The original version of this story appeared in Quanta Magazine.
In 1994, an earthquake of a proof shook up the mathematical world. The mathematician Andrew Wiles had finally settled Fermat’s Last Theorem, a central problem in number theory that had remained open for over three centuries. The proof didn’t just enthral mathematicians—it made the front page of The New York Times.
But to accomplish it, Wiles (with help from the mathematician Richard Taylor) first had to prove a more subtle intermediate statement—one with implications that extended beyond Fermat’s puzzle.
This intermediate proof involved showing that an important kind of equation called an elliptic curve can always