Tuesday, August 29, 2006

"A pure mind" -- reclusive Russian mathematician turns his back on honors and money, and the world wonders why

New York Times/Xianfeng David Gu and Shing-Tung Yau

Sorry, I just love this picture and can't resist linking to it again -- which I first did a couple of weeks ago in this post. It was mainly a pretext to show the picture and link to this New York Times story that used it as an illustration. The story tried to explain why the proof of "PoincarĂ©’s conjecture" might prove to be the single greatest mathematical discovery of the 21st century.

The man who was, more than anyone, responsible for the feat was Grigory Perelman, a reclusive, brilliant Russian mathematician who lives alone in St. Petersburg with his mother -- although he also has worked in the U.S. and has corresponded with mathematicians around the world by email. Recently he stunned the world by turning down the Fields Medal, the highest honor in mathematics, which also comes with a $13,400 cash award. He left open the possibility that he might also turn down the really big bucks -- all or part of the $1 million The Clay Mathematics Institute in Cambridge, Mass has offered for the solution to the PoincarĂ©’s conjecture.

Perelman -- a declared foe of politics in the field of mathematics --seemed to be saying that no one person should receive all the credit for proving a theorem, and that the proof itself should be gratification enough. George Johnson, the science correspondent of the Times, summed up the controversy recently.
Unlike Brando turning down an Academy Award or Sartre a Nobel Prize, Dr. Perelman didn’t appear to be making a political statement or trying to draw more attention to himself. It was not so much a medal that he was rejecting but the idea that in the search for nature’s secrets the discoverer is more important than the discovery.

“I do not think anything that I say can be of the slightest public interest,” he told a London newspaper, The Telegraph, instantly making himself more interesting. “I know that self-promotion happens a lot and if people want to do that, good luck to them, but I do not regard it as a positive thing.”

Mathematics is supposed to be a Wikipedia-like undertaking, with thousands of self-effacing scriveners quietly laboring over a great self-correcting text. But in any endeavor -- literature, art, science, theology -- a celebrity system develops and egos get in the way. Newton and Leibniz, not quite content with the thrill of discovering calculus, fought over who found it first.
In the New Yorker recently, Sylvia Nasar (author of a biography of mathematician John Forbes Nash, who was portrayed onscreen by Russell Crowe in "A Beautiful Mind") and David Gruber set off in pursuit of Perelman and establish just how ego-driven an enterprise the world of higher mathematics really is. They eventually are able to speak briefly with Perelman in St. Petersburg.
We arranged to meet at ten the following morning on Nevsky Prospekt. From there, Perelman, dressed in a sports coat and loafers, took us on a four-hour walking tour of the city, commenting on every building and vista. After that, we all went to a vocal competition at the St. Petersburg Conservatory, which lasted for five hours. Perelman repeatedly said that he had retired from the mathematics community and no longer considered himself a professional mathematician. He mentioned a dispute that he had had years earlier with a collaborator over how to credit the author of a particular proof, and said that he was dismayed by the discipline’s lax ethics. “It is not people who break ethical standards who are regarded as aliens,” he said. “It is people like me who are isolated.” We asked him whether he had read Cao and Zhu’s paper. “It is not clear to me what new contribution did they make,” he said. “Apparently, Zhu did not quite understand the argument and reworked it.” As for Yau, Perelman said, “I can’t say I’m outraged. Other people do worse. Of course, there are many mathematicians who are more or less honest. But almost all of them are conformists. They are more or less honest, but they tolerate those who are not honest.”

The prospect of being awarded a Fields Medal had forced him to make a complete break with his profession. “As long as I was not conspicuous, I had a choice,” Perelman explained. “Either to make some ugly thing -- a fuss about the math community’s lack of integrity -- “or, if I didn’t do this kind of thing, to be treated as a pet. Now, when I become a very conspicuous person, I cannot stay a pet and say nothing. That is why I had to quit.” We asked Perelman whether, by refusing the Fields and withdrawing from his profession, he was eliminating any possibility of influencing the discipline. “I am not a politician!” he replied, angrily. Perelman would not say whether his objection to awards extended to the Clay Institute’s million-dollar prize. “I’m not going to decide whether to accept the prize until it is offered,” he said.
The names Pereleman mentioned are other mathematicians who have worked on the problem -- and who might share in the Clay Institute prize when it is announced. (They include the two mathematicians who designed the rabbit diagram at the top of this post.)

Part of what makes Nasar and Gruber's article so fascinating is the way they sketch the relationships between all these contending mathematical egos -- exactly the situation Perelman seems to be trying to opt out of. They conclude by quoting another mathematician.
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."

1 comment:

Dr Diablo said...

Kudos to Perelman for solving the problem while the rest of us were just trying to balance our checkbooks. I think, though, that we should withhold slack-jawed admiration of the man's purity of spirit until events unfold further.

I myself would spurn the $13,400 for publicity worth many times that amount. Christ, I've lost that much in my brokerage account this year due to the inexplicable failure of uranium stocks to track the upward movement of the commodity.

I would, however, accept the Clay mil "to establish a grant program for mathematicians working outside the academic community," and then appoint a committee to take years to lay the groundrules.

I predict that Perelman will prove to have feet of Clay.