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OpenAI Releases AI Math and CS Proofs, Withholds Physics Artifacts for Expert Review

·2026.10.27 06:35

Key point

OpenAI released AI-generated proofs for the local smoothing conjecture and a refutation of the Exponential Time Hypothesis, while deferring the release of physics results to external expert collaborations.

Details

  • OpenAI announced three new discoveries in mathematics, computer science, and physics, treating the AI outputs as raw research data to be interpreted by external academic collaborations.
  • The models produced a proof of the local smoothing conjecture in every dimension, resolving the Kakeya and Stein’s restriction conjectures. The AI output was obtained on October 18, 2026, formalized in Lean the next day, and released publicly.
  • The system refuted the Exponential Time Hypothesis (ETH). The natural language disproof was found on October 16, 2026, and Lean formalization was completed on October 17, 2026. The raw data and proofs were made public for independent verification.
  • The models produced existence proofs for interacting quantum field theories, including QCD and a unified completion of the Standard Model. However, the external expert group decided to hold off on releasing the AI-produced artifacts and will work on writing them up themselves.
  • External expert groups led by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams are shepherding the computer science result, while David Gross leads the group for the physics result.
  • OpenAI committed to funding a conference to discuss the implications of the ETH refutation and contributed $5 million to the Simons Foundation to support workshops and programs for researchers to examine AI-generated results.
openaimathematicsphysicsai-researchcomputer-scienceleanproof-generation
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