Fermat’s Last Theorem

fermat coverI was a sucker for this book, having been fascinated by the history of mathematics from an early age. As Simon Singh’s book Fermat’s Last Theorem explains, the origins of this theorem came from the early days of mathematics, with Pythagoras in Ancient Greece. Everyone knows Pythagoras’ theorem that the sum of the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides, e.g:

32 + 42 = 52

In fact, it was eventually demonstrated that there are an infinite number of triples of integers x,y,z for which

x2 + y2 = z2

Mathematicians puzzled for centuries as to whether a similar equation might be possible with higher powers of any integers, i.e. cubes, power of 4, 5, 6,…

xn + yn = zn

Pierre de Fermat was a supreme mathematician of the 17th century, who worked largely alone, rather than with colleagues. When his work was subsequently examined he was found to have made major advances to mathematics in a number of areas. In particular there was a famous note written in a margin that he had found ‘a truly marvellous proof’ that there could be no instance where such an equation was possible, yet there was insufficient space in the margin to explain it. This became a challenge to all the top mathematicians since then.

Simon Singh takes us through much of the history of mathematics in recounting the development of efforts to solve what had become known as Fermat’s Last Theorem. And a fascinating tale he tells, with potted histories of the involvement of many leading mathematicians over the centuries – including the story of the 21-year-old Frenchman Evariste Galois, who jotted down what proved to be key insights during the night before he was shot and killed in a duel early the next morning.

Finally there came the assault by Cambridge mathematician Andrew Wiles, working for some years in a solitary fashion similar to that adopted by Fermat himself. Finally, in June 1993 Wiles outlined to a packed meeting of leading mathematicians a proposed argument that demonstrated that Fermat’s Last Theorem was true. But this was only a prelude to drama, as a fault was discovered in the logic of his proof. It was not until October 1994 that Wiles and a colleague finally laid rest to centuries of speculation and completed their proof of Fermat’s Last Theorem.

Simon Singh makes the development of deep ideas in mathematics in some way accessible to us, even though we could never understand the detail. Few people do!

Featured image of Pierre de Fermat from Wikimedia Commons