Moonshine conjecture

mathematics

Written by

The Information Architects of Encyclopaedia Britannica

Last updated

June 30, 2026

Quick Summary

The Moonshine conjecture, a significant topic in mathematics, posits a mysterious connection between certain modular functions and the representation theory of the largest sporadic simple group, known as the "Monster".1

This conjecture was proven by mathematician Richard Ewen Borcherds, who received the Fields Medal in 1998 for his work in algebra, specifically for his contributions to vertex algebras and Kac-Moody Lie algebras. Borcherds's work also drew upon superstring theory and had profound implications for conformal field theory. Modern algebra, the broader field to which this work belongs, is concerned with the general algebraic structure of various sets, rather than specific rules for manipulating elements.12

Summary created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

2 Britannica Sources

Ask Britannica AI about this topic

Britannica doesn't have a full article on this topic, so we've curated a list of our relevant coverage.

Richard Ewen Borcherds
…used to prove the so-called Moonshine conjectures. The Moonshine conjectures asserted a mysterious connection between certain families of modular functions and the representation theory of the largest sporadic simple group (the “Monster”). Borcherds’s work also drew on superstring theory and had profound implications for conformal field theory.
Read More
…used to prove the so-called Moonshine conjectures. The Moonshine conjectures asserted a mysterious connection between certain families of modular functions and the representation theory of the largest sporadic simple group (the “Monster”). Borcherds’s work also drew on superstring theory and had profound implications for conformal field theory.
Read More