OpenAI says its models generated a proof on October 18, 2026, of the local smoothing conjecture, which has been open since 1991, in every dimension. According to the company, the result also settles the Kakeya and Stein conjectures, following the resolution of the two-dimensional local smoothing case in 2019 and the three-dimensional Kakeya conjecture in 2025. The proof was formalized the next day in Lean, a theorem prover that checks every step, and was published on GitHub with a natural-language explanation. The work is the centerpiece of a broader release that includes more than 700 AI-generated mathematical preprints.
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