Organisers of the 25th International Congress of Mathematicians, in Madrid, said that the eccentric genius had won the coveted Fields Medal, the equivalent of a Nobel Prize, "for his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow”.

However, when the time came for the prize to be presented by King Juan Carlos in front of 3,000 leading mathematicians, Dr Perelman was nowhere to be seen.

Organisers said that he had rejected the prize, which includes a $12,000 (£6,500) stipend, saying that he felt isolated from the mathematics community.

The bearded polymath, who is affectionately known as “Grisha”, dropped out of view in 2003 shortly after publishing his solution to a conundrum that had vexed colleagues for a century.

He is said to be unemployed and living with his mother in a small flat on the outskirts of St Petersburg.

Dr Perelman was to have been anointed a true star of the mathematics world after his revolutionary work on the Poincaré conjecture, regarded as a sort of Holy Grail by mathematicians because it had resisted all previous attempts to solve it.

Posed in 1904 by the French mathematician Jules Henri Poincaré, the problem relates to the characteristics of spheres and other three-dimensional objects and is central to topography, a branch of maths that studies shapes. The solution could help theorists to figure out the shape of the universe.

The logic behind Dr Perelman’s solution, which draws from several seemingly unrelated branches of mathematics, has amazed colleagues.

Some have described it is a landmark achievement in human thought and say that it could take decades to fully understand its implications.

“Dr Perelman’s combination of deep insights and technical brilliance mark him as an outstanding mathematician,” the ICM said today. "He has had a profound impact on mathematics.”

If his solution stands the test of time, Dr Perelman would become eligible for a $1 million prize from the Clay Mathematics Institute, in Cambridge, Massachusetts, which declared it to be one of the seven most important outstanding maths problems.

But friends have said that Dr Perelman would almost certainly turn it down. Dr Perelman has said that he is not interested in fame or recognition and merely wants to be left alone.

The medal “was completely irrelevant for me", he told The New Yorker magazine in an interview published this week. "Everybody understood that if the proof is correct then no other recognition is needed.”

He said that he had retired from mathematics and implied that he had become disillusioned with the profession, which he said tolerated dishonourable people in its ranks.

Dr Perelman was felt by some to have been given insufficient credit in the work of two Chinese mathematicians trying to reach a broader theory that would encompass the Poincaré conjecture.

He is said to have left the Steklov Institute of Mathematics in St Petersburg, where he worked, on January 1 without giving any reasons.

Three other mathematicians won Fields medals today, a Frenchman, an Australian and another Russian. The medals are restricted to people under 40 years of age “to encourage future endeavour”, the organisers say.Dr Perelman, who turned 40 this year, will not be eligible again.

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