STEVE INSKEEP, host:
Math's version of the Nobel Prizes were given out this morning in Spain. The math awards are called The Fields Medals, and this morning we have the story of one winner who did not show up for the ceremony.
He's a reclusive Russian mathematician named Grigory Perelman. He's credited with helping solve the Poincaré Conjecture, a famous math problem about spheres and doughnuts.
NPR's David Kestenbaum reports.
DAVID KESTENBAUM reporting:
This was a math problem that needed a lighthouse because everyone who came near got shipwrecked. Henri Poincaré proposed the problem in 1904, and for a century people tried to solve it.
Mr. JOHN MORGAN (Chair of Department of Mathematics, Columbia University): And nobody had any luck.
KESTENBAUM: This is John Morgan, chair of the math department at Columbia University.
Mr. MORGAN: There were many failed attempts. There were always false proofs floating around. There's even an article from the 1960s entitled How Not to Prove the Poincaré Conjecture giving all the standard mistakes that the author and others had made.
KESTENBAUM: Then in 2002, a Russian mathematician published a short paper online promising a solution. Morgan's reaction was, yeah, yeah, yeah - until the Russian's second paper appeared.
His name was Grigory Perelman. He'd studied in the United States, and he made a short trip back to explain his ideas.
Mr. MORGAN: When he was first here, he had the long fingernails. When I met him in 2003, the only remnant of that was a long thumbnail. And he would use it to stroke his beard to give him sort of a slightly otherworldly effect.
KESTENBAUM: Poincaré's problem, called the Poincaré Conjecture, has to do with how shapes are defined. For instance, you can describe a ball this way.
Mr. MORGAN: If you draw a loop on the surface of a ball which you can actually see - if you take any loop, you can shrink it down to a point on the sphere; just think about shrinking it up to the North Pole.
KESTENBAUM: That is not true with a doughnut, however. You're shrinking loop could get stuck around the hole.
Poincaré's Conjecture was that the same should hold true if you add a dimension. So however strange or twisted the shapes, anything without a hole in it had to be a sphere; you could shrink any loop on its surface to a point.
Now no one can visualize what a four-dimensional universe would look like, which made proving or disproving the conjecture difficult. Mathematicians made progress though, using an unusual idea that seemed more physics than math. An equation that showed how these complicated shapes might smooth themselves out and be seen for what they really were.
But serious problems remained - the mathematical equivalent of black holes popping up in the equations - until Grigory Perelman came along.
Mr. MORGAN: He worked for five or seven years incredibly intensively on this, and he's incredibly brilliant and powerful. And he did something that I don't think anybody else could have done.
KESTENBAUM: Morgan says there are probably fewer than 20 people who understand the proof. He's one of them, and with a colleague he wrote it out in full detail. It fills 473 pages.
Morgan was in e-mail contact with Perelman, but slowly that stopped. A British paper tracked Perelman down in St. Petersburg the other week. He was living at his mother's house, and he told the paper, quote, I do not think anything that I say can be of the slightest public interest.
Jim Carlson, president of the Clay Mathematics Institute, says this story reminds him that great things have sometimes come from long periods of quiet thought.
Mr. JIM CARLSON (President, Clay Mathematics Institute): It's a little bit like, you know, what Newton did during the plague years. All of his great work came when he was isolated in some country manor trying to not catch the plague.
KESTENBAUM: The Clay Institute offered a million dollar prize to encourage someone to solve the Poincaré Conjecture, but the man in the spotlight doesn't seem very interested in money.
David Kestenbaum, NPR News.
MONTAGNE: The man who first posed Poincaré's Conjecture believed that intuition was more crucial to discovery than logic. You can read about Henri Poincaré at npr.org.