The world of mathematics is in uproar over rumours that its most prestigious prize will be turned down next week by one of its brightest stars.
The Fields Medal, the equivalent of a Nobel Prize in mathematics, is awarded every four years to young mathematicians who have made the biggest impact in their fields. It is due to be presented by the King of Spain in a ceremony in Madrid on Tuesday 22 August.
But Gregori Perelman, who has been widely tipped to receive it, has resigned his post at the Steklov Institute of Mathematics in St Petersburg, Russia, and gone to ground. 鈥淣obody knows where he is,鈥� says Marcus du Sautoy, a mathematician at Oxford University in the UK. Perelman is thought to have become disillusioned with mathematics and disassociated himself from the field.
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Perelman achieved fame in the mathematics world for his work on the Poincar茅 Conjecture, one of topology鈥檚 most celebrated problems. The conjecture, conceived by the French mathematician Henri Poincar茅 in 1904, relates to the question of whether it is possible to deform a holed doughnut into a sphere by bending and stretching it 鈥� without cutting or tearing it.
It turns out that there is no way to remove the 鈥渉ole鈥� in the doughnut and so it cannot be turned into a sphere. However, any shape that has no holes can always be deformed into a sphere. The Poincar茅 Conjecture and a more general problem, called the Thurston Geometrization Conjecture, assert that the same is true for shapes in higher dimensions.
Unprecedented refusal
Perelman鈥檚 proof of both problems, published in 2002, received widespread admiration for its inventiveness, even though mathematicians have yet to officially pronounce on its validity. 鈥淭he consensus is that it is probably correct,鈥� says du Sautoy.
The Poincar茅 Conjecture is also famous as one of the Millennium Prize problems established by the Clay Mathematics Institute in Boston in 2000. The Institute is offering a prize of $1 million to the first correct proof. 鈥淧erelman doesn鈥檛 seem to be interested in medals or money,鈥� du Sautoy notes.
A refusal of a Fields Medal would be unprecedented. In 1966, the German mathematician Alexander Grothendieck refused to pick up his award in Moscow in protest against the Soviet Union鈥檚 military intervention in Eastern Europe, although he did later accept it. But Grothendieck also became disillusioned with mathematics and left the field. He is now believed to be living as a hermit in Andorra.
