Microsoft Research claims proof of the 31-year-old KLS conjecture, aided by human-directed AI
LesterMackey · x · 2026-10-22
Microsoft Research announced that researcher Xinzhi Zhang and a collaborator resolved the Kannan–Lovász–Simonovits (KLS) conjecture, a central open problem in high-dimensional geometry and probability that had resisted proof for 31 years.
The work combined new mathematical ideas with human-directed AI. Resolving KLS removes a major barrier to understanding the efficiency of randomized algorithms used throughout science and computing — a fundamental breakthrough with implications well beyond mathematics.
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