Andrew Wiles shocked the world when he broke out of his reclusive studies at Princeton to reveal that he had solved one of the world’s most notorious mathematical problems: Fermat’s Last Theorem (FLT). This theorem (or conjecture, as it had not been proved yet) has haunted mathematicians for over three centuries. It was the last puzzle left by Fermat, who claimed he had a proof for which “this margin is too small to contain.”
The problem itself is simple, and any grade school child can understand it. FLT states that whole number solutions to the equation x^n + y^n = z^n do not exist for n greater than 2. It seemed simple at first, and all the best mathematicians in the world threw all their techniques at it without success. Almost every mathematician you have ever heard of–Gauss, Euler, and Fourier, to name a few–have tried and knelt in submission to FLT.
The key to Wiles’s proof is the use of the Taniyama-Shimura conjecture. This conjecture allowed Wiles to attack the problem from a different angle: if he showed the T-S conjecture to be true, he would show FLT to be true. The T-S conjecture has to do with elliptic curves and modular forms. Basically, the FLT equation can be rearranged to an elliptic equation that is so weird that no solutions can possibly exist if the T-S conjecture is true. Thus, the T-S conjecture implies that FLT is true.
The book Fermat’s Enigma, by Simon Singh, details the struggles and triumphs of Wiles’s eight years of mounting a proof for FLT. The story is written with a historical eye, revealing of bits of mathematical history whenever Wiles stands upon the shoulders of giants to further his proof. The narrative is also gripping, and you will find yourself immersed in the realm of mathematical genius and perspiration as you read about Wiles’s risky endeavor on wasting eight years proving a theorem that was possibly out of reach.
Even if you’re not a big math fan, you will find Fermat’s Enigma to be well written, accessible, and exciting.
