Tag Archives: gowers

Statement on the Elsevier boycott

A group of mathematicians, myself included, have prepared and signed a statement which attempts to summarize the reasons so many mathematicians and other scientists (nearly 5000 at this count) have signed on to boycott Elsevier publications.

This is an important moment for mathematical publishing, a rare time when the attention of the community is really fixed on an issue that’s been torturing our librarians for many years.  What’s the next step?  A good place to follow people’s thinking will be Gowers’s blog.  Tim, of course, has been a driving force behind the current movement to stop complaining about rent-seeking academic publishers and start doing something about it.


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Best Writing on Mathematics 2011, and Nathanson on massive collaboration

In my mail:  The Best Writing On Mathematics 2011 (Mircea Pitici, ed.) from Princeton University Press.  Just to get this out of the way:  I’m in here!  They reprinted my compressed sensing article from Wired.

You might now be wondering:  are there really enough popular math articles published in a given calendar year to fill up an anthology?  No.  There are not.  But this is part of the charm of what Pitici has done.  His very broad definition of “writing on mathematics” allows him to include useful professional advice for young mathematicians from Andrew Schultz, reflections on a career in math education from John Mason,  and academic-yet-readable philosophy (“What Makes Math Math?”) from Ian Hacking, whose The Emergence of Probability is my favorite book in history of mathematics.

I especially like Mel Nathanson’s pessimistic take on massive collaboration in mathematics — because it is a forcefully written, carefully argued case for a position with which I mostly disagree.  “I would guess that even in the already interactive twentieth century,” he writes, “most of the new ideas in mathematics originated in papers written by a single author.”  I would guess otherwise — at least if you restrict to the second half of the century, when joint papers started to become really common.   Mel calls me out for writing about Tim Gowers’ Polymath Project in the New York Times with “journalistic hyperbole” — and here he is right!  It is very hard, in the genre of 300-word this-year-in-science snippet, to keep the “gee whiz!” knob turned down and the “jury is still out” knob turned up.

Gowers claims the classification of finite simple groups as a pre-Internet example of massively collaborative mathematics.  Nathanson agrees, but characterizes the classification as fundamentally uninteresting, “more engineering than art.”  What would he say, I wonder, about recent progress towards modularity of Galois representations?  It’s very hard to imagine him, or anyone, seeing everything that’s happened in the last 15 years as a mere footnote to Wiles.  (But maybe some of the experts who read this blog would like to weigh in.)

Nathanson concludes:

Recalling Mark Kac’s famous division of mathematical geniuses into two classes, ordinary geniuses and magicians, one can imagine that massive collaboration will produce ordinary work and, possibly, in the future, even work of ordinary genius, but not magic.  Work of ordinary genius is not a minor accomplishment, but magic is better.

Yes, but:  magic can only happen in the already-enchanted environment created by the hard work of many minds, alone and in teams.  Math is like earthball.




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Math linkdump Nov 11

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Gowers & co. on the cap set problem

On the off chance you read my blog and not Gowers’ — Tim is talking about one of my very favorite open questions, the affine cap set problem, over at his place.

I’m a little ambivalent about reading his posts — every time I think about this problem, I get sucked in and spend a certain amount of time gnawing at it.  And the sum total of all this gnawing has so far produced not even the tiniest toothmark on the gleaming surface of the affine cap set problem.

And yet…. and yet…..

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July math link dump

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The Year in Mathematical Ideas

I have a short piece about Tim Gowers’ Polymath project in the 2009 edition of the New York Times Year in Ideas feature.

In January, Timothy Gowers, a professor of mathematics at Cambridge and a holder of the Fields Medal, math’s highest honor, decided to see if the comment section of his blog could prove a theorem he could not.

It’s been years since we’ve been New York Times subscribers; looking at Sunday’s paper I was struck by how much math was in it. In the Year in Ideas section, besides my piece, there’s one about using random walks to identify species critical to the survival of an ecosystem, another about the differential equations governing zombie diffusion, and a third about Nate Silver’s detective work on the fishy final digits of poll results.  (I blogged about DigitGate a few months back.)  Elsewhere in the paper, John Allen Paulos writes about the expected value of early breast cancer screening, and the Book Review takes on Perfect Rigor, Masha Gessen’s new biography of Perelman.  Personally, I think Gessen missed a huge commercial opportunity by not titling the book He’s Just Not That Into Yau.

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What is arithmetic geometry?

My colleague Timothy Gowers is very close to finishing a project of really immense ambition: the Princeton Companion to Mathematics, a gigantic book which aims to be a panorama of all of contemporary mathematics, presented at an undergraduate or even interested-amateur level. He has jokingly suggested that a good alternate title would be Mathematics: A Very Long Introduction. Some of the book consists of expository articles on the subfields in math — things you might take a course in, like analytic number theory, probability, or partial differential equations. Others treat notable theorems (Mostow Rigidity, Hilbert’s Nullstellensatz), notable mathematicians (charmingly alphabetized by first name), and notable applications to other fields. And some of the articles — to my mind the most ambitious of all — attempt to give some sense the nature of the mathematical project to outsiders. (“The general goals of mathematical research,” “The language and grammar of mathematics.”) The editors have made many sample articles available online (userid: Guest, pwd: PCM) — I encourage people to have a look! In particular, if you are wondering what I do all day, you can read my article on “Arithmetic Geometry.” If you want to start from the beginning of things, try Gowers himself on “Some Fundamental Mathematical Definitions” or “The Language and Grammar of Mathematics.” For an applied article, try Madhu Sudan’s “Reliable Transmission of Information.” Or if you just want inspiration, see Sir Michael Atiyah on “Advice to a Young Mathematician.”

Important biographical notes: Tim has a Fields Medal and a blog.

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