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# Fermat's Last Theorem (BBC Horizon)

In 1637, Pierre de Fermat, proposed a theorem, in Number Theory, stating that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two. Fermat claimed to have a proof which was never provided, thus back in 1637 this was merely a conjecture.

In spite of Fermat's last theorem being quite famous, and anyone who could offer a successful proof would instantly be recognized world wide, and whose name would be famous in mathematics forever, however 358 years later no one had yet offered a proof with any significant weight until 1995. Countless mathematicians had secretly or not so secretly been working on this holy grail without success. In fact the Guinness Book of World Records reported Fermat's last theorem as one of the "most difficult math problems."

After 9 years of work, struggle, and setbacks, British mathematician Andrew Wiles, successfully submitted his revised proof of Fermat's Last Theorem, who later became Sir Andrew Wiles after being Knighted for his intellectual achievements.

Simon Singh and John Lynch's film (BBC 1996) 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.

Then, 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.

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