OpenAI hands three major maths and physics claims to reviewers

On 26 October OpenAI announced three results and passed them to academic communities for review: a disproof of the Exponential Time Hypothesis (ETH), a proof of the local smoothing conjecture in all dimensions, and a proof that certain four-dimensional quantum field theories exist, including pure Yang-Mills theory. OpenAI says all three face months of independent review.

The ETH disproof was found on 16 October and formalised in the Lean proof assistant the next day; paper and proof are on GitHub. If correct, local smoothing also settles the Kakeya and Stein restriction conjectures in all dimensions. A group led by Nobel laureate David Gross is preparing its own account of the physics, whose materials remain unreleased.

ETH says 3-SAT cannot be solved in sub-exponential time; many "no faster algorithm" results rested on it. Kakeya asks how small a set can be that lets a needle point in every direction. Yang-Mills is a Clay Millennium Problem, but the prize also needs a mass gap, which OpenAI does not claim.

All claims currently rest on OpenAI's own account, and reports differ on reviewers and dates. A Lean proof is machine-checked, but people must still confirm it states the right theorem.

Mathematicians accept such claims only once peer review is complete, which is why OpenAI frames the release as an invitation to academic communities rather than a finished result.

Independent ETH review has begun; the Gross group's assessment is pending.

In the same week Axiom Math said agent swarms formalised the Classification of Finite Simple Groups in Lean in 24 days, a 43.1-million-line proof that found 34 deviations from published proofs. Machine-checked proof is becoming the basis of trust.

• Demand verifiable output: tests, sources or calculations that check AI results.
• Get a second reviewer before big claims reach clients.
• Watch optimisation tools; if ETH falls, faster planning and routing methods may follow.