Solving a 31-year-old grand challenge in mathematics – the KLS conjecture

Microsoft researcher Xinzhi Zhang and a collaborator proved the Kannan–Lovász–Simonovits (KLS) conjecture, proposed in 1995, showing that for log-concave distributions the best hyperplane cut is within a universal constant of the best cut of any shape regardless of dimension. The proof emerged from a human-directed agentic process exploring more than 100 candidate approaches, and was followed by independent parallel proofs and a Lean 4 formalization. The authors say unguided attempts with leading AI models using a similar token budget fell short, while the success depended on both AI capabilities and researchers' mathematical judgment.