I've been reading a lot about Perelman recently and felt prompted to write something about him. In case you're not aware, he was recently awarded the Fields medal which he declined. The Fields medal is the equivalent of the Nobel prize for mathematics and is awarded once in 4 years and to mathematicians under the age of 40. It is the most prestigious award in all of mathematics and because of the strict guidelines an incredibly hard award to win. He's also likely to win the Clay millenium award of a million dollars for solving one of the millenium problems - which he'll probably decline as well.
He proved the Poincare conjecture about 3 years ago and posted his papers on the internet. After people became aware of his results he was invited to lecture at various universitites in the US. I was a student in Boston at the time and went to MIT to listen to his lectures. Having studied in Boston for 5 years encountering math geniuses, freaks and prodigies was not out of the ordinary but this man was something else.
I reached MIT a bit late and sneaked in through the back door with a couple of friends. Very rarely are mathematics lectures packed to the point where people fight for standing room - this was one of those occasions. Perelman was standing in front of 5 blackboards, with every leading geometry/topology expert in the audience waiting to find a mistake in his lecture/proof and expose him. For any normal person presenting such a high profile proof in front of an audience like this would have been daunting. Not for him though.
He was dressed awkwardly. I can imagine a professor telling him to dress slightly decently as it was such a big occasion. He wore a jacket and pair of pants but underneath was a dirty zip-up jersey and a pair of old, beatup sneakers. The look on his face was one of a crazy man - eyes staring out into infinity, long fingernails and unkempt hair. If he'd stood in Harvard Square with a paper cup asking for change he would have looked like any other homeless guy hanging around. He kept staring away from the audience almost as if he was in a trance even while lecturing.
His lecture started with him writing a simple equation of about 6-7 symbols (The Ricci flow equation). That was it for the next 45 minutes. He held a wireless mike close to his lips and started talking math. Not a single slide was used, no notes and no more equations on the board. I understood almost nothing of what was going on but I could see the bigshot mathematicians leaning forward and their phd students scribbling away. Since the mike was close to his lips, one could hear him breathing heavily and he kept making a weird noise from his throat. I managed to imitate it at the back and forced a lot of other clueless people at the back into fits of laughter.
After 45 minutes of talking he proceeded to write a long equation with at least 20 different indices (I tried counting them as that was the only thing I could do to keep busy) which stretched across 3 blackboards. He paused, looked at it again and then changed a couple of symbols and then looked back and said something to the effect - I think that's it. The whole audience burst out into spontaneous applause but he seemed unruffled. He went on to give 3 lectures almost flawlessly and everyone believed he'd proved what he claimed.
He has a reputation of being a bit crazy. He loves to walk and once on his way to a conference met another participant at the airport. The other guy asked him how he was going and Grisha replied he was going to walk. The other guy walked along with him and 8 hours later, they reached the conference venue! He's retired from mathematics now and lives with his mother off the money he saved from his visiting positions in the US about ten years ago.
It's a bit sad to see how a lot of other mathematicians have tried to plagiarise and build on his work for the sake of tenure, prestige or money. But it's reassuring to know that among the math community it's accepted that he's the one who proved it and it's understandable why he's refused to accept an award in such circumstances. The Chinese mathematicians who claim to have proved it (using his ideas) should take a cue from him. He cared only about proving it to his own satisfaction and that was it. The rest can fight for all they want but he's going to sit happily in St Petersburg knowing he proved one of the hardest problems in all of mathematics - even Terrance Tao (one of the other Fields medalists) claims Perelman's work was easily the most important mathematical breakthrough in the last 10 years.