Miscellaneous matters

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.

PCM errata III

A quick note to say that I’ve just been asked by PUP to send all the corrections I have, so I have sent the corrections that are listed in comments on the post PCM errata II. Further errata should therefore ideally be pointed out here. I think this means that a reprint with corrections should appear in the next few months, but I’m not sure of the exact time scale.

Once again, many thanks to those who have notified me of errors. Particular thanks this time round go to Axel Boldt, who sent a very long list. He was to PCM errata II as Joseph Myers was to PCM errata I. But others too made observations that will lead to significant improvements when the reprint comes out. It has been disconcerting to see just how many mistakes remained after the effort we spent on eliminating them, but I suppose in a book this size it is inevitable, and I imagine that there are several more lurking there. So do please continue to let me know of any errors that you find. At some point in the not too distant future I’ll try to merge the second list with the first to make it easier for people to see which mistakes have already been spotted. For now, after the break, here is a copy of the instructions I have sent to PUP.

PCM errata II

Very many thanks to all who have written in pointing out errors in the Princeton Companion. I am told that it won’t be too long before the next printing, so I have finally been forced to collect together the errata in a systematic way. I am copying the list I have just sent to Princeton University Press so that if anyone finds an error now they can easily check whether it has already been spotted. (I was asked if I would do this some time ago — now at last I have.) The list appears after the break. From now on if people point out further errors I will add them to the list, with some indication of whether they have yet been corrected.

The secondary purpose of this post is to suggest that you should wait a bit if you are thinking of buying the book. I don’t want to hit sales too hard, but I’m guessing that not all PCM buyers are avid readers of this blog so I might as well reward those who are. Of course, you could take the attitude that the error-strewn version is a collector’s item: if so, hurry while stocks last.

Princeton Companion errata

I finally got a copy of the Princeton Companion to Mathematics in my hands today, and within a depressingly (but not unexpectedly) short time found my first mistake, in an article written by me. I’ve established that small corrections can almost certainly be made in time for the next printing, so this post is to invite anybody who happens to spot an error to let me know in a comment on this post. (That way, all the corrections that are needed will be in one convenient place.) I’m particularly interested in mathematical mistakes, though typos are also good to know about. Just to get the ball rolling, here’s the one I spotted, together with a reflection on how it arose, since it’s relevant to mathematical writing in general.

Incidentally, before I say any more, I want to say that a huge amount of proofreading has gone into the book, so I expect the density of mistakes to be pretty small. But because the book is a big one, I also expect the number of mistakes to be not all that small.

Princeton Companion latest

A quick post to give an update on the Princeton Companion to Mathematics. It’s been off my hands for a few weeks now. If all goes well it will be printed by the middle of September and should appear in bookshops about a month later. The illustration to the right is what the cover will be like. Click here if you want to see it in more or less full size. If you go to this page on the PUP website then you will find a podcast interview that I gave, which contains information that does not appear on this blog.

UPDATE 14TH OCTOBER: here are links to a few blog posts that have discussed the Princeton Companion recently. Terence Tao had a few thoughts on receiving his copy. Brian Hayes did too. Fred Shapiro, editor of The Yale Book of Quotations, has an interest in reference books and commented about the PCM in the New York Times Freakonomics blog. Dmitry Vostokov recommends the PCM for people wanting a broad overview of mathematics. Isallaboutmath points out that the Nautilus shell on the cover does not in fact have anything to do with the golden ratio. And the book has five reviews on Amazon, some more sensible than others.

FURTHER UPDATE (to which I’ll add as the occasion arises): Peter Woit has written a short review on his blog. Ian Stewart has written a review for The Times. Edmund Harriss has reviewed it on his blog. Alexander Bogomolny reviews it here. Does Antonio Cangiano like it? Perhaps you’d better judge for yourself. Having honed your interpretative skills, you’ll be in a better position to appreciate Scott Guthery’s helpful antidote. A different Scott, Scott Aaronson, reviews it on his blog. And Robin Wilson reviews it for the LMS newsletter. A nice review here, in French.

29TH OCTOBER: It’s been a long time coming, but I’ve just noticed that the PCM now appears to be available on Amazon UK, and not just from third-party sellers. According to them, it’s popular amongst geographers. If I knew how, I’d suggest they recategorized it.

Punctuation question

The Princeton Companion to Mathematics is even more nearly nearly finished than it was last time I said it was nearly finished. In fact, this time I can give a date — July 13th — past which it will be too late for me to do any work on it. The book will be printed in September and available in November.

As an example of the important issues we now face, here is a question about hyphens: I’m fairly sure there will be a small but passionate minority of mathematicians who care about these, and a question has come up. I am curious to know what other people think, so I’m not going to say what I think: I’ll just try to present the question as neutrally as possible. And here it is.

The Princeton Companion to Mathematics

I have decided to follow the excellent example of Terence Tao and start up a blog. For the moment I am too busy to do this properly, because, with the help of June Barrow-Green and Imre Leader, I am editing a book called The Princeton Companion to Mathematics. However, it is partly for that very reason that I want to set up the blog. It is somewhat hard to explain what the book is, but if you want to get quite a good idea, there is a substantial (though out of date) description of it, with several sample articles available here. You can get into this site with userid Guest and password PCM. Comments welcome. A sufficiently sensible comment could even influence what goes into the book, but I should warn that, because we are at a rather late stage of the editing process, I no longer have much room for manoeuvre. So I may end up having to say, “Yes, great point, but unfortunately it’s too late to do anything about it.”

Actually, I hope that the PCM blog will really come into its own after the book comes out. In particular, if you feel that there are unfortunate gaps (as there undoubtedly will be) then maybe it will be possible to do something about it online — I might even start up a wiki consisting of PCM supplements. (The distinction between that and the regular mathematics articles in Wikipedia would be some kind of certification that an article had reached PCM levels of comprehensibility. I’d probably be unwilling to put in the sort of editorial efforts I’ve been putting in over the last few years, but would try to distribute that task by using the blog medium. If you are reading this, maybe you will have a suggestion about how to go about it — in particular, I don’t yet know anything about the technicalities of this kind of thing.)