AI and the World's Hard Problems · Mathematics · Microsoft Research · 2026-10-21
Solving a 31-year-old grand challenge in mathematics – the KLS conjecture
Researchers resolved the Kannan–Lovász–Simonovits (KLS) conjecture, proposed in 1995 and widely regarded as one of the central open questions in high-dimensional geometry. The proof emerged from a human-directed agentic process in which AI systems explored mathematical possibilities while researchers evaluated, pruned, and redirected the search. The result establishes that simple flat cuts capture the narrowest bottlenecks of log-concave distributions within a fixed factor regardless of dimension, and it was confirmed by independent researchers followed by machine-checked formal verification.