Monstrous moonshine

Connection between representation theory of the monster group and the modular j-invariant

Borcherds proved the Conway–Norton conjecture for the Moonshine Module in 1992. He won the Fields Medal in 1998 in part for his solution of the conjecture.

Richard Borcherds' proof of the conjecture of Conway and Norton can be broken into the following major steps:

This is a generalization of the Conway–Norton conjecture, because Borcherds's theorem concerns the case where g is set to the identity.