Monday, April 19, 2010

Perelman and the Poincaré Conjecture

A riveting account of the life and mathematical achievements of the recluse Grigory (Grisha) Perelman, who recently cracked the Poincaré Conjecture:
Masha Gessen’s Perfct Rigor is a fascinating biography of Grigory (Grisha) Perelman, the fearsomely brilliant and notoriously antisocial Russian mathematician. Perelman proved the Poincaré Conjecture, one of mathematics’ most important and intractable problems, in 2002—almost a century after it was first posed, and just two years after the Clay Mathematics Institute offered a one-million-dollar prize for its solution.


Up until March of this year, there remained one more chapter to the Perelman saga. Would he accept the one-million-dollar prize promised by the Clay Mathematics Institute for solving one of the seven so-called Millennium Problems? While the rules say that a proof must appear in a peer-reviewed mathematics journal (not just in an Internet posting), the mathematicians mentioned above have published papers in such journals expounding and amplifying the proof. Surely Perelman deserves the prize, which he was finally and officially offered on March 18.

Five days later, on March 23, Perelman rejected the Clay prize. 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."

Some might argue that monetary awards for mathematical work are inappropriate, or that the Poincaré Conjecture is of little practical value and not worth the one-million-dollar prize. The aesthetic and epistemic value of the proof is priceless, however, and it may eventually yield more earthly consequences as well. As for the size of the award—how many no-name hacks are there on Wall Street who make a million dollars or more not just once but every year, and contribute exactly what? Whether Perelman has practical need for the money or not, he could use it to help support his mother or mathematicians of his liking, or to advance the kind of education conceived by Andrei Kolmogorov, or for some purpose only he could imagine. Reconsider your decision, Grisha.

1 comment:

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