Microsoft Researchers Prove the KLS Conjecture via Human-AI Collaboration

On October 22, 2026, Microsoft Research announced that its researchers Xinzhi Zhang and Zhao Song have proven the Kannan-Lovász-Simonovits (KLS) conjecture. Proposed in 1995, the conjecture states that for log-concave distributions, the difference between the flattest hyperplane cut and the optimal arbitrary-shaped cut is bounded by a universal constant independent of dimension. This problem went unsolved for 31 years, and the proof was completed through a human-guided AI collaboration approach. Apart from the official Microsoft Research announcement, there have been no follow-up reports from other sources; details of the proof, its peer review status, and further reactions from the academic community have not yet been disclosed.

AI overview of reporting · Updated 2 h前

Not enough continuous observations to show a trend yet.