Historic: Mathematicians Prove the Geometric Langlands Conjecture

15/07/2025

A team of mathematicians has achieved a major breakthrough by proving the geometric Langlands conjecture, a key part of the Langlands programme often called the "grand unified theory of mathematics." Led by Dennis Gaitsgory and Sam Raskin, the proof spans five papers and nearly 1,000 pages, and confirms deep connections between number theory, geometry, and harmonic analysis. The work, earned Gaitsgory the $3-million Breakthrough Prize.

The conjecture, first proposed in the 1980s, links algebraic geometry to representation theory through the study of Riemann surfaces. Beyond its mathematical significance, the geometric Langlands conjecture has surprising ties to physics, particularly to S-duality in gauge theories.