I've just read a fantastic article from the 2007 Best American Science Writing collection, "Manifold Destiny," by Sylvia Nasar and David Gruber, which originally appeared in The New Yorker. It provides a fascinating account of the controversy surrounding the proof of Poincare's conjecture, a result about three-dimensional spheres that had stumped scientists for decades until an extremely talented but eccentric Russian mathematician named Grigory Perelman solved the problem.
Here's why the story warrants an article in The New Yorker: the Chinese mathematician Shing-Tung Yau, who has achieved super-stardom after his breakthroughs that "helped launch the string-theory revolution in physics and earned him, in addition to a Fields Medal - the most coveted award in mathematics - a reputation in both disciplines as a thinker of unrivalled technical power" (he's the Yau in the Calabi-Yau manifolds), tried to gain credit for the proof and push Perelman to the sidelines. He is portrayed in the article as a power-hungry, recognition-obsessed man who, according to a professor at Stony-Brook, "wants to be the king of geometry. He believes that everything should issue from him, that he should have oversight. He doesn't like people encroaching on his territory." (My only source of information on the matter is the New Yorker article. I tend to find the articles in that publication well-written and well-researched, so I have no reason to doubt Nasar and Gruber's work.)
Perelman's proof was dry and compact, which made it hard to follow for the average scientist (and even the not-so-average one), and Perelman was already known for his antics back in graduate school, saying for instance "If they know my work, they don't need my CV; if they need my CV, they don't know my work" when a member of a hiring committee asked him for his resume. He's proved results but hasn't bothered to publish the proof in peer-reviewed journals, and after proving the Poincare conjecture, declined the Fields medal on the ground that "if the proof is correct then no other recognition is needed." In other words, Perelman belongs to the idealist school where the work speaks for itself and doesn't need to be promoted.
Which turns out to have been a very naive position, because of Yau. The journalists explain that the two main ways to reach academic fame is to (1) find a new proof, or (2) identify gaps or errors in an already-existing proof and fixing them. But in most cases, gaps in proofs are gaps in exposition, where the researcher simply didn't bother writing down all the implicit steps, rather than mathematical gaps, where a part is truly missing. The first type of gaps is of course nothing special - graduate students deal with those all the time. The second type is more interesting, because it allows the scientists who fixed the proof to gain recognition along with the original authors, but it raises the question: how do you distinguish between the two?
This is at the center of the controversy surrounding Perelman's proof. The New Yorker states that "on at least one occasion, Yau and his students have seemed to confuse [mathematical gaps with gaps in exposition], making claims of originality that other mathematicians believe are unwarranted." The journalists give the example of a proof by a young geometer at Berkeley named Alexander Givental. Later, "a former student of Yau's who taught at Stanford gave a talk at Harvard on mirror symmetry [...and] proceeded to present a proof strikingly similar to Givental's, describing it as a paper that he had co-authored with Yau and another student of Yau's." In the final paper, Yau and his co-authors "mention Givental's work only in passing", write that his proof, "which has been read by many prominent experts, is incomplete" but do "not identify a specific mathematical gap." An inquiry later established that "Givental's proof was complete."
The fit Yau had when his former student Gang Tian was chosen to give a plenary address at the IMU's congress in Beijing (IMU stands for International Mathematical Union), and the incredible accusations he leveled at Tian to discredit him, are worth reading on p.35 and p.37-38 of the paperback edition. I'd repeat them here, but then you would have less incentive to read the whole piece (also available for free on the New Yorker's website), which would be a pity. Let me just quote this one line: "[Then the leading Chinese mathematician died] and Yau's efforts to insure that he - not Tian - was recognized as his successor turned vicious."
To gain credit for Perelman's proof, Yau apparently used a similar approach as he had for Givental's work, and again "mathematicians familiar with Perelman's proof disputed the idea that [Yau's co-authors] had contributed significant new approaches to the Poincare." A professor stated: "I don't see that they did anything different." Yau himself said: "If you can attach your name in any way, it is a contribution." On p.45: "As Perelman put it, 'if everyone is honest, it is natural to share ideas.' Many mathematicians view Yau's conduct over the Poincare as a violation of this basic ethic."
Sadly, Perelman was so revolted by the lack of integrity in the mathematics community that he decided to quit. He told the journalists: "It is not people who break ethical standards who are regarded as aliens. It is people like me who are isolated."
Yau has obviously not been thrilled by the article, published in August 2006. A more positive profile in the New York Times, published in October 2006, still quotes a professor as saying that Yau has "an outsized ego and great ambition, and has done things that dismay his peers" (the title itself, "The Emperor of Math", does nothing to change that impression), but he claims he's doing all this for "the younger generation" (even in the New Yorker article, he justified part of his behavior regarding Perelman as a way to help one of his young co-authors, who is a professor in China): "I have to fix my reputation in China in order to help younger students." According to the New York Times: "The New Yorker has said it stands by its reporting." And with the story's inclusion in the Best American Science Writing series, it is going to remain alive for a very long time.
As in a numb3rs episode...
"Ooh, math fight!"
But other than that, it seems this isn't the first time I've heard of professors going all nutso over credit and looking good. I remember in Emanuel Derman's book about how T.D. Lee and the other guy that won the nobel with him eventually split on very bad terms due to bickering over credit.
As for Grisha Perelman...oy vey...it seems us Russians are crazy smart but always have quirks about us >.<...of course, when Jim Simons was asked about it, he said "I'd never have turned that down. In fact, I don't turn down anything!"
I had a laugh at that one.
Posted by: Ilya ^_^ | May 13, 2009 at 12:36 PM
Dear Aurelie,
after having read your post I dug deeper into it and found the site http://www.doctoryau.com/ . You might be interested in the "letter to the New Yorker" regarding this article.
All the best.
Posted by: anonymous | May 19, 2009 at 07:26 PM