OpenAI claims AI models prove 1991 math conjecture in all dimensions
OpenAI announced on October 26, 2026, that its AI models proved the local smoothing conjecture, an unsolved math problem since 1991. The company says the proof also resolves the Kakeya conjecture and Stein’s restriction conjecture across all dimensions. OpenAI’s models generated the proof on October 18, which was formalized in Lean, a theorem prover, and published on GitHub alongside a…
Key points
- OpenAI claims its models proved the **local smoothing conjecture** (1991) and linked conjectures in all dimensions using a new PDE
- Proof was generated on **October 18, 2026**, formalized in **Lean**, and published on **GitHub** with a natural-language summary
- Over **700 AI-generated math preprints** were released alongside, but the conjecture’s proof is the most significant claim
The breakthrough relies on a new partial differential equation introduced by OpenAI. While prior progress addressed specific cases—like the 2D local smoothing proof in 2019 and the 3D Kakeya conjecture in 2025—this marks the first time all dimensions were resolved simultaneously. The Lean formalization shifts scrutiny from AI errors to whether the proof aligns with mathematicians’ original intent. Over 700 AI-generated math preprints accompanied the announcement, though the conjecture’s proof stands out for its potential impact on harmonic analysis and Fourier theory.
OpenAI says its models proved the local smoothing conjecture in every dimension
cryptobriefing.com · 26 October 2026
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2sources- OpenAI Says Its Models Produced Three Proofs in Math, CS, and PhysicsPress · Unite.AI ·
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