The Langlands program, described as the grand unified theory of mathematics, connects various mathematical domains including number theory and harmonic analysis. Initiated by Robert Langlands in 1967, it has evolved, leading to the geometric Langlands program in the 1990s. In 2024, Dennis Gaitsgory and colleagues made a significant breakthrough with nearly 1,000 pages of work linking geometric objects to calculus. Gaitsgory received the Breakthrough Prize in Mathematics for this achievement and reflected on the long journey of research and collaborative efforts that made it possible.
There was a very crucial step that was always a mystery. This got solved by a former graduate student of mine, [mathematician] Sam Raskin, and his graduate students in the winter of 2022.
I've always perceived it as some kind of long-term project for self-entertainment. So I obviously felt happy when it started to become clear that we could actually prove it.
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