Sylvia Nasar and David Gruber got the only media interview of Perelman, by dint of actually going to Saint Petersburg and asking him for one. But the real subject of their article in the latest issue of the New Yorker, Manifold Destiny, A legendary problem and the battle over who solved it, is Shing-Tung Yau, who (if the article is to be believed) has systematically downplayed the significance of Perelman’s contribution. Reading the article, it’s hard to figure out what Yau’s motivation would be: possibilities seem to be his friendship with Richard Hamilton, a desire to emphasize his own contribution or that of his proteges. The article also reports on a feud that Yau had with Gang Tian in Chinese newspapers.

I don’t have any first-hand knowledge of any of this (I had seen some rumors here and there on the internet, but I’ve seen rumors that Iran would nuke the United States as of yesterday, which demonstrates the incredible reliability of internet rumors), but if the article is right, then I do see one motivation for Yau that I would even find admirable (though probably wrong-headed): to fight the growing tendency of considering an theorem proven if experts can fill in the details. “Experts” can mean fewer people than can fill a jury. In theory, you could just become an expert, but in any sufficiently technical field there will be results that “everyone knows” but won’t be published anywhere, so unless you are part of “everyone”, it will be difficult for you to fill in the gaps without a great deal of rediscovery. (I don’t know if that is the case with Perelman’s proof.)

Perelman comes across better in the article than I had expected, though his motivation for turning down the Fields seems to be less because of otherworldliness, and more because he feels hard done by the mathematics establishment. Amazingly, he really does live with his mother, and is currently unemployed (though retired might be a better way to describe it). He claims to have quit mathematics, but without an actual substitute, it’s easier to quit smoking.

(The article quotes a post by an unidentified Brazilian blogger. On a whim, I tracked the quote down in Google to this post by Victor Rivelles.

Link to New Yorker article via an anonymous commenter to Scott Aaronson’s blog.

The 2006 Field Medalists have been announced:

Andrei Okounkov “for his contributions briding probability; representation theory and algebraic geometry.”

Grigori Perelman “for his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow.”

Terence Tao “for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory.”

Wendelin Werner “for his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory.”

The Nevanlinna Prize went to Jon Kleinberg, while the very first Gauss Prize was awarded to Kiyoshi Itō.

As was widely predicted, Perelman declined his prize, and did not attend the ICM.

What has caused more human misery, botulism or real analysis? Discuss.

Update. Before you answer, remember that botulism has given us less wrinkly foreheads.

For the state of the art on sheaves of sets, see this chapter-length introduction to sheaf theory by Claudia Centazzo and Enrico M. Vitale.

Today’s Guardian, one of Britain’s leading national daily newspapers, has a front-page story and photo about Grigory Perelman’s proof of a generalization of the Poincare Conjecture.  The article is more about the man than the mathematics, but I guess this is the price of a Page-1 story.

William Fulton is writing a new book on algebraic stacks. He is posting each chapter online as he finishes them. So far he has posted the preface and the first chapter.

For an introduction to the concept, see Dan Edidin’s What is… a stack? from the Notices of the AMS, and for a more detailed introduction, try Introduction to algebraic stacks by Alberto Canonaco.