FERMATs LAST THEOREM

Description At the age of ten, browsing through his public library, Andrew Wiles stumbled across the world's greatest mathematical puzzle. Fermat's Last Theorem had baffled mathematicians for over 300 years. But from that day, little Andrew dreamed of solving it. Tonight's HORIZON tells the story of his obsession, and how, thirty years later, he gave up everything to achieve his childhood dream.

Deep in our classroom memories lie the enduring notion that "the square of the hypotenuse is equal to the sum of the squares of the other two sides": Pythagoras's Theorem for right-angled triangles. Written down, it is also the simplest of mathematical equations: (x*x)+(y*y) = (z*z)

In 1637, a French mathematician, Pierre de Fermat said that this equation could not be true for (x*x*x) + (y*y*y) = (z*z*z) or for any equation xn + yn = zn where n is greater than 2. Tantalisingly, he wrote on his Greek text: "I have discovered a truly marvellous proof, which this margin is too narrow to contain." No one has found the proof, and for 350 years attempts to prove "F.L.T." attracted huge prizes, mistaken and eccentric claims, but met with failure.

Simon Singh and John Lynch's film tells the enthralling and emotional story of Andrew Wiles. A quiet English mathematician, he was drawn into maths by Fermat's puzzle, but at Cambridge in the '70s, FLT was considered a joke, so he set it aside.

In 1986, an extraordinary idea linked this irritating problem with one of the most profound ideas of modern mathematics: the Taniyama-Shimura Conjecture, named after a young Japanese mathematician who tragically committed suicide. The link meant that if Taniyama was true then so must be FLT.

When he heard, Wiles went after his childhood dream again. "I knew that the course of my life was changing."

For seven years, he worked in his attic study at Princeton, telling no one but his family. "My wife has only known me while I was working on Fermat", says Andrew. In June 1993 he reached his goal.

At a three-day lecture at Cambridge, he outlined a proof of Taniyama - and with it Fermat's Last Theorem. Wiles' retiring life-style was shattered. Mathematics hit the front pages of the world's press.

Then disaster struck. His colleague, Dr Nick Katz, made a tiny request for clarification. It turned into a gaping hole in the proof. As Andrew struggled to repair the damage, pressure mounted for him to release the manuscript - to give up his dream. So Andrew Wiles retired back to his attic. He shut out everything, but Fermat.

A year later, at the point of defeat, he had a revelation. - "It was the most important moment in my working life. Nothing I ever do again will be the same." The very flaw was the key to a strategy he had abandoned years before. In an instant Fermat was proved; a life's ambition achieved; the greatest puzzle of maths was no more