A math problem older than Google has been solved, with AI doing much of the searching. A Microsoft researcher proved the 31-year-old Kannan–Lovász–Simonovits conjecture after AI agents explored over 100 approaches.

Microsoft Research announced on October 21, 2026 that senior researcher Xinzhi Zhang and collaborator Zhao Song have proved the Kannan–Lovász–Simonovits conjecture, a central open problem in high-dimensional geometry proposed in 1995. Their 140-page paper "An O(1) Bound for the KLS Constant" (arXiv, Oct 1, revised Oct 4) establishes a dimension-free bound, produced through a human-directed agentic AI process in which AI systems explored roughly 100 research trajectories while the researchers pruned and redirected the search. Why it matters: KLS underpins the theory of high-dimensional sampling used in statistics, optimization and algorithms — and the proof, already corroborated by independent teams and a Lean 4 machine-checked verification, marks a milestone for AI-assisted mathematical discovery.

• Rohan Paul2026-10-22 06:11