Grigory Perelman, the Russian who seems to have solved one of the hardest problems in mathematics, the Poincaré conjecture, has declined one of the discipline’s top awards. Dr Perelman was to have been presented with the prestigious Fields Medal by King Juan Carlos of Spain, at a ceremony in Madrid on Tuesday. 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 Fields Medals are commonly regarded as mathematics’ closest analog to the Nobel Prize (which does not exist in mathematics), and are awarded every four years by the International Mathematical Union to one or more outstanding researchers. “Fields Medals” are more properly known by their official name, “International medals for outstanding discoveries in mathematics.”
He is possibly the cleverest person on the planet: an enigmatic and reclusive genius who shocked the academic world with his claim to have solved one of the hardest problems in maths. He is tipped to win a “maths Nobel” for his work on possible shapes of the universe. But rumours are rife that the brilliant Russian mathematician will spurn the greatest accolade his peers can bestow. Since Grigory “Grisha” Perelman revealed his solution in 2002 to a century-old maths problem, it has been subjected to unparalleled scrutiny by the best academic minds. But no one has been able to find a mistake and there is a growing consensus that he has cracked the problem. Little is known about Dr Perelman, who refuses to talk to the media. He was born on June 13 1966 and his prodigious talent led to his early enrolment at a St Petersburg school specialising in advanced mathematics and physics. At the age of 16, he won a gold medal with a perfect score at the 1982 International Mathematical Olympiad, a competition for gifted schoolchildren. After receiving his PhD from the St Petersburg State University, he worked at the Steklov Institute of Mathematics before moving to the US in the late 80s to take posts at various universities. He returned to the Steklov about 10 years ago to work on his proof of the universe’s shape. The maths world was set humming in 2002 by the first instalment of his ground-breaking work on the problem which was set out by the French mathematician, physicist and philosopher Jules Henri Poincaré in 1904. The conjecture, which is difficult for most non-mathematicians even to understand, exercised some of the greatest minds of the 20th century.
It concerns the geometry of multidimensional spaces and is key to the field of topology. Dr Perelman claims to have solved a more general version of the problem called Thurston’s geometrisation conjecture, of which the Poincaré conjecture is a special case. “It’s a central problem both in maths and physics because it seeks to understand what the shape of the universe can be,” said Marcus Du Sautoy at Oxford University, who will be giving this year’s Royal Institution Christmas Lectures. “It is very tricky to pin down. A lot of people have announced false proofs of this thing.” The obsession with the problem, shared by several great mathematicians, has been dubbed Poincaritis. But Dr Perelman seems to have succeeded where so many failed. “I think for many months or even years now people have been saying they were convinced by the argument,” said Nigel Hitchin, professor of mathematics at Oxford University. “I think it’s a done deal.”
In mathematics, the Poincaré conjecture is a conjecture about the characterization of the three-dimensional sphere amongst three-dimensional manifolds. Loosely speaking, the conjecture surmises that if a closed three-dimensional manifold is sufficiently like a sphere in that each loop in the manifold can be tightened to a point, then it is really just a three-dimensional sphere. The analogous result has been known to be true in higher dimensions for some time. The Poincaré conjecture is widely considered one of the most important questions in topology. It is one of the seven Millennium Prize Problems for which the Clay Mathematics Institute is offering a $1,000,000 prize for a correct solution. After nearly a century of effort by mathematicians all over the world, a series of papers made available in 2002 and 2003 by Grigori Perelman, following the program of Richard Hamilton, produced an outline for a solution. Following Perelman’s work, several groups of mathematicians have produced works filling in the details for the full proof, though review by the mathematics community is ongoing.
Grigori Perelman proved the Poincare conjecture and then refused a million dollar prize (the Millennium Prize). He is the only mathematician who has declined the Fields medal.