Wednesday, August 23, 2006

Is it "weird" to have principles?

This post isn't really about the Poincaré conjecture, so the conjecture isn't mentioned in the title.

Nevertheless, what I'm talking about, of course, is the Perelman affair, and especially the media narrative on it, as related in the previous post. As you can see from the popular media articles referenced there, the narrative is very much focused on Perelman's supposedly odd behavior: mysterious, reclusive, and all that.

Perhaps it's even typical of brilliant mathematicians? Nope, it's not. I've known plenty of brilliant mathematicians, and most are pretty "normal". Often a little bit eccentric, perhaps, but still pretty normal. In fact, most would (figuratively) kill for the honor that Perelman turned down. And that, it turns out, is a large part of the problem.

Since this story has actually been brewing for some time, it should come as no surprise that a few savvy journalists have had an in-depth article all ready to go. And that is what Sylvia Nasar and David Gruber offer in their article Manifold Destiny appearing in the lastest New Yorker. ("Manifold" isn't a typo; it's a pun.)

It's an excellent article, but you'll be disappointed if you expect to learn much about the Poincaré conjecture from it. Instead it's mostly about Perelman and the intrigues of a number of other mathematicians involved in the quest to solve the Poincaré conjecture. As Nasar and Gruber tell the story, it's very reminiscent of other stories of intense competitions to solve major scientific problems. One thinks, for instance, of the story of how the structure of DNA was determined, as recounted in Jim Watson's Double Helix. In short, it's largely about ambition and ego and jockeying to receive credit for the solution of a major problem.

Nasar is very qualified to write about the mathematical psyche, as she's well-known for her book A Beautiful Mind about another mercurial mathematician, John Nash, who even plays a small part in the Poincaré conjecture drama.

Nasar brings on another bit-player in the drama, another top Russian geometer, Mikhail Gromov, to summarize at the very end, Shakespeare-like, what the play's all been about:
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.”

In other words, Perelman isn't some nerdy nutter. There's a principled logic to what he has done in refusing the Fields medal. It's a statement of his objection to the ego-centric way that the game of high-stakes mathematics (and science in general) is often played. This may be a quixotic gesture, but it's not daft.

Sadly, the villain in this drama, at least as Nasar and Gruber tell it, is another famous mathematician, Shing-Tung Yau, known especially in connection with Calabi-Yau manifolds, which are so important for superstring theory. Ironically, Yau seems to have gotten the short end of the stick, much earlier in his own career, in a credit struggle for his work on Calabi-Yau manifolds.

If the portrayal is accurate, it's sad. I crossed paths with Yau in the early 70s at Stanford, when he was at the beginning of his academic career. He seemed like a very decent, easy-going person then, though I hardly knew him. Perhaps the appearance was different from the reality, but I suppose I'll never know. Just as likely, if not more so, is that Perelman is right -- covetousness of honors and the high esteem of others is not good for us. And yet, how many brilliant scientists can put forth the great efforts usually required for high achievement without some degree of ego and strong motivation?

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