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A 31-year-old unsolved problem in mathematics, the KLS conjecture, has been proven: a fundamental breakthrough has been achieved in high-dimensional geometry and the theory of randomized algorithms.
On October 4, 2026, Zhang Xinzhi, a researcher at Microsoft Research, together with his collaborators, completed a rigorous proof of the Kannan–Lovász–Simonovits (KLS) conjecture, thereby resolving a long-standing central problem that had remained open since its formulation in 1995. This achievement establishes a dimension-independent constant bound for the “plane‑cut bottleneck” in high-dimensional log-concave distributions, providing an unconditional theoretical foundation for random sampling, convex optimization, and theoretical computer science.