OpenAI Announces Three Major AI-Driven Discoveries in Math, CS, and Physics

Around October 27, OpenAI published an update on its collaborative research with the academic community, headlined by a striking claim: an internal model produced an alleged refutation of the Exponential Time Hypothesis (ETH) in computational complexity theory — namely, that 3SAT requires exponential time. If valid, it would overturn a number of established results that presuppose ETH. A circulating screenshot (relayed by @felpix) further claims the proof has since been formally verified in the Lean proof assistant.

Confirmed

• OpenAI officially announced the research progress, stating that model-assisted research refuted ETH (@EnvironmentalMix22).
• Theoretical computer scientist Ryan Williams (rrwilliams) announced that he, along with Russell Impagliazzo and Mohan Paturi, has been invited to organize a public, independent review of the refutation claim.
• Williams noted that the review team has signed no NDAs with OpenAI and receives no compensation, and pledged to keep the community updated with findings throughout the review; the team has formally requested that OpenAI promptly release all materials related to the ETH refutation claim.
• Fields Medalist Tim Gowers shared the news, noting that ETH is a major claim in complexity theory and will undergo independent review.

Not Yet Confirmed

• Whether ETH has actually been refuted: the review is not complete, and the verdict rests on its outcome.
• The claim that "the proof has been formally verified in Lean" comes only from a circulating screenshot and has not been confirmed by OpenAI or the review team.

Why It Matters

ETH is a long-standing core conjecture about the computational complexity of Boolean satisfiability (SAT), closely tied to P vs NP, and a large body of complexity results assumes it holds. A confirmed refutation would be a landmark achievement for AI-assisted mathematical research and would force the field to re-examine a host of theorems that rely on ETH. Meanwhile, the review team's arrangement — no NDAs, no compensation, full transparency throughout — offers a replicable model for how major scientific claims produced by AI can be subjected to human peer review.

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