THE search is on for a reclusive Russian mathematics genius who has solved a century-old problem called the Poincaré conjecture.
Grigori Perelman, 40, known as “Grisha”, is a leading contender to win the Fields Medal, the mathematics equivalent of a Nobel prize, at the International Congress of Mathematicians in Madrid next Tuesday.He is also in line to receive a $1 million (£530,000) cash prize from an American institute for his proof of one of the seven greatest mathematical mysteries.
However, colleagues describe Dr Perelman, who is said to have resigned his post at the renowned Steklov Institute of Mathematics in St Petersburg, as an unworldly figure who may not turn up in Madrid even if he wins his profession’s top honour.
Gang Tian, a Princeton professor who has co-written a 473-page guide to Dr Perelman’s proof of Poincaré’s conjecture, said: “He certainly has no interest in material things. If he gets the Fields Medal, there is the issue of whether or not he will accept it.”
John Ball, Sedleian Professor of Natural Philosophy at The Queen’s College, Oxford, who was involved in picking this year’s Fields Medal winner as the president of the International Mathematical Union, refused to say if he had been in contact with Dr Perelman. But he noted that the Russian recluse refused an invitation to give a lecture at the congress.
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Mathematicians have been struggling with Poincaré’s conjecture since it was posed in 1904 by Jules Henri Poincaré, a French polymath. The conjecture tackles the nature of three-dimensional space. Simply stated, it posits that an object such as a pear or a banana is deformable into a sphere, whereas a bagel or American-style doughnut with a hole in the middle is not.
The British mathematician J. H. C. Whitehead claimed to have proved the Poincaré conjecture in the 1930s, but then retracted it. By 1960 Stephen Smale, now at the Toyota Technological Institute at Chicago, had proved it true in five or more dimensions. In 1983 Michael Freedman, currently at Microsoft, demonstrated that it was also true in four dimensions. Both won Fields Medals.
But mathematicians found it harder to prove it for three- dimensional space. In the 1980s Richard Hamilton of Columbia University proposed a new approach using a technique called the Ricci flow. It was this ground-breaking approach that Dr Perelman used for his proof.
Professor Tian first met Dr Perelman at New York University in the early 1990s. “He is easy to talk to on mathematics. He likes to walk a lot,” he said. “I did not find him strange.”