Microsoft Research and co-author prove the 31-year-old KLS conjecture

Microsoft researcher Xinzhi Zhang and a co-author have proved the Kannan-Lovász-Simonovits (KLS) conjecture, a 31-year-old open problem in high-dimensional geometry, showing the bound holds with a universal constant independent of dimension. The proof grew out of a human-directed agentic process in which AI agents explored more than 100 candidate approaches while researchers pruned and redirected the search, and a separate unguided attempt with leading models on a comparable token budget fell short. Two other proofs appeared the same day, and a Lean 4 formalization was subsequently released.