Microsoft Research Solves 31-Year-Old KLS Conjecture in Mathematics
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Microsoft Research has proven the KLS conjecture, a 31-year-old problem in mathematics, by combining new mathematical ideas with AI guidance. The research establishes a geometric principle for log-concave distributions: simple planar cuts can capture the narrowest bottleneck within a fixed factor, independent of dimension. The proof resolves a long-standing grand challenge in mathematics.
Written with AI from the reporting · updated 10/21/2026
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New at this step ·Microsoft researchers resolve 31-year-old KLS conjecture in high-dimensional geometry
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- Microsoft Research · First-partyMicrosoft researchers resolve 31-year-old KLS conjecture in high-dimensional geometryOriginal source ↗
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1 developments10/22/2026, 12:58:14 AM
Microsoft researchers resolve 31-year-old KLS conjecture in high-dimensional geometryMicrosoft Research
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- 1Oct 4, 00:00recorded Oct 22, 00:58single source
解决KLS conjecture 31年难题
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- Microsoft Research · Oct 22, 00:00Microsoft researchers resolve 31-year-old KLS conjecture in high-dimensional geometry
Researchers proved the Kannan-Lovász-Simonovits conjecture, establishing that flat cuts can capture the narrowest bottlenecks of log-concave distributions within a fixed factor, regardless of dimension. The breakthrough, achieved through human-directed AI collaboration, removes a major theoretical obstacle to understanding randomized algorithms.
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- Microsoft ResearchSelectedMicrosoft researchers resolve 31-year-old KLS conjecture in high-dimensional geometry
Researchers proved the Kannan-Lovász-Simonovits conjecture, establishing that flat cuts can capture the narrowest bottlenecks of log-concave distributions within a fixed factor, regardless of dimension. The breakthrough, achieved through human-directed AI collaboration, removes a major theoretical obstacle to understanding randomized algorithms.