It's all conjecture

August 24, 2006

What would cause someone to take a pass on fame, honors, a lot of money and everything he worked toward in life? After years of work, Grigory Perelman of St. Petersburg, Russia, solved one of mathematics' most tantalizing challenges - the century-old Poincare conjecture - and at the age of 40 he has apparently decided that that was enough.

At the 25th International Congress of Mathematicians, meeting in Madrid, Spain, he was announced as one of the winners of the Fields Medal, considered as great an honor in its field as the Nobel. His achievement made him eligible for a $1 million reward offered in 2000 by the Clay Mathematics Institute of Cambridge, Mass. But he wasn't in Madrid, and for now, at least, he won't be picking up the money. He has refused invitations to make a return lecture tour of the United States, and he has quit his position at the Steklov Institute in St. Petersburg.

Call it math for math's sake. The question posed by Poincare had to do with connectivity and the difference between objects that can be reconfigured as spheres and those - such as doughnuts, to use the favorite example - that cannot, because they have a hole in them. Having an answer to the conjecture doesn't have any obvious effect on human culture, or the way we live - but a lot of people suspect that someday someone will be able to put that answer to use.

Our guess is that that someone won't be Mr. Perelman. The topology of a doughnut is one thing; the topology of the human personality is considerably harder to map. But, judging by his conversation with two writers for The New Yorker, it appears that the solution is the thing, the prize, the satisfaction, the life's work. What more is there to say or do? What is money, or acclaim, next to that?

If he accepted the Fields award, he would become a public person - in his words, either a pet or a politician.

Mathematics is not a discipline based on experience the way, for instance, novel writing is, and some of its greatest practitioners have done their most important work while still very young. Mr. Perelman, at 40, is a Methuselah. He is said to enjoy mushroom hunting, an appropriately solitary activity, but in a nation of 145 million people it's one that's enjoyed by about 144 million, so that tidbit doesn't tell us much.

The birch leaves will soon be turning yellow in the woods on the level outskirts of St. Petersburg; in the mind's eye, at least, it's possible to imagine Mr. Perelman tramping about, alone with his thoughts. A life unburdened by vanity or material aspiration, or now, even ambition - just math, and a basket full of mushrooms.

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