Working with academic communities to build scientific understanding

OpenAI has announced three results it says its internal models produced: a proof of the local smoothing conjecture in every dimension, which would also settle the Kakeya and Stein restriction conjectures in all dimensions; a disproof of the Exponential Time Hypothesis, a long-standing assumption in computer science; and a rigorous existence proof for certain four-dimensional quantum field theories, including Quantum Chromodynamics and pure Yang-Mills theory, which is part of a Clay Millennium Prize problem.

OpenAI says the math and computer science results have been formalized in the Lean proof assistant, and the Yang-Mills existence piece was formalized too. These are among the hardest open problems in their fields. The ETH claim alone affects hundreds of papers that use it to argue certain problems can't be solved quickly.

These are extraordinary claims announced by the company that benefits from them. Until working mathematicians and physicists finish checking, we're treating them as claims.

We want to be careful here, because the stakes are enormous in both directions. If an AI system has really refuted the ETH and proven Yang-Mills existence, this is one of the biggest moments in the history of science, and a strong case that AI can do original research at the very top level. If it doesn't hold up, the damage to trust in AI-for-science announcements would be real.

The Lean formalization is the strongest signal. A machine-checked proof is much harder to fake than a confident write-up. But formal proofs only verify what they state. Experts still need to confirm that the formal statements match the actual conjectures, with no hidden assumptions or definitional shortcuts. That is exactly the kind of checking the outside groups are set up to do.

We think OpenAI's process deserves credit. It isn't claiming academic credit for the discoveries. Collaborators aren't asked to sign NDAs, aren't paid, and speak for themselves. The ETH group is led by Russell Impagliazzo and Ramamohan Paturi, who first proposed the hypothesis, along with MIT's Ryan Williams, and it asked for all raw data to be public plus an OpenAI-funded conference. The physics group is led by Nobel laureate David Gross with Arthur Jaffe, Michael Douglas, Igor Klebanov and Nikita Nekrasov. Those are serious people.

OpenAI also names the tradeoff itself: picking the first shepherds shapes who gets in early and creates an information gap. The physics group is holding back the AI-produced materials for now, which means the wider community can't yet check that work directly. That's a reasonable choice for something this complex, but it puts weight on a small circle.

Where this leads if it scales is the big question. A lab that can produce major results faster than humans can absorb them changes how science works: who gets credit, who gets access to the models, and whether academic fields become reviewers of corporate output. I'm watching whether the verification is truly independent and whether these tools reach university researchers, not just partners.

OpenAI says the ETH disproof was found October 16 and formalized October 17, the local smoothing proof was obtained October 18 and formalized the next day, and the Yang-Mills and QCD proofs date to September, with Yang-Mills formalization finished October 16. It follows an October 6 release using a similar process, and a $5 million OpenAI contribution to the Simons Foundation for workshops and programs on AI-produced results.