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From Tim Gowers’ blog comes the announcement that the Tricki – a wiki for various tricks and strategies for proving mathematical results – is now live. (My own articles for the Tricki are also on this blog; also Ben Green has written up an article on using finite fields to prove results about infinite fields which is loosely based on my own post on the topic, which is in turn based on an article of Serre.) It seems to already be growing at a reasonable rate, with many contributors.
[This article was guest authored by Frank Morgan, the vice president of the American Mathematical Society.]
The American Mathematical Society (AMS) has launched a new blog
http://mathgradblog.williams.edu/
by and for graduate students, with initial entries ranging from “Finding an Advisor” to “Getting a Job.” Although graduate students have long been institutional members of the AMS, the two groups may not always have fully appreciated each other. Graduate students sometimes wonder why they are getting all this “junk mail,” and AMS governance has had relatively minor contact with graduate students. In fact, graduate students are the future of the AMS, and conversely they need the AMS and its support for mathematics. Hence I think that it is a bright sign of the times to see the AMS launching this blog by and for graduate students. Graduate students interested in joining the editorial board or others interested in helping out can email me at Frank.Morgan@williams.edu; we seek a large and diverse board. Meanwhile check out the new blog and post some comments on the entries you find there.
For the last ten years or so, I used to maintain a list of conferences in the area of analysis & PDE (see e.g. this page for a partial archive of this conference list). However, due to many other demands on my time, I eventually ceased to maintain it, instead passing it over to the Harmonic Analysis and Related Problems (HARP) group that was supported by the European Mathematical Society. Unfortunately, the EMS funding ran out a few years back, the HARP group dissolved, and so the page drifted for a while.
This week, I talked to my good friend Jim Colliander (who maintains the DispersiveWiki) and he agreed to host a new version of the conferences page on the Wiki, where it can be collaboratively updated. It is rather sparse right now, but I hope people will contribute to it, either by adding new conferences and related content, or by cleaning up the organisation of existing content. I have also migrated a list of lecture notes and courses in analysis and PDE which is badly in need of updating.
[One can presumably use the Wiki to also host other items of this nature than just a conference list; any suggestions for expanding the page would also be welcome.]
My good friend Tim Gowers has just started an experimental “massively collaborative mathematical project” over at his blog. The project is entitled “A combinatorial approach to density HalesJewett“, and the aim is to see if progress can be made on this problem by many small contributions by a large number of people, as opposed to the traditional model of a few very large contributions by a small number of people (see this article for more on the “rules of the game”, and this article for why this particular project was picked as a test project). I think this is an interesting experiment, and hopefully a successful one, though it is far too early to tell as yet.
I can describe the problem here. Let n be a large integer, and let be the set of all strings of length n using the alphabet , thus for instance . A combinatorial line in is a triple of points in that can be formed by taking a string of length n using the alphabet with at least one occurrence of the “wildcard” x, and then substituting the values of 1, 2, 3 for the wildcard. For instance, the string would lead to the combinatorial line in . The (k=3) case of the density HalesJewett theorem of Furstenberg and Katznelson asserts:
Density HalesJewett theorem. Let . Then if n is sufficiently large depending on , every subset of of density at least contains a combinatorial line.
[Furstenberg and Katznelson handled the case of general k in a subsequent paper. The k=1 case is trivial, and as pointed out in this post by Gil Kalai, the k=2 case follows from Sperner’s theorem.]
Furstenberg and Katznelson’s proof uses ergodic theory, and in particular does not obviously give any bound as to how large n has to be depending on before the theorem takes effect. No other proofs of this theorem are currently known. So it would be desirable to have a combinatorial proof of the k=3 density HalesJewett theorem. Since this theorem implies Roth’s theorem, and Roth’s theorem has a combinatorial proof based on the triangle removal lemma (see e.g. my Simons lecture on the subject, or Tim Gowers’ background article for the project), it is thus natural to ask whether the density HalesJewett theorem has a proof based on something similar to the triangle removal lemma. This is basically the question being explored in the above project. (Some further motivation for this problem can be found here.)
Further articles on this project are collected at this page.

I was very pleased today to obtain a courtesy copy of the Princeton Companion to Mathematics, which is now in print. I have discussed several of the individual articles (including my own) in this book elsewhere in this blog, and Tim Gowers, the main editor of the Companion, has of course also discussed it on his blog. Browsing through it, though, I do get the sense that the whole is greater than the sum of its parts. One particularly striking example of this is the final section on advice to younger mathematicians, with contributions by Sir Michael Atiyah, Béla Bollobás, Alain Connes, Dusa McDuff, and Peter Sarnak; the individual contributions are already very insightful (and almost linearly independent of each other!), but collectively they give a remarkably comprehensive and accurate portrait of how mathematical progress is made these days.
The other immediate impression I got from the book was the sheer weight (physical and otherwise – the book comprises 1034 pages) of mathematics that is out there, much of which I still only have a very partial grasp of at best (see also Einstein’s famous quote on the subject). But the book also demonstrates that mathematics, while large, is at least connected (and reasonably bounded in diameter, modulo a small exceptional set). I myself certainly plan to use this book as a first reference the next time I need to look up some mathematical theory or concept that I haven’t had occasion to really use much before.
Given that I have been heavily involved in certain parts of this project, I will not review the book fully here – I am sure that will be done more objectively elsewhere – but comments on the book by other readers are more than welcome here.
[Update, Sep 29: link to advice chapter added.]
[This post is authored by Timothy Chow.]
I recently had a frustrating experience with a certain outofprint mathematics text that I was interested in. A couple of used copies were listed at over $150 a pop on Bookfinder.com, but that was more than I was willing to pay. I wrote to the American Mathematical Society asking if they were interested in bringing the book back into print. To their credit, they took my request seriously, and solicited the opinions of some other mathematicians.
Unfortunately, these referees all said that the field in question was not active, and in any case there was a more recent text that was a better reference. So the AMS rejected my proposal. I have to say that I was surprised, because the referees did not back up their opinions with any facts, and I knew that in addition to the high price that the book commanded on the usedbook market, there was some circumstantial evidence that it was in demand. A MathSciNet search confirmed my belief that, contrary to what the referees had said, the field was most definitely active. Plus, another text on the same subject that Dover had recently brought back into print had a fine Amazon sales rank (much higher than that of the recent text cited by the referees).
A colleague then suggested that maybe I should instead contact the author directly, asking him to regain the copyright from the publisher. The author could then make the book available on his website or pursue printondemand options, if conventional publishers were not interested. I tried this, but was again surprised to discover that the author thought it was not worth the trouble to get the copyright back, let alone to make the text available. Again the argument was that, allegedly, nobody was interested in the book.
In both cases I was frustrated because I did not know how to find other people who were interested in the same book, to prove to the AMS or the author that there were in fact many of us who wanted to see the book back in print.
Now for the good news. After hearing my story, Klaus Schmid promptly set up a prototype website at
Anyone can go to this site and suggest a book, or vote for books that others have suggested. This is precisely the kind of information that I believe would have greatly helped me argue my case. Of course, the site works only if people know about it, so if you like the idea, please spread the word to your friends and colleagues.
It might be that a better longterm solution than Schmid’s site is to convince a bookselling website to tally votes of this sort, because such a site will catch users “redhanded” searching for an outofprint book. I have tried to contact some sites with this suggestion; so far, Booksprice.com and Fetchbook.info have said that they like the idea and may eventually implement it. In the meantime, hopefully Schmid’s site will become a useful tool in its own right.
Let me conclude with a question. What else can we be doing to increase the availability of outofprint books, especially those that are still copyrighted? Several people have told me that the solution is for authors to regain the copyrights to their outofprint books and make their books available themselves, but authors are often too busy (if they are not deceased!). What can we do to help in such situations?
I’ve joined the inaugural editorial board for a new mathematical journal, Analysis & PDE. This journal is owned by Mathematical Sciences Publishers, a nonprofit organisation dedicated to highquality, lowcost, and broadavailability mathematical publishing, and run primarily by professional mathematicians. The scope of the journal is, of course, selfexplanatory; MSP’s other journals have titles such as Geometry & Topology, Algebra & Number Theory, and Algebraic & Geometric Topology.
We’re just starting out (and haven’t even filled up our first issue yet), so we are looking for strong and significant submissions in all areas of analysis and PDE (broadly defined). If you have a good paper in these areas and are deciding on which journal to submit to, you might want to take a look at the submission guidelines for our journal. Of course, the papers are subject to the usual peer review process and will be held to high standards in order to be accepted.
[Update, Nov 11: Link fixed.]
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