Fermat’s Last Theorem

It looks like it will be Math Thursday today on this blog so it seems like a good time to post the story about the quest to prove Fermat’s last theorem.

In 1963 a ten-year-old boy borrowed a book from his local library in Cambridge, England. The boy was Andrew Wiles, a schoolchild with a passion for mathematics, and the book that had caught his eye was The Last Problem by the American mathematician Eric Temple Bell. The book recounted the history of Fermat’s Last Theorem, the most famous problem in mathematics, one which had baffled the greatest minds on the planet for over three centuries.

There can be no problem in the field of physics, chemistry or biology that has so vehemently resisted attack for so many years. Indeed E.T. Bell predicted that civilisation would come to an end as a result of nuclear war before Fermat’s Last Theorem would ever be resolved. Nonetheless young Wiles was undaunted. He promised himself that he would devote the rest of his life to addressing the ancient challenge.

What is his famous equation?

The mathematical short-hand for this family of insoluble equations is:

xn + yn = zn , where n is any number greater than 2.

According to Fermat, none of these equations could be solved, and he noted this in the margin of his Arithmetica. To back up his theorem he had developed an argument or mathematical proof, and following the first marginal note he scribbled the most tantalising comment in the history of science:

Cuius rei demonstrationem mirabilem sane detexi hanc marginis exiguitas non caperet.

I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.