Microsoft researchers prove 31-year-old KLS conjecture
What happened
On 22 October 2026, Xinzhi Zhang of Microsoft Research's machine learning and optimisation group and co-author Zhao Song proved the Kannan-Lovász-Simonovits (KLS) conjecture, posed in 1995. According to Microsoft Research's first-hand report, the proof shows the relationship is bounded by a fixed constant in high dimensions and does not grow with dimension. The conjecture had remained open for 31 years. The report does not mention how AI assisted the proof, nor does it disclose the proof's details or its peer-review status.
Written by AI from the reports · updated 2 h ago
Timeline
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- Microsoft ResearchSelectedSolving a 31-year-old grand challenge in mathematics – the KLS conjecture
For decades, a fundamental question about the difficulty of computing in high-dimensional spaces has resisted proof. New research resolves this question, removing a major theoretical obstacle to understanding the efficiency of randomized algorithms used across science and computing. The Kannan–Lovász–Simonovits (KLS) conjecture was proposed in 1995.
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