Professor puzzles near pinnacle of 'maths Everest': British academic dithers over QED for the mother of all theorems

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The Independent Online
ONE YEAR ago Andrew Wiles, a shy British maths professor at Princeton, amazed colleagues by announcing that he had solved the world's most famous and tantalising maths problem, known as Fermat's Last Theorem. He went off to his study to prove his method worked, but a year later there is no QED, only silence.

Some of his colleagues are beginning to wonder whether he can do it because they found a snag in his proof. Dr Wiles does not want to talk about it. He has been spotted at the Princeton swimming pool and is reported to be in good spirits. He is working alone on the puzzle and, out of courtesy, his colleagues do not ask how the work is going.

The theorem is primarily of symbolic significance and was created by the 17th-century French mathematician Pierre de Fermat, who wrote it in the margin of his copy of Arithmetics, by Diophantus, a third-century Greek mathematician. Fermat apparently intended to include the proof sequence, but the margin was too small. Disarmingly simple to state, the theorem says that in the equation x to the power of n plus y to the power of n equals z to the power of n - there are no whole-number solutions where n is greater than 2. Ever since, mathematicians have been trying to supply the missing proof.

Andre Weil, a mathematician at Princeton's Institute for Advanced Study, described the theorem as a mathematical Everest. 'I am willing to believe (Dr Wiles) has had some good ideas,' he said in an interview in Scientific American. 'Proving Fermat's theorem is like climbing Everest. If a man falls short of it by 100 yards, he has not climbed the mountain.'

Dr Wiles submitted his 200-page solution to the journal Inventiones Mathemat icae, and the manuscript was sent out for a peer-group review which revealed the gap in the reasoning. Mathematicians are praising Dr Wiles's work so far. 'The whole wonderful idea is just as good as it was a year ago,' Nicholas Katz, of Princeton, told the New York Times. 'Everyone thought Dr Wiles' idea would work. The only thing that makes one less optimistic now is the fact that time is passing.'

(Photograph omitted)