Archive for the ‘Mathematics on the internet’ Category

What I did in my summer holidays

October 24, 2013

This post is intended to accomplish several things at once. First and foremost, I want to explain (not just in the post) why I have been interested in Borel determinacy and in the natural proofs barrier. Roughly speaking (or should I say tl;dr?) I think that Martin’s proof of Borel determinacy has features that might just conceivably offer a way past that barrier.

As long-term readers of this blog will be aware, the P versus NP problem is one of my personal mathematical diseases (in Richard Lipton’s sense). I had been in remission for a few years, but last academic year I set a Cambridge Part III essay on barriers in complexity theory, and after marking the essays in June I thought I would just spend an hour or two thinking about the problem again, and that hour or two accidentally turned into about three months (and counting).

The trouble was that I had an idea that has refused to die, despite my best efforts to kill it. Like a particularly awkward virus, it has accomplished this by mutating rapidly, so that what it looks like now is very different from what it looked like at the beginning of the summer. (For example, at that stage I hadn’t thought of trying to model a proof on the proof of Borel determinacy.) So what am I to do?

Why I’ve also joined the good guys

January 16, 2013

For some months now I have known of a very promising initiative that until recently I have been asked not to publicize too widely, because the people in charge of it did not have a good estimate for when it would actually come to fruition. But now those who know about it have been given the green light. The short version of what I want to say in this post is that a platform is to be created that will make it very easy to set up arXiv overlay journals.

What is an arXiv overlay journal? It is just like an electronic journal, except that instead of a website with lots of carefully formatted articles, all you get is a list of links to preprints on the arXiv. The idea is that the parts of the publication process that academics do voluntarily — editing and refereeing — are just as they are for traditional journals, and we do without the parts that cost money, such as copy-editing and typesetting.

Why I’ve joined the bad guys

January 14, 2013

A few months ago I was alerted by a pingback to the existence of a blog post by Orr Shalit entitled Worse than Elsevier which included the assertion that Terence Tao and I had “joined the bad guys”. That is an allusion to the fact that we are editors for Forum of Mathematics, CUP’s new open-access journal. This post serves a dual purpose: to draw attention to the fact that Forum of Mathematics is now accepting submissions, and to counter some of the many objections that have been raised to it. In particular, I want to separate out the objections that are based on misconceptions from the objections that have real substance. Both kinds exist, and unfortunately they tend to get mixed up.

If you are not already familiar with this debate, the aspect of Forum of Mathematics that many people dislike is that it will be funded by means of article processing charges (which I shall abbreviate to APCs) rather than subscriptions. For the next three years, these charges will be waived, but after that there will be a charge of £500 per article. Let me now consider a number of objections that people have to APCs.

A new open-access venture from Cambridge University Press

July 2, 2012

The formal launch has just taken place at the European Congress of Mathematicians in Krakow of the Forum of Mathematics, which to a first approximation is a new open-access electronic journal. However, the singular “journal” is misleading, because in some ways it is more like a whole set of journals. But there will be considerable interdependence between the elements of the set, so “journals” is misleading too. We need an intermediate number between singular and plural. Also, although the journal(s) is/are primarily electronic, there will be a print-on-demand option if anyone wants it.

What is the Forum of Mathematics?

Terminological questions aside, how will this new journal-like object work? I think the easiest way of explaining it is to describe the process for submitting an article, which is similar to the process for submitting an article to a conventional maths journal, but with one or two unusual aspects.

What’s wrong with electronic journals?

January 29, 2012

It probably sounds disingenuous of me to say this, but when I sat down to write a post about Elsevier I wasn’t really trying to start a campaign. My intention was merely to make public, and a little more rigid, a policy that I and many others had already been applying, in my case without much difficulty, for several years. The idea of setting up a website occurred to me as I was writing the post: I considered it (and still consider it) not as a petition to Elsevier to change its ways — since I don’t believe there is any realistic chance of that — but as a simple way to bring out into the open all the private boycotts and semi-boycotts that were going on, and thereby to encourage others to do the same.

By accident, the post seems to have been quite well timed. Probably it’s not an accident at all, and that whatever atmosphere it was that prompted me to get round to writing the post (for example, certain discussions I had had with other mathematicians, some of them online) was the same as what made it a good moment. Anyhow, accident or no, the result is that some people have talked about “momentum”, and I’m starting to feel a responsibility, not particularly welcome (because it threatens to involve work), not to squander that momentum.

A more modest proposal

November 3, 2011

In my previous post I suggested a way in which an online system of submitting and commenting on papers might perhaps work better than our current system of journals, editors and anonymous referees. I am very grateful to all who commented, both positively and (more often) negatively. It has given me a lot to think about. One thing that I wasn’t expecting, but should have expected, was that a number of people just plain don’t like the idea of an online alternative, regardless of the rational arguments. I don’t mean that there aren’t arguments to back up the dislike — merely, that I think that there is a dislike there, which becomes an argument in itself, since if many people have an emotional reaction against a new system, then that makes it less likely that the system will be adopted by enough people to become as officially recognised as the journal system. To avoid misunderstanding, let me stress that I’ve got nothing against emotional reactions, as long as they are backed up with arguments; and in the comments on my previous post they have been. Indeed, the arguments against various aspects of what I suggested have caused me to realize that there are some disadvantages I didn’t think of and others that I underestimated.

In this post, I want to summarize the points made in the comments (for the benefit of anyone who is interested in what was said but doesn’t have time to read through them all), and then make a second suggestion, which I think deals with a number of objections to the first. As with the first, I don’t see the details as set in stone. I think it’s an improvement on the first, but doubtless it can itself be improved on. Whether it reaches the level where one should actually consider trying to implement it is of course quite another matter. But I do think that these issues should be discussed: if we were designing a system from scratch for disseminating and evaluating mathematical output, I don’t think we would come up with the current journal system, though of course that’s not the situation, and historical accidents often result in quite good ways of doing things.

How might we get to a new model of mathematical publishing?

October 31, 2011

This is a post I’ve been intending to write for several months, but now seems to be quite a good moment, since the issue is in the air somewhat. For example, I’ve just read a post by Michael Nielsen on a similar topic, which itself was responding to things that other people have written. However, he is addressing a different issue: that of the restriction of access to journal articles once they are published. I am more interested in whether mathematicians really need journal articles at all, now that we have the internet. (Just in case anyone hasn’t noticed, this post is not part of the series about first-year mathematics at Cambridge …)

Before I go any further, let me make clear right from the outset that I’m not merely saying, “We can stick our papers on the internet, so let’s forget about journals.” I think that journals still have a vital role to play, even though the internet exists. However, like many people, I do not think it is at all obvious that they will continue to have a vital role to play, so I’d like to discuss two questions.

1. If we didn’t have journals, then what might we have instead?

2. How could the change from journals to whatever replaces them actually take place?

Online mathematics finally takes off …

October 3, 2010

… or does it?

Is the Tricki dead?

September 24, 2010

This is a post I’ve been meaning to write for some time. As most readers will know, at the very end of 2008 Alex Frolkin, Olof Sisask and I started the Tricki, a wiki-like website where people could post articles about mathematical techniques. The hope was that after the site had reached some level of completeness, it would be possible to take a mathematics research problem (or subproblem) and search efficiently for known techniques that were likely to be relevant. It would be doing something a little different from Wikipedia mathematics articles, which concentrate more on what I like to think of as “things with names”. For instance, if you suspect that discrete Fourier analysis is likely to be a useful tool for your problem, then you can type “discrete Fourier analysis” into Google and find many links, including to a Wikipedia article that contains many of the basic facts. But what if it doesn’t occur to you that discrete Fourier analysis is what you need (even though it in fact is)? The idea was that, using easily identifiable features of your problem, you would be able to follow links to ever more specific Tricki pages until you would reach a page that explained when discrete Fourier analysis was useful and how it was used. In general, the whole site would be about how to do mathematics rather than about lists of facts.

Miscellaneous matters

October 20, 2009

Michael Nielsen and I have written an Opinion Piece for Nature about the Polymath project and related matters. Thanks almost entirely to Ryan O’Donnell, a preprint at last exists that contains Polymath’s proof of the density Hales-Jewett theorem with all the details. It will be posted on the arXiv very soon and I will update this post when it is.

Update: it can be found here. Owing to a misunderstanding, it was posted before I had any input into it, but in any case, the full proof is here, even if the version that is submitted for publication will have some changes.

The Notices of the AMS have published five back-to-back reviews of the Princeton Companion to Mathematics. They are by Bryan Birch, Simon Donaldson, Gil Kalai, Richard Kenyon and Angus Macintyre.

From Quomodocumque I learned of a new website, Math Overflow, where you can ask and answer mathematical questions. It seems to be very active, with a lot of users, rating systems for comments and commenters, and the like. So in principle it could be another mechanism for pooling the resources of mathematicians with the help of the internet. For example, if you need a certain statement to be true and do not know whether it is known, then my guess is that you could find out pretty quickly if you post a question there. For more discussion, see a post over at the Secret Blogging Seminar.


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