Last month at MIT, mathematician Grigori Perelman delivered a series of lectures with the innocuous title “Ricci Flow and Geometrization of Three-Manifolds.” In the unassuming social universe of mathematics, the equally apt title “I Claim To Be the Winner of a Million-Dollar Prize” would have been considered a bit much. Perelman claims to have proved Thurston’s geometrization conjecture, a daring assertion about three-dimensional spaces that implies, among other things, the truth of the century-old Poincaré conjecture. And it’s the Poincaré conjecture that, courtesy of the Clay Foundation, carries a million-dollar bounty. If Perelman is correct–and many in the field would bet his way–he’s made a major and unexpected breakthrough, brilliantly using the tools of one field to attack a problem in another.
There’s only one problem with this story. Perelman is almost 40 years old.
In most people’s minds, a 40-year-old man is as likely to be a productive mathematician as he is to be a major league center fielder or an interesting rock musician. Mathematical progress is supposed to occur not through decades of experience and toil but all at once, in a numinous blaze, to a born genius. Think of the young John Nash in A Beautiful Mind, discovering the Nash equilibrium in a smoky bar where his less precocious classmates think they’re just picking up coeds, or the aged mathematician in Proof who “revolutionized the field twice before he was twenty-two.”
It’s not hard to see where the stereotype comes from; the history of mathematics is strewn with brilliant young corpses. Evariste Galois, Gotthold Eisenstein, and Niels Abel–mathematicians of such rare importance that their names, like Kafka’s, have become adjectives–were all dead by 30. Galois laid down the foundations of modern algebra as a teenager, with enough spare time left over to become a well-known political radical, serve a nine-month jail sentence, and launch an affair with the prison medic’s daughter; in connection with this last, he was killed in a duel at the age of 21. The British number theorist G.H. Hardy, in A Mathematician’s Apology, one of the most widely read books about the nature and practice of mathematics, famously wrote: “No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man’s game.”