Microsoft Research

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On Oct 21, Microsoft Research said a human-directed AI process helped prove the 31-year-old KLS conjecture.

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On Oct 21, Microsoft Research said a human-directed AI process helped prove the 31-year-old KLS conjecture.

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  1. Official

    Microsoft Research says a human-directed AI process helped prove the 31-year-old KLS conjecture

    Microsoft Research published this on Oct 21, 2026 (source: microsoft.com).

    Microsoft researcher Xinzhi Zhang and co-author Zhao Song say they proved the Kannan-Lovász-Simonovits conjecture from 1995, showing the bound holds with a constant independent of dimension. AI agents explored about 100 candidate approaches while the researchers pruned and directed the search. A parallel proof from another group and a Lean 4 formalization appeared separately.

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