Maverick genius turns down maths 'Nobel'

James Randerson, Science Correspondent
Guardian, Tuesday August 22, 2006


In a major snub to the international maths community, one of the winners of the discipline's most coveted prize has refused the award.
The enigmatic and reclusive mathematician Grigory "Grisha" Perelman has turned down a Fields medal - an award many consider the Nobel Prize of maths.
The Russian genius shocked academics in 2002 with his claim to have solved the Poincaré conjecture. The problem, which has stumped the best mathematical minds for a century, relates to the possible shapes the universe can take.
The jury is still out over whether his proof is correct, but a consensus is developing among his peers that he is right.
"It looks pretty clear that whether or not the complete proof has been demonstrated, what Perelman did is a major breakthrough," said Arthur Jaffe, a mathematician at Harvard University.
Even by the standards of troubled maths virtuosos such as John Nash, portrayed in the film A Beautiful Mind, Dr Perelman is widely considered "unconventional".
He has already publicly refused a $1m (£520,000) prize offered by a private maths research institute in the US if his proof turns out to be correct.
"He's totally focused on mathematics," said Prof Jaffe. "He does not worry at this stage of his life about personal things like wealth and position. But he carries it to an extreme which people might describe as a little crazy"
The maths world was set abuzz in 2002 by the first instalment of Dr Perelman's groundbreaking work on the Poincaré conjecture, a problem set out by the French mathematician, physicist and philosopher Jules Henri Poincaré in 1904.
The celebrated problem concerns the geometry of multidimensional spaces and is key to the field of topology, the branch of maths that deals with shapes.
To give a flavour of it, mathematicians favour an analogy involving a sheet of rubber and a noose. One way to bundle the sheet of rubber up into a 3D shape is to fold it into the shape of a ball.
Now imagine tying the noose around the ball. By slowly tightening the noose it can be gently slid off until the noose is completely closed. This property applies to lots of basically sphere-like objects that have seemingly very different shapes, such as rugby balls and Welsh cakes.
Another way to make a 3D shape with the rubber is to roll it into a tube and bend the ends round so they meet each other and make a bagel shape. Now tighten the noose when it is passed through the hole in the bagel. No matter how you try, the only way to close the noose is to cut through the bagel.
This is a demonstration that 3D objects come in at least two types and that only the ball-shaped objects have the "noose sliding off" property. Poincaré is said to have conjectured that the same is true for 4D "hyperballs", but he could not prove it.
"It's a little bit spacey. We can't picture this so easily, but maths is all about trying to make pictures of things you can't see," said Marcus Du Sautoy, a maths professor at Oxford University who will deliver this year's Royal Institution Christmas lectures.
This year's other three Fields medals were awarded to Andrei Okounkov at Princeton University, Terence Tao at the University of California, Los Angeles and Wendelin Werner at the University of Paris-Sud in Orsay. They were handed out by the king of Spain at a ceremony in Madrid that is part of the International Congress of Mathematicians.
Between two and four of the gold-minted medals can be awarded at each ICM, which happens every four years.
Only mathematicians under the age of 40 at the beginning of the prize-giving year are eligible for the award, which is meant to encourage future endeavour.
Only one person has refused a Fields medal previously. The German mathematician Alexander Grothendieck declined his 1966 award in Moscow in protest against the Soviet Union's military intervention in Eastern Europe, though he later accepted it.
He subsequently became disillusioned with the upper echelons of the maths world and is said to live as a hermit in Andorra.