The Poincaré conjecture is solved.

Russian topologist Grigory Perelman seemed to be playing to type, or stereotype, when he refused to accept the highest honor in mathematics, the Fields Medal, for work pointing toward the solution of Poincaré’s conjecture, a longstanding hypothesis involving the deep structure of three-dimensional objects. He left open the possibility that he would also spurn a $1 million prize from the Clay Mathematics Institute in Cambridge, Mass.

By George Johnson

LONG before John Forbes Nash, the schizophrenic Nobel laureate fictionalized onscreen in “A Beautiful Mind,” mathematics has been infused with the legend of the mad genius cut off from the physical world and dwelling in a separate realm of numbers. In ancient times, there was Pythagoras, guru of a cult of geometers, and Archimedes, so distracted by an equation he was scratching in the sand that he was slain by a Roman soldier. Pascal and Newton in the 17th century, Gödel in the 20th — each reinforced the image of the mathematician as ascetic, forgoing a regular life to pursue truths too rarefied for the rest of us to understand.

Last week, a reclusive Russian topologist named Grigory Perelman seemed to be playing to type, or stereotype, when he refused to accept the highest honor in mathematics, the Fields Medal, for work pointing toward the solution of Poincaré’s conjecture, a longstanding hypothesis involving the deep structure of three-dimensional objects. He left open the possibility that he would also spurn a $1 million prize from the Clay Mathematics Institute in Cambridge, Mass.

Unlike Brando turning down an Academy Award or Sartre a Nobel Prize, Dr. Perelman didn’t appear to be making a political statement or trying to draw more attention to himself. It was not so much a medal that he was rejecting but the idea that in the search for nature’s secrets the discoverer is more important than the discovery.

“I do not think anything that I say can be of the slightest public interest,” he told a London newspaper, The Telegraph, instantly making himself more interesting. “I know that self-promotion happens a lot and if people want to do that, good luck to them, but I do not regard it as a positive thing.”

Mathematics is supposed to be a Wikipedia-like undertaking, with thousands of self-effacing scriveners quietly laboring over a great self-correcting text. But in any endeavor — literature, art, science, theology — a celebrity system develops and egos get in the way. Newton and Leibniz, not quite content with the thrill of discovering calculus, fought over who found it first.

As the pickings grow sparser and modern proofs sprawl in size and complexity, it becomes that much harder, and more artificial, to separate out a single discoverer. But that is what society with its accolades and heroes demands. The geometry of the universe almost guarantees that a movie treatment heralding Dr. Perelman is already in the works: “Good Will Hunting” set in St. Petersburg, where he lives, unemployed, with his mother, or a Russian rendition of “Proof.”  full article