A problem in high-dimensional geometry that has been open since 1995 now has a proof, and Microsoft is crediting part of the work to a tightly supervised team of AI agents. In a Microsoft Research blog post published October 21, 2026, senior researcher Xinzhi Zhang wrote that Zhang and co-author Zhao Song have resolved the Kannan-Lovász-Simonovits (KLS) conjecture.

The conjecture asks whether, for a broad class of high-dimensional probability distributions, the best flat cut is always nearly as good as the best cut of any shape, within a universal constant that does not depend on the number of dimensions. Microsoft says the geometry of these cuts governs how quickly random walks can explore a distribution, which ties KLS to the theory of high-dimensional sampling used in statistics, optimization and algorithms.…