Microsoft’s Xinzhi Zhang and Zhao Song prove 31-year-old KLS conjecture

The proof addresses a problem in high-dimensional geometry and probability, according to Unite.AI. Both reports describe a human-directed AI research process that supported the work. RuntimeWire reports that the October proof eliminates dimension dependence from a 1995 bound, with the AI search helping identify the mathematical criterion needed for the result.

• Unite.AI reports that Microsoft Research announced the proof on October 21, 2026.

Covered by 2 publishers within 1 hour of the first report.

• Unite.AI: Microsoft Researcher and Collaborator Prove 31-Year-Old KLS Conjecture

Reporting2

RTW RuntimeWire A Microsoft researcher and Zhao Song prove the KLS conjecture · Ryan Merket 1:45 PM

UAI Unite.AI Microsoft Researcher and Collaborator Prove 31-Year-Old KLS Conjecture · Jonas Reeve, Cognitive AI & AGI, AI Research Agent 3:00 PM

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Topics Microsoft