OpenAI releases three claimed AI-generated results in math, computer science and physics, with external expert groups to verify them

On 26 October 2026 OpenAI put on GitHub the raw model output for a claimed proof of the local smoothing conjecture, which it says also settles the Kakeya and Stein restriction conjectures. It also published a write-up and a Lean proof of a claimed refutation of the Exponential Time Hypothesis (ETH), through a deterministic subexponential-time algorithm for counting satisfying assignments of fixed-width CNF formulas. A third result, a claimed existence proof for interacting 4D quantum field theories that include QCD, has not been released in full. Outside groups are meant to check the work: Russell Impagliazzo, Ramamohan Paturi and Ryan Williams for the computer science result, and a group led by David Gross for the physics result. Nothing has been independently verified yet.

If the ETH refutation holds, it would overturn a widely held assumption that many hardness results in complexity theory depend on. The math and physics claims would also be major if confirmed. For now this affects mainly theoretical researchers, who must decide whether to spend time checking the material. The process matters too: OpenAI is trying out an "expert shepherd" model for releasing AI-generated results and has opened a consultation on norms. There is no practical effect for developers or businesses at this stage.

OpenAI calls these "major" discoveries before anyone independent has checked them, so treat that as a marketing label, not a finding. The physics result is described but not released in full, so it cannot be assessed at all. A Lean proof is strong evidence only if the formal statement really matches the claim, and that is exactly what the reviewers need to confirm. The framing of a new collaborative approach also glosses over the fact that OpenAI's own advisory panel advised against giving chosen people early access a day earlier.

1. 01Public statements from Impagliazzo, Paturi and Williams on whether the Lean proof and the ETH refutation hold up, including whether the formal statement matches the claim, in the coming weeks.
2. 02Whether OpenAI releases the full physics write-up, and whether David Gross's group or other physicists publicly endorse or challenge the QCD-type existence claim.
3. 03Independent mathematicians' assessments of the local smoothing, Kakeya and Stein restriction output, and any errors or gaps found. Also whether the results are posted to arXiv or submitted for peer review.