Fermats Last Theorem

Fermat's Last Theorem.

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. 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.

BFermat's Last Theorem is the name of the statement in number theory that: It is impossible to separate any power higher than the second into two like powers, or, more precisely: If an integer n is greater than 2, then the equation a n + b n = c n has no solutions in non-zero integers a, b, and c. In 1637 Pierre de Fermat wrote, in his copy of Claude-Gaspard Bachet's translation of the famous Arithmetica of Diophantus, "I have a truly marvellous proof of this proposition which this margin is too narrow to contain." (Original Latin: "Cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.") Fermat's Last Theorem is strikingly different and much more difficult to prove than the analogous problem for n = 2, for which there are infinitely many integer solutions called Pythagorean triples (and the closely related Pythagorean theorem has many elementary proofs). That the problem's statement is understandable by schoolchildren makes it all the more frustrating, and it has probably generated more incorrect proofs than any other problem in the history of mathematics. No correct proof was found for 357 years, until one was finally published by Andrew Wiles in 1995. The term "Last Theorem" resulted because all the other theorems and results proposed by Fermat were eventually proved or disproved, either by his own proofs or by those of other mathematicians, in the two centuries following their proposition. Although it is a theorem now that it has been proved, the status of Fermat's Last Theorem before then, in spite of the name, was that of a conjecture, a mathematical statement whose status (true or false) had not been conclusively settled.

Fermat's Last Theorem is the most famous solved problem in the history of mathematics, familiar to all mathematicians, and had achieved a recognizable status in popular culture prior to its proof. The avalanche of media coverage generated by the resolution of Fermat's Last Theorem was the first of its kind, including worldwide newspaper accounts and various popularizations in books and a BBC Horizon programme (which aired in the United States as a PBS NOVA special, The Proof).

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