Fermat's Last Theorem

Simon Singh

Fermat's last theorem is one of the most famous stories from the world of maths. Here's a brief recap, in case it has up till now passed you by. Everyone knows the equation

x² + y² = z²

has many whole number solutions for x, y and z. In fact, we've all sat in maths lessons and used the equation to work out the lengths of the sides of a right-angled triangle. But in 1637 the amateur number theorist Pierre de Fermat made the extravagant claim that there were no whole number solutions to the equation

xⁿ + yⁿ = zⁿ

where n > 2. He also commented in the margin of his notes "I have a marvellous proof for this, which this margin is too small to contain". You get the impression Fermat must have been something of "dog ate my homework" kind of a boy back when he was at school. After his death this claim, his last "theorem", was taken up as a challenge by fellow mathematicians. The decades passed and the theorem was proved for n=3 and n=4. In 1828, the theorem was proved for n=5 and in 1840 it was proved for n=7. By 1983 it had been proved for all values of n up to a million but, since the problem in theory stretched away into infinity, it was really no nearer to being proved.

So far, so interesting and Simon Singh moves the story on well enough, with entertaining digressions into the lives and times of the mathematicians who worked on the problem through the ages. But as in all good thrillers a solution is required and at this point Andrew Wiles, a senior mathematician at Cambridge, enters the story. Wiles cracked the problem in 1993 having worked on it secretly for seven years. But it's just at this point the book begins to fail. To be fair to Simon Singh there probably is no way to explain in simple terms the nature of Wiles' proof and Singh doesn't really try. But Singh also has a problem in Wiles himself. Wiles is clearly not quite mad enough to be truly interesting nor quite normal enough to be someone the ordinary reader can relate to and warm to.

I had another problem with Singh's approach. On the last but one page, Singh addresses in a couple of quick paragraphs the question I'd been fidgetting over for the last 300 years (and 300 pages) of the story. I won't say what I'm talking about but read it and tell me whether you agree that it's strange to relegate almost to a footnote the puzzle which I think is at the heart of the Fermat story.