In 2002, the Russian claimed to have solved a century-old problem called the Poincare Conjecture.

So far, experts working to verify his proof have found no significant flaws.

There had been considerable speculation that Grigory "Grisha" Perelman would decline the award. The Russian has been described as an "unconventional" and "reclusive" genius who spurns self-promotion.

The medals were presented to three other winners at the International Congress of Mathematicians (ICM) in Madrid.

John Ball, retiring president of the International Mathematical Union, said he had travelled to St Petersburg to meet Perelman in person to try to understand his reasons for declining the award.

Professor Ball said he had spoken to Perelman of personal experiences with the mathematical community during his career that had caused him to remain at a distance.

"However, I am unable to disclose these comments in public," he said, adding: "He has a different psychological make up, which makes him see life differently."

Manuel de Leon, chairman of the ICM said: "The reason Perelman gave me is that he feels isolated from the mathematical community and therefore has no wish to appear as one of its leaders."