OpenAI claims AI proofs on Kakeya, the ETH and Yang-Mills, and hands them to outside experts

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, part of a Clay Millennium Prize problem. OpenAI says the math and computer science results and the Yang-Mills existence piece were formalized in Lean. The ETH claim alone touches hundreds of papers that use it to argue certain problems cannot be solved quickly (what the ETH result means).

By OpenAI’s timeline, the ETH disproof was found October 16 and formalized October 17, local smoothing 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, earlier Navier–Stokes claims (Navier–Stokes) and a $5 million OpenAI contribution to the Simons Foundation for workshops on AI-produced results. These claims come from the company that benefits from them and are treated here as claims until experts finish checking.

If these hold, it is one of the biggest moments in the history of science and a strong case that AI can do original research at the top level; if they do not, trust in AI-for-science announcements takes real damage. Lean formalization is the strongest signal, since a machine-checked proof is much harder to fake than a confident write-up. But formal proofs verify only what they state. Experts still need to confirm the formal statements match the actual conjectures without hidden assumptions or definitional shortcuts.

OpenAI’s process deserves some credit. It is not claiming academic credit; collaborators are not asked to sign NDAs, are not paid and speak for themselves. The ETH group is led by Russell Impagliazzo and Ramamohan Paturi, who first proposed the hypothesis, with MIT’s Ryan Williams, and 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.

OpenAI acknowledges that choosing the first shepherds shapes who gets in early and creates an information gap. The physics group is holding back AI-produced materials for now, so the wider community cannot check that work directly, a choice researchers have criticized as gatekeeping (gatekeeping complaints). Earlier episodes left some mathematicians feeling scooped and squeezed (OpenAI and mathematicians).

If labs can produce major results faster than humans can absorb them, science changes: who gets credit, who gets model access, and whether academic fields become reviewers of corporate output. The measures are whether verification is truly independent and whether these tools reach university researchers, not only partners. More in our OpenAI coverage and research coverage.