Still More on Poincare

The August 28 issue of The New Yorker features this magisterial article about the Poincare conjecture. The focus of the article is on the priority dispute between Grigory Perelman on the one hand, and a team of Chinese mathematicians led by Harvard’s Shing-Tung Yau on the other. According to the article, Yau believes that the proof posted to the internet by Perelman was deficient in several key respects, and that the first complete proof should be credited to two of his students. Thus far, most of the mathematical community seems to disagree:

This, essentially, is what Yau’s friends are asking themselves. “I find myself getting annoyed with Yau that he seems to feel the need for more kudos,” Dan Stroock, of M.I.T., said. “This is a guy who did magnificent things, for which he was magnificently rewarded. He won every prize to be won. I find it a little mean of him to seem to be trying to get a share of this as well.” Stroock pointed out that, twenty-five years ago, Yau was in a situation very similar to the one Perelman is in today. His most famous result, on Calabi-Yau manifolds, was hugely important for theoretical physics. “Calabi outlined a program,” Stroock said. “In a real sense, Yau was Calabi’s Perelman. Now he’s on the other side. He’s had no compunction at all in taking the lion’s share of credit for Calabi-Yau. And now he seems to be resenting Perelman getting credit for completing Hamilton’s program. I don’t know if the analogy has ever occurred to him.”

Articles like this remind me that there is a whole world of mathematics that I am not a part of. Most mathematicians go their entire career without worrying about priority disputes, or Fields Medals, or solving big open problems. We merely teach our classes, write expository articles and textbooks, give short talks at conferences, and do research on the far more modest problems we have some home of making progress on. The Perelman’s and Yau’s of the world are simply in a different profession.

It requires an almost monastic level of dedication to really achieve great things in mathematical research. The closing of the article says it well:

Mikhail Gromov, the Russian geometer, said that he understood Perelman’s logic: “To do great work, you have to have a pure mind. You can think only about the mathematics. Everything else is human weakness. Accepting prizes is showing weakness.” Others might view Perelman’s refusal to accept a Fields as arrogant, Gromov said, but his principles are admirable. “The ideal scientist does science and cares about nothing else,” he said. “He wants to live this ideal. Now, I don’t think he really lives on this ideal plane. But he wants to.”

It’s a level of dedication most of us find impossible to muster. After all, progress on big problems requires that you first assimilate the huge body of work that came before you. Since this work is described mostly in impenetrable research papers, it is difficult even for professional mathematicians to wade in to a new subject.

I do find it frustrating that though I have a PhD in mathematics, I know I would find the published proof of the Poincare utterly unreadable. It is a pity that all of this brilliant work can be enjoyed only by a handful of geniuses at the top of the mathematical food chain.

Oh well. Go read the whole article if you want some behind the scenes dirt from the highest level of the mathematical world.