After having it recommended to me several times, I finally picked up this book when I happened to see it at our favorite local used bookstore. I think I was a bit reluctant because I previously read another book about Fermat’s Last Theorem which I didn’t like at all. I needn’t have worried; this one is fantastic. It does a wonderful job conveying the mathematical landscape surrounding this (in)famous theorem and telling a gripping story about people who also happen to be mathematicians. In fact, I think that’s one of the things I like best about it—the degree to which it brings out the essential humanity of the characters, their desires, struggles, and triumphs. I think even readers without much background in mathematics will have no trouble connecting with the characters and getting drawn into the story.
So, what is Fermat’s Last Theorem? It is the claim that the simple-looking equation
has no solutions when , , and are positive integers and is a positive integer greater than . For example, it is definitely not true that , and furthermore no equation of this type will be true, no matter what values we substitute in (as long as ). When , however, there are lots of solutions (infinitely many, in fact!), which are called Pythagorean triples since they correspond to the side lengths of right triangles. So it’s a bit surprising, perhaps, that by increasing we suddenly go from infinitely many solutions to none! Pierre de Fermat claimed he had a proof—which, famously, the margin of the book in which he was writing was too small to contain—but it took a few hundred years for someone else to finally find a proof, using lots of difficult mathematics that was a long way from being invented in Fermat’s time. (So, did Fermat really have a proof? No one knows—but probably not.)
What makes this simple claim so difficult to handle? And why is it worth writing a whole book about the story of its solution? Well, to learn the answers to those questions, you’ll have to read it!