Now, I readily admit that my relationship to the more esoteric planes of mathematics is rather like that of Voltaire to God: when we meet on the street, we tip our hats to one another but do not speak. In fact, when I first heard of the Poincaré Conjecture – oh, about an hour ago – my thoughts immediately turned to Raymond Poincaré, the French statesman whose career extended from the late 19th century through the first quarter of the 20th. What, I wondered, could he have been conjecturing about? The dubious wisdom of letting all those German tourists into the country? The chances of slipping that bill for dinner with the can-can dancer past the accountants?
But no, it turns out that the famous conjecture belonged to Raymond’s cousin, Henri Poincaré. The theorem pertains to…er…well, perhaps you’d better read about it for yourself. The book, which patient readers will recall that I referenced way back there in the first paragraph, is Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century, by Masha Gessen (reviewed here by John Allen Paulus). A brilliant fellow, Perelman also fulfills our seeming desire for oddball geniuses: long hair, anti-social, lives with his mother. Gessen and Paulus explain:
Gessen, on the basis of many incidents of Perelman’s prickliness, his long hair and fingernails and Rasputin-like appearance, and his often asocial behavior, suggests that he has Asperger’s syndrome, sometimes referred to as autism-lite. Quoting the psychologist Simon Baron-Cohen, an expert in the field, she writes that people with Asperger’s have limited social skills, have trouble communicating, often speak oddly (their speech is characterized sometimes by jarring transitions, literal interpretations, or obliviousness to nuance), and frequently need help with the minutiae of everyday living and so are dependent on others, such as their mothers, as was the case with Perelman…And there is, of course, the genius’ disdain for lesser mortals:
Still, Perelman’s behavior, unusual as it sometimes has been, doesn’t seem all that peculiar to me. I suspect that a small part of the appeal of his story depends on the satisfaction people derive from reading about unbalanced scientists and mathematicians. Witness the popularity of A Beautiful Mind , the biography of John Nash, or The Strangest Man , the recent biography of the physicist Paul Dirac. The phenomenon is vaguely akin to the schadenfreude elicited by tabloids’ tales of celebrities’ faults and foibles.
The next year the European Mathematical Society planned to announce the award of a prize to Perelman, and he responded by saying he’d create an unpleasant scene if he was given it. According to Gromov, he believed that his work was not complete, that the judges were not qualified to assess it, and that he, not they, should decide when he should receive a prize.This disdain shouldn’t necessarily be taken as mere arrogance, however; perversely enough, there is an admixture of humility:
In 2006, Perelman turned down the prestigious Fields Medal, sometimes described as the Nobel Prize of mathematics, for his work in proving the Poincaré Conjecture. He explained, “Everybody understood that if the proof is correct then no other recognition is needed”…There is much more along strictly mathematical lines that may appeal to brainy coves like Smitty and Jeff S. As for myself, I revel in the character and his narrative, and am content to merely goggle at the math from within my personal cloud of unknowing, like a cow in a pasture watching a truck go by.
Perelman rejected the Clay prize [He turned down one million dollars! Genius? You make the call – Paco]. He reportedly said through the closed door to his spartan apartment, “I have all I want.” The comments he made after rejecting the Fields Medal probably reflect his present state of mind as well:
I don’t want to be on display like an animal in a zoo. I’m not a hero of mathematics. I’m not even that successful. That is why I don’t want to have everybody looking at me.