微软研究者证明 31 年悬而未决的 KLS 猜想
原标题：Solving a 31-year-old grand challenge in mathematics – the KLS conjecture
AI 摘要
微软研究院研究员 Xinzhi Zhang 与合作者证明了悬置 31 年的 KLS 猜想，该猜想是高维几何与概率论的核心开放问题，对统计、优化、算法和计算机科学均有影响。证明采用人类主导、AI 代理辅助的研究流程，AI 探索了 100 多种候选路径，最终由研究者确定方向并完成论证。结果确立了 log-concave 分布的维度无关几何原理，并获多个独立研究组同日发布的证明及 Lean 4 形式化验证确认。
正文节选
Microsoft researcher and collaborator combine new mathematical ideas with human-directed AI to resolve a central problem in high-dimensional geometry and probability At a glance - Fundamental scientific breakthrough: Researchers resolved the Kannan-Lovász-Simonovits (KLS) conjecture, a 31-year-old problem widely regarded as one of the central open questions in high-dimensional geometry, with implications for statistics, optimization, algorithms, and computer science. - A universal geometric prin