Grigory Perelman Declines the Fields Medal

The Fields Medal has indeed gone to Grigory Perelman for his solution to the Poincaré conjecture. He’s pulled a Sartre and has declined the award. Andrei Okounkov of Princeton, Terence Tao of UCLA (age 31) and Wendelin Werner of the University of Paris-Sud in Orsay also won Fields Medals, which are awarded every four years.

Grigory Perelman, a reclusive Russian mathematician who solved a key piece in a century-old puzzle known as the Poincaré conjecture, was one of four mathematicians awarded the Fields Medal today.

But Dr. Perelman refused to accept the medal, as he has other honors, and he did not attend the ceremonies at the International Congress of Mathematicians in Madrid.

Dr. Ball, president of the International Mathematical Union, which is holding the conference, told The Associated Press that he did not think Dr. Perelman’s decision to turn down the award was intended as a snub. “I am sure he did not mean it that way,” he said.

And in the BBC:

Perelman gained international in 2002 and 2003 when he published two papers online that purported to solve the Poincare Conjecture.

The riddle had perplexed mathematicians since it was first posited by Frenchman Henri Poincare in 1904.

It is a central question in topology, the study of the geometrical properties of objects that do not change when the they are stretched, distorted or shrunk.

The hollow shell of the surface of the Earth is what topologists call a two-dimensional sphere. If one were to encircle it with a lasso of string, it could be pulled tight to a point.

On the surface of a doughnut however, a lasso passing through the hole in the centre cannot be shrunk to a point without cutting through the surface meaning that spheres and doughnuts are different from a topological point of view.

Since the 19th Century, mathematicians have known that the sphere is the only enclosed two-dimensional space with this property. But they were uncertain about objects with more dimensions.

The Poincare Conjecture says that a three-dimensional sphere is the only enclosed three-dimensional space with no holes. But proof of the conjecture has so far eluded mathematicians.