Title: Fermat's Last Theorem
Author: Singh, Simon
Published by: Harper Perennial
Year: 2011
First published: Fourth Estate, 1997
Date reviewed: 01.20
ISBN: 078-1-84115-791-7

This is an excellent book!

Almost everyone learns Pythagoras’ Theorem at school, which says that when the squares of each of the two shorter sides of a right-angle triangle are added together, the answers equals the square of the longest side. The most familiar example is 3² + 4² = 5² (9 + 16 = 25). Written algebraically

x² + y² = z²

has a solution where x, y and z are all whole numbers –  x = 3, y = 4, and z = 5 – but there are many other solutions, an infinite number in fact.

In 1637 the mathematician Pierre de Fermat famously wrote in the margin of one of his books that he could prove that similar equations but with any power higher than 2, such as

x³ + y³ = z³ ,or x⁴ + y⁴ = z⁴

and so on had no whole-number solutions, but he didn’t have room in the margin to show the proof.

Since then mathematicians have struggled unsuccessfully to find a proof for what has turned out to be the most challenging mathematical riddle ever.

Singh tells the story of how Andrew Wiles, with help from Richard Taylor, finally cracked the problem in 1994. Singh’s account spans the history of mathematics from the early Greeks through the medieval Islamic scholars to the present day. His achievement is not only to put Fermat’s conjecture and the attempts to prove it in that broader context but to do so in a way which is consistently entertaining, even exciting. Moreover he does it with hardly any maths, so anyone without even the vaguest recollection of the maths they did at school will be able to follow the story. It even has a cliff-hanger at the end: will Wiles be able finally to plug the one gap in his proof which he has wrestled with to the point of despair?

Along the way there are the stories of many of the key figures in mathematics over the past centuries. The book shows how single-minded and dedicated the very top mathematicians have to be to explore the most arcane areas of their work. Wiles himself worked on his proof of Fermat, alone, for about seven years. His proof pushed the boundaries of modern mathematics and for the first time demonstrated a link between two obscure and specialised fields. I was struck by a quote from one current mathematician about some aspect of Wiles’ work: “If I had to understand that I’d need to take at least six months reading up and researching it before I could even start.”

So even though I came a bit late to this party reading the book more than 20 years after it was first published, I can say I thoroughly enjoyed this excellent piece of writing about a difficult but fascinating subject.