A Russian mathematician has turned down one of the discipline's most prestigious awards because he doesn't want to involve himself in self promotion. He was due to have been presented with the Fields Medal by King Juan Carlos of Spain on Tuesday this week.

Grigory Perelman published an outline of a proof for the Poincare conjecture back in 2003 as part of his work on the Geometrisation Conjecture, proposed by American mathematician William Thurston in the 1970s. This seeks to characterise all three dimensional surfaces.

So far, other researchers working to check and flesh out his idea have not found any flaws. Perelman himself has not spoken publicly about his work, saying that before the checking is completed it would be premature to do so.

John Ball, retiring president of the International Mathematical Union, told the BBC that he had gone to visit the reclusive mathematician in St Petersburg to discuss his reasons for declining the award.

He said that he wouldn't disclose Perelman's statements beyond saying that Perelman said he felt isolated from the mathematical community, and therefore had no wish to appear to be one of its leaders.

"He has a different psychological makeup that makes him see life differently," he added.

The Poincare conjecture is one of seven Millennium Prize Problems listed by the Clay Mathematics Institute, with a million dollar bounty offered for a solution. It is considered to be one of the most important questions in topology - the study of the nature of geometric structures.

The Fields Medal is awarded to mathematicians under the age of 40 who are judged to have produced "an outstanding body of work". The three other winners this year were Andrei Okounkov of the University of California, Berkeley, Terence Tao from the University of California, Los Angeles, and Wendelin Werner of the University of Paris-Sud in Orsay, France.

Andrei Okounkov said "I suppose we will have to exhibit exemplary behaviour from now on, because a lot of people will be watching."

The conjecture "asserts that a simply connected closed three-dimensional manifold is a three-dimensional sphere"*

Essentially, topology is concerned with the study of geometric shapes - whether a shape has holes in it, whether it is all connected, or can be separated into parts. Topologically speaking, there is no difference between a doughnut and a teacup, because one can deform into the other without being broken.

The Poincare conjecture just says that the same is true of a three dimensional sphere, and any other simply connected, closed three dimensional manifold.

As with many things in maths (c.f. Fermat, theorem, the last), the conjecture may be relatively easy to state, but the proof is rarely easy to find.

Bootnote

*"topology". Encyclopædia Britannica. 2006. Encyclopædia Britannica Premium Service. 23 Aug. 2006

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