MADRID, Spain — A reclusive Russian won the math world’s highest honor Tuesday for solving a problem that has stumped some of the discipline’s greatest minds for a century — but he refused the award.
Grigory Perelman, a 40-year-old native of St. Petersburg, won a Fields Medal — often described as math’s equivalent of the Nobel prize — for a breakthrough in the study of shapes that experts say might help scientists figure out the shape of the universe.
John Ball, president of the International Mathematical Union, said that he had urged Perelman to accept the medal but Perelman said he felt isolated from the mathematics community and “does not want to be seen as its figurehead.” Ball offered no further details of the conversation.
Besides shunning the award for his work in topology, Perelman also seems uninterested, according to colleagues, in a separate $1 million prize he could win for proving the Poincaré conjecture, a theorem about the nature of multidimensional space.
The award, given out every four years, was announced at the mathematical union’s International Congress of Mathematicians. Three other mathematicians — Russian Andrei Okounkov, Frenchman Wendelin Werner and Australian Terence Tao — won Fields medals in other areas of mathematics.
They received their awards from King Juan Carlos to loud applause from delegates to the conference. But Perelman was not present.
“I regret that Dr. Perelman has declined to accept the medal,” Ball said.
Perelman’s work is still under review, but no one has found any serious flaw in it, the math union said in a statement.
The Fields medal was founded in 1936 and named after Canadian mathematician John Charles Fields. It come with a $13,400 stipend.
Perelman is eligible for far more money from a private foundation called The Clay Mathematics Institute in Cambridge, Mass.
In 2000, the institute announced bounties for seven historic, unsolved math problems, including the Poincaré conjecture.
If his proof stands the test of time, Perelman will win all or part of the $1 million prize money. That prize should be announced in about two years.
The Poincaré conjecture essentially says that in three dimensions you cannot transform a doughnut shape into a sphere without ripping it, although any shape without a hole can be stretched or shrunk into a sphere.
Proving the conjecture — an exercise in acrobatics with mindboggling imaginary doughnuts and balls — is anything but trivial. Colleagues say Perelman’s work gives mathematical descriptions of what the universe might look like and promises exciting applications in physics and other fields.
“It is very important indeed because it really gives us an insight into geometry and in particular the geometry of the space we live in,” said Oxford University math professor Marcus du Sautoy. “It does not say what the shape (of the universe) is. It just says, 'look, these are the things it could be.'”
Academics have been studying Perelman’s proof since he left the first of three papers on it on a math Web site in Nov. 2002. Normal procedure would have been to seek publication in a peer-approved journal.
Three separate teams have presented papers or books explaining the details of Perelman’s work, which draws heavily from a technique developed by another mathematician, Richard Hamilton of Columbia University. The Clay Mathematics Institute says the two men could conceivably share the Poincaré money.
Ball said he asked Perelman if he would accept that money. Perelman said that if he won, he would talk to the Clay institute.
Perelman is believed to live with his mother in St. Petersburg. Repeated calls over many days to a telephone number listed as Perelman’s went unanswered. Acquaintances refused to give out his address or the number they use to contact him, saying he did not want to talk to the media.
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