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Mathematical dilemma is solved at last ... perhaps

"It's just so damn complicated, [Perelman] said. It really can take two or three years to certify the thing."

Keith Devlin, a mathematician from Stanford University in California

One of the seven great unsolved mysteries of mathematics may have been cracked by a reclusive Russian who is not remotely interested in the million-dollar prize his solution could win him.

The Poincare Conjecture involves the study of shapes, spaces and surfaces and makes predictions about the topology of multi-dimensional objects.

Basically, it says that a three-dimensional sphere can be used in an analogous way to describe higher-dimensional objects that are impossible to visualize.

Since Henri Poincare suggested the theorem in 1904, some of the greatest mathematicians of the 20th century have struggled to prove it either right or wrong.

All have failed. But now the world of maths is buzzing with the news that an answer might at long last have been found.

Dr Grigori Perelman, from the Steklove Institute of Mathematics at the Russian Academy of Sciences in St Petersburg, has published two papers offering a solution to a larger-scale problem called the Geometrization Conjecture.

This is also concerned with geometry, and experts say that contained within it is proof that the Poincare Conjecture works.

If Perelman can satisfy his peers that this is the case, he stands to win a US$1 million dollar cash prize from the Clay Mathematics Institute in the US.

The Institute is offering million dollar prizes for solutions to each of the mathematical conundrums it calls the Seven Millennium Problems.

But there is a more fundamental problem the general community of mathematicians needs to solve first. Perelman does not seem to be interested.

Dr Keith Devlin, a leading mathematician from Stanford University in California, explained: "He's very reclusive, and won't talk to anyone. He's shown no indication of publishing this as a paper, and he's shown no interest in the prize whatsoever.

"Has it been proved? We don't know, but there's good reason to think it has been. My guess is that in about 12 months people will start to say okay, this is right, but there's not going to be a golden moment."

Perelman published his two papers in November 2002 and March last year.

A third is yet to be published.

If the conjecture was proved it would have profound ramifications, he told the British Association Festival of Science at the University of Exeter.

Scientists working on the frontiers of cosmology and physics frequently deal with hyperdimensions. A solution to the Poincare Conjecture would greatly increase their understanding of the shape of the universe.

"It can't fail to have enormous implications; it will just be huge."

He said solving mathematical problems such as the Poincare Conjecture was more like writing a story than doing a sum, which was why it took so long.

"It's just so damn complicated, he said. It really can take two or three years to certify the thing."

Proving the Poincare Conjecture would be the first great mathematical breakthrough since Andrew Wiles solved Fermat's Last Theorem in 1994.

This year, Professor Louis de Branges de Bourcia, from Purdue University in the US, claimed to have proven another of the Millennium Problems called the Riemann Hypothesis.

The hypothesis is a 150-year-old theory about prime numbers -- numbers that divide only by one and themselves and are considered the atoms of arithmetic.

De Branges claimed to have confirmed a conjecture made by the German mathematician Bernhard Riemann in 1859 about the way prime numbers were distributed.

But, unlike in the case of Poincare Conjecture, the worlds mathematicians are becoming increasingly convinced that he has got it wrong.

Marcus du Sautoy, Professor of Mathematics at Oxford University, said: "The mathematical community is skeptical whether the methods of Louis de Branges are capable of proving the Riemann Hypothesis."

If de Branges turned out to be right, it would have a dramatic impact on both global business and national security.

Encrypted codes are based on the randomness of prime numbers. If a system could be found that made them predictable, no secret would be safe.

"What mathematics has been missing is a sort of maths prime spectrometer, like the machine chemists use to tell them what things are made of," said du Sautoy. "If we had something like that it would bring the world of e-commerce to its knees overnight."
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