Perelman's proof

He came once, he explained things, and that was it... Anything else was superfluous.

That's Grigory Perelman. He found a proof for the Poincaré conjecture, but now they can't find him:

Three years ago, a Russian mathematician by the name of Grigory Perelman, a k a Grisha, in St. Petersburg, announced that he had solved a famous and intractable mathematical problem, known as the Poincaré conjecture, about the nature of space.

After posting a few short papers on the Internet and making a whirlwind lecture tour of the United States, Dr. Perelman disappeared back into the Russian woods in the spring of 2003, leaving the world's mathematicians to pick up the pieces and decide if he was right.

Now they say they have finished his work, and the evidence is circulating among scholars in the form of three book-length papers with about 1,000 pages of dense mathematics and prose between them.

As a result there is a growing feeling, a cautious optimism that they have finally achieved a landmark not just of mathematics, but of human thought.
.....
Quoting Poincaré himself, [Dr. Shing-Tung Yau of Harvard] said, "Thought is only a flash in the middle of a long night, but the flash that means everything."

But at the moment of his putative triumph, Dr. Perelman is nowhere in sight. He is an odds-on favorite to win a Fields Medal, math's version of the Nobel Prize, when the International Mathematics Union convenes in Madrid next Tuesday. But there is no indication whether he will show up.

Read the rest (free registration). See also here:

Mathematicians have been struggling with Poincaré's conjecture since it was posed in 1904 by Jules Henri Poincaré, a French polymath. The conjecture tackles the nature of three-dimensional space. Simply stated, it posits that an object such as a pear or a banana is deformable into a sphere, whereas a bagel or American-style doughnut with a hole in the middle is not.

The British mathematician J. H. C. Whitehead claimed to have proved the Poincaré conjecture in the 1930s, but then retracted it. By 1960 Stephen Smale, now at the Toyota Technological Institute at Chicago, had proved it true in five or more dimensions. In 1983 Michael Freedman, currently at Microsoft, demonstrated that it was also true in four dimensions. Both won Fields Medals.

But mathematicians found it harder to prove it for three-dimensional space. In the 1980s Richard Hamilton of Columbia University proposed a new approach using a technique called the Ricci flow. It was this ground-breaking approach that Dr Perelman used for his proof.

(Thanks: MK.)