OpenAI says its AI disproved a core computer-science assumption, gives $5M to review it
What's the deal? OpenAI said on 26 October 2026 that one of its internal models disproved the Exponential Time Hypothesis (ETH), a 1999 conjecture about how hard Boolean satisfiability problems are to solve. The model produced the disproof on 16 October and formalised it in the Lean proof assistant the next day; the paper and proof are public on GitHub.
Why it matters: Hundreds of papers in graph algorithms, computational biology, database query optimisation, and computational geometry treat ETH as a conditional hardness assumption. If the disproof holds, it removes the assumption those results rest on.
What else? OpenAI announced two more results alongside ETH. Its models proved the local smoothing conjecture in every dimension — settling the Kakeya and Stein restriction conjectures — and produced existence proofs for quantum field theories in four dimensions, including quantum chromodynamics and pure Yang-Mills theory, a Clay Millennium Prize problem. A separate group led by Nobel laureate David Gross will shepherd the physics result, which OpenAI has held back from public release while the group writes it up.
What could go wrong? Lean checks the formal argument, not whether the result is correctly interpreted or what it means in practice. Russell Impagliazzo and Ramamohan Paturi of UC San Diego, who first proposed ETH, will lead a review with MIT's Ryan Williams — but they stress it is not an endorsement.
"Our involvement should not be taken as certification of the claim," the three wrote in an open letter.
The approach: OpenAI handed all three results to outside expert groups and says it seeks no academic credit for discoveries made by its models. Reviewers signed no non-disclosure agreements and are unpaid. The company gave $5 million to the Simons FoundationDealroom has a profile for this one. Try Dealroom → for workshops on the work's implications and agreed to make all raw data public.
The signal: OpenAI is positioning its models as research tools that produce raw data for scientists to verify, not finished science. Even if upheld, the ETH result would not solve P vs. NP or deliver fast practical algorithms — but it could force researchers to revisit a widely used complexity assumption.
Read more: The Verge · openai.com
