Researched
Geometric Langlands Proved
Gaitsgory, Raskin and collaborators prove the geometric Langlands conjecture in 2024, bridging number theory, geometry and physics.
Open in the interactive tree →The Langlands program (since 1967) is a web of conjectures linking seemingly separate fields; Wiles's proof of Fermat was a special case. On 6 May 2024 Dennis Gaitsgory, Sam Raskin and coauthors released a proof of the unramified, categorical form in five papers totaling over 1,000 pages. Gaitsgory received the 2025 Breakthrough Prize and Raskin the New Horizons Prize. The original arithmetic version (numbers instead of curves) remains open.