections. And each section has precisely the same organization: it is divided into subsections entitled, “What I used to believe”, “Sources of inspiration”, “My takeaway”, and “What I do now”. These are reasonably self-explanatory, but just to spell it out, the first subsection sets out a plausible belief that Craig Barton used to have about good teaching practice, often ending with a rhetorical question such as “What could possibly be wrong with that?”, the second is a list of references (none of which I have yet followed up, but some of them look very interesting), the third is a discussion of what he learned from the references, and the last one is about how he put that into practice. Also, each chapter ends with a short subsection entitled “If I only remember three things …”, where he gives three sentences that sum up what he thinks is most important in the chapter.

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## Taylor and Francis doing Trump’s dirty work for him

December 9, 2018The following story arrived in my email inbox (and those of many others) this morning. Apparently a paper was submitted to the Taylor and Francis journal *Dynamical Systems*, and was accepted. The published version was prepared, and it had got to the stage where a DOI had been assigned. Then the authorS received a letter explaining that “following internal sanctions process checks” the article could not after all be published because one of them was based in Iran.

I don’t know what the legal consequences would have been if Taylor and Francis had simply gone ahead and published, but my hunch is that they are being unduly cautious. I wonder if they turned down any papers by Russian authors after the invasion of Ukraine.

This is not an isolated incident. An Iranian PhD student who applied for funding to go to a mathematics conference in Rome was told that “we are unable to provide financial support for Iranians due to administrative difficulties”.

I’m not sure what one can do about this, but at the very least it should be generally known that it is happening.

**Update.** Taylor and Francis have now reversed their decision.

## Worrying news from Turkey

November 16, 2018One should of course be concerned when anybody is detained for spurious reasons, but when that person is a noted mathematician, the shock is greater. Six academics have recently been detained in Turkey, of whom one, Betül Tanbay, is due to become vice president of the European Mathematical Society in January. I do not know of any petitions for their release, but if they are not released very quickly I hope that there will be a strong reaction. The EMS has issued the following statement.

The European Mathematical Society is outraged at the news that the Turkish police have detained, in Istanbul on the morning of 16th November 2018, Professor Betül Tanbay, a member of the EMS Executive Committee. We are incredulous at the subsequent press release from the Istanbul Security Directorate accusing her of links to organized crime and attempts to topple the Turkish government.

Professor Tanbay is a distinguished mathematician and a Vice President Elect of the European Mathematical Society, due to assume that role from January 2019. We have known her for many years as a talented scientist and teacher, a former President of the Turkish Mathematical Society, an open-minded citizen, and a true democrat. She may not hesitate to exercise her freedom of speech, a lawful right that any decent country guarantees its citizens, but it is preposterous to suggest that she could be involved in violent or criminal activities.

We demand that Professor Tanbay is immediately freed from detention, and we call on the whole European research community to raise its voice against this shameful mistreatment of our colleague, so frighteningly reminiscent of our continent’s darkest times.

**Update.** I have just seen this on Twitter:

Police freed 8 people, incl. professors Turgut Tarhanli and Betul Tanbay, while barring them from overseas travel, & is still questioning 6 others

## A quasirandomness implication

November 10, 2018This is a bit of a niche post, since its target audience is people who are familiar with quasirandom graphs and like proofs of an analytic flavour. Very roughly, a quasirandom graph is one that behaves like a random graph of the same density. It turns out that there are many ways that one can interpret the phrase “behaves like a random graph” and, less obviously, that they are all in a certain sense equivalent. This realization dates back to seminal papers of Thomason, and of Chung, Graham and Wilson.

I was lecturing on the topic recently, and proving that certain of the quasirandomness properties all implied each other. In some cases, the proofs are quite a bit easier if you assume that the graph is regular, and in the past I have sometimes made my life easier by dealing just with that case. But that had the unfortunate consequence that when I lectured on Szemerédi’s regularity lemma, I couldn’t just say “Note that the condition on the regular pairs is just saying that they have quasirandomness property ” and have as a consequence all the other quasirandomness properties. So this year I was determined to deal with the general case, and determined to find clean proofs of all the implications. There is one that took me quite a bit of time, but I got there in the end. It is very likely to be out there in the literature somewhere, but I haven’t found it, so it seems suitable for a blog post. I can be sure of at least one interested reader, which is the future me when I find that I’ve forgotten the argument (except that actually I have now found quite a conceptual way of expressing it, so it’s just conceivable that it will stick around in the more accessible part of my long-term memory).

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## Additional thoughts on the Ted Hill paper

September 13, 2018First, I’d like to thank the large number of commenters on my previous post for keeping the discussion surprisingly calm and respectful given the topic discussed. In that spirit, and to try to practise the scientific integrity that I claimed to care about, I want to acknowledge that my views about the paper have changed somewhat as a result of the discussion. My understanding of the story of what happened to the paper has changed even more now that some of those attacked in Ted Hill’s Quillette article have responded, but about that I only want to repeat what I said in one or two comments on the previous post: that my personal view is that one should not “unaccept” or “unpublish” a paper unless something was improper about the way it was accepted or published, and that that is also the view of the people who were alleged to have tried to suppress Ted Hill’s paper on political grounds. I would also remark that whatever happened at NYJM would not have happened if all decisions had to be taken collectively by the whole editorial board, which is the policy on several journals I have been on the board of. According to Igor Rivin, the policy at NYJM is very different: “No approval for the full board is required, or ever obtained. The approval of the Editor in Chief is not required.” I find this quite extraordinary: it would seem to be a basic safeguard that decisions should be taken by more than one person — ideally many more.

To return to the paper, I now see that the selectivity hypothesis, which I said I found implausible, was actually quite reasonable. If you look carefully at my previous post, you will see that I actually started to realize that even when writing it, and it would have been more sensible to omit that criticism entirely, but by the time it occurred to me that ancient human females could well have been selective in a way that could (in a toy model) be reasonably approximated by Hill’s hypothesis, I had become too wedded to what I had already written — a basic writer’s mistake, made in this case partly because I had only a short window of time in which to write the post. I’m actually quite glad I left the criticism in, since I learnt quite a lot from the numerous comments that defended the hypothesis.

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## Has an uncomfortable truth been suppressed?

September 9, 2018**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.

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## A new journal in combinatorics

June 4, 2018This post is to announce that a new journal, Advances in Combinatorics, has just opened for submissions. I shall also say a little about the journal, about other new journals, about my own experiences of finding journals I am happy to submit to, and about whether we are any nearer a change to more sensible systems of dissemination and evaluation of scientific papers.

### Advances in Combinatorics

Advances in Combinatorics is set up as a combinatorics journal for high-quality papers, principally in the less algebraic parts of combinatorics. It will be an arXiv overlay journal, so free to read, and it will not charge authors. Like its cousin Discrete Analysis (which has recently published its 50th paper) it will be run on the Scholastica platform. Its minimal costs are being paid for by the library at Queen’s University in Ontario, which is also providing administrative support. The journal will start with a small editorial board. Apart from me, it will consist of Béla Bollobás, Reinhard Diestel, Dan Kral, Daniela Kühn, James Oxley, Bruce Reed, Gabor Sarkozy, Asaf Shapira and Robin Thomas. Initially, Dan Kral and I will be the managing editors, though I hope to find somebody to replace me in that role once the journal is established. While I am posting this, Dan is simultaneously announcing the journal at the SIAM conference in Discrete Mathematics, where he has just given a plenary lecture. The journal is also being announced by COAR, the Confederation of Open Access Repositories. This project aligned well with what they are trying to do, and it was their director, Kathleen Shearer, who put me in touch with the library at Queen’s.

As with Discrete Analysis, all members of the editorial board will be expected to work: they won’t just be lending their names to give the journal bogus prestige. Each paper will be handled by one of the editors, who, after obtaining external opinions (when the paper warrants them) will make a recommendation to the rest of the board. All decisions will be made collectively. The job of the managing editors will be to make sure that this process runs smoothly, but when it comes to decisions, they will have no more say than any other editor.

The rough level that the journal is aiming at is that of a top specialist journal such as Combinatorica. The reason for setting it up is that there is a gap in the market for an “ethical” combinatorics journal at that level — that is, one that is not published by one of the major commercial publishers, with all the well known problems that result. We are not trying to destroy the commercial combinatorial journals, but merely to give people the option of avoiding them if they would prefer to submit to a journal that is not complicit in a system that uses its monopoly power to ruthlessly squeeze library budgets. Read the rest of this entry »

## Two infinities that are surprisingly equal

September 19, 2017It has been in the news recently — or rather, the small corner of the news that is of particular interest to mathematicians — that Maryanthe Malliaris and Saharon Shelah recently had an unexpected breakthrough when they stumbled on a proof that two infinities were equal that had been conjectured, and widely believed, to be distinct. Or rather, since both were strictly between the cardinality of the natural numbers and the cardinality of the reals, they were widely believed to be distinct in some models of set theory where the continuum hypothesis fails.

A couple of days ago, John Baez was sufficiently irritated by a Quanta article on this development that he wrote a post on Google Plus in which he did a much better job of explaining what was going on. As a result of reading that, and following and participating in the ensuing discussion, I have got interested in the problem. In particular, as a complete non-expert, I am struck that a problem that looks purely combinatorial (though infinitary) should, according to Quanta, have a solution that involves highly non-trivial arguments in proof theory and model theory. It makes me wonder, again as a complete non-expert so probably very naively, whether there is a simpler purely combinatorial argument that the set theorists missed because they believed too strongly that the two infinities were different.

I certainly haven’t found such an argument, but I thought it might be worth at least setting out the problem, in case it appeals to anyone, and giving a few preliminary thoughts about it. I’m not expecting much from this, but if there’s a small chance that it leads to a fruitful mathematical discussion, then it’s worth doing. As I said above, I am indebted to John Baez and to several commenters on his post for being able to write much of what I write in this post, as can easily be checked if you read that discussion as well.

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