Welcome to the Quanta Audio Edition.

In each of these bi-weekly episodes, we bring you a story direct from the Quanta website

about developments in basic science and mathematics.

I'm Susan Vallett.

In 1994, an earthquake of a proof shook

up the mathematical world. Mathematician Andrew Wiles had finally settled Fermat's

last theorem, a central problem in number theory that had remained open for over three centuries.

An extension of this groundbreaking proof

could be making great strides toward building

a grand unified theory of math.

That's next.

Quantum Magazine is an editorially independent

online publication supported by the Simon's Foundation

to enhance public understanding of science.

Andrew Wiles' proof about Fairmont's Last Theorem in the mid-1990s didn't just enthrall mathematicians.

It made the front page of the New York Times. But to accomplish it,

whilst with help from mathematician Richard Taylor first had to prove a more subtle intermediate

statement. It was one with implications that extended beyond Fairmas puzzle. This intermediate proof

involved showing that an important kind of equation called an elliptic

curve can always be tied to a completely different mathematical object called a modular form.

Wiles and Taylor had essentially unlocked a portal between disparate mathematical realms,

revealing that each looks like a distorted mirror image of the other. Wiles and Taylor

...