In 1637 Pierre de Fermat scribbled in the margin of a copy of Diophantus that no cube can be split into two cubes, nor any higher power into two like powers, adding that he had a marvelous proof the margin was too narrow to hold. This episode follows that taunt through three centuries of partial progress by Euler, Sophie Germain, and Kummer, and into the mind of a ten-year-old Andrew Wiles who found the problem in a library book and decided to solve it.

The episode explains, in plain language, how the Taniyama-Shimura conjecture linked elliptic curves to modular forms, how Gerhard Frey and Ken Ribet showed that a counterexample to Fermat would create an impossible curve, and why that gave Wiles a respectable route to a career-killing problem. It recounts his six years of secrecy in an attic office, the cycle through Galois theory, Iwasawa t ...