MADRID, Spain — A reclusive Russian genius won the Fields Medal on Tuesday, an award given by a University of Toronto-based institute that is named for a Canadian mathematician and considered the math world's highest honour, but Grigory Perelman shunned the ceremony and stayed out of the spotlight.

The 40-year-old scientist was cited for solving the 100-year-old Poincare conjecture, a conundrum concerning the nature of three-dimensional space that experts said might help determine the shape of the universe.

Three other scholars won Fields Medals, named after Canadian mathematician John Charles Fields. They carry a $13,400 US stipend each and are often described as math's equivalent of the Nobel prize. The other winners accepted their prizes from Spain's King Juan Carlos amid rapturous applause at the International Congress of Mathematicians in Madrid.

But Perelman stayed home in St. Petersburg, Russia, said Alexander Abramov, a member of the Russian Education Academy.

Not only that, one of the few people in contact with the scientist said Perelman, may forsake math altogether as his main subject of research.

Serge Rukshin, Perelman's former teacher and scientific supervisor, said Perelman apparently has no interest in medals or money - only in knowledge.

"Grigory is a devoted scientist in the pure sense of the word. He believes that the most important thing is that the problem is solved," Rukshin said in an interview in St. Petersburg.

Perelman is eligible for far more money from a private foundation called The Clay Mathematics Institute in Cambridge, Mass. for proving the Poincare conjecture, which has fascinated - and defeated - some of the world's most brilliant minds since it was proposed in 1904.

Perelman, who has a beard, long stringy hair and piercing blue-green eyes, could not be reached for comment.

He 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 does not want to talk to the news media

Abramov said in Moscow he spoke with Perelman by phone and had the impression he may completely give up on math.

"Now I'm most worried about how he feels and what will happen to him. He is a brilliant mathematician."

"Such talents should not go away," Abramov said.

John Ball, president of the International Mathematical Union that is holding the convention in Madrid, said Perelman is still considered a Fields medalist.

"I regret that Dr. Perelman has declined to accept the medal," he said.

Ball said later he met with Perelman in St. Petersburg in June to tell him he had won a Fields medal and to try and persuade him to accept it. But Perelman said he felt isolated from other mathematicians and refused the medal because "he does not want to be seen as its figurehead," Ball said.

Ball said he asked Perelman if he would accept the money. Perelman said if he won, he would talk to the Clay institute.

The three other winners were Russian Andrei Okounkov, Frenchman Wendelin Werner and Australian Terence Tao.

In 2000, the institute announced bounties for seven historic, unsolved math problems, including the Poincare 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. Until then academics can challenge Perelman's work.

That work draws heavily from a technique developed by another mathematician, Richard Hamilton of Columbia University. The Clay Mathematics Institute said the two men could conceivably share the Poincare money.

The Poincare conjecture is key to the field of topology, which studies shapes. It basically states 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.

Perelman spent eight years wrestling with it, left the first of three short papers with what he called proof on an Internet archive in Nov. 2002 and gave a lecture tour on it at top U.S. universities. Then he returned to Russia and all but vanished, sitting back to let the math world sink its teeth into his work.

Experts around the world, who did not even know Perelman was working on the theorem, have been scrutinizing the proof papers since. The review continues - but no one has found a serious flaw, the International Mathematical Union said.

Colleagues said Perelman's work gives mathematical descriptions of what the universe might look like and promises exciting applications in physics and other fields.

There is some controversy, however. Two Chinese scientists who have been fleshing out Perelman's extremely abbreviated and technical work have said is they who added new ideas and actually completed the Poincare proof.