OpenAI says its internal models have produced three new results in pure research, and the claims are among the boldest any lab has made. In mathematics, it reports a proof of Sogge's 1991 local smoothing conjecture in every dimension, which would also settle the Kakeya and Stein restriction conjectures. In computer science, it says its system has shown the Exponential Time Hypothesis to be false, a widely believed assumption used in hundreds of hardness proofs. In physics, it claims a rigorous existence proof for four-dimensional quantum field theories including quantum chromodynamics, with pure Yang-Mills theory, part of a Clay Millennium Prize problem, as a sub-result.
The interesting part is what OpenAI is doing with them. Rather than publish papers in its own name, it calls the model output raw research data and has asked outside experts to decide how each result is released. The maths output and its Lean proof are simply public. The complexity result goes to a group led by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams, which asked for all raw data to be published and for OpenAI to fund a conference; the natural-language proof and Lean formalisation are already on GitHub. The physics group, led by Nobel laureate David Gross with Arthur Jaffe, Michael Douglas, Igor Klebanov and Nikita Nekrasov, chose to hold back the AI material and write the result up themselves.
OpenAI sets four rules for these groups: no non-disclosure agreements, no academic credit claimed by OpenAI, recognition for the people who explain the work, and unpaid, independent participation. It also points to a $5 million contribution to a Simons Foundation programme for studying AI-produced results. This follows an earlier release on 6 October and a growing habit among labs, Anthropic included, of publishing research said to come from their models.
Lean formalisation is the strongest evidence offered, since a machine-checked proof is hard to fake. It is not the whole story. A formal proof is only as good as the statement it proves, and whether the formal definitions match the conjectures as mathematicians understand them is exactly what the working groups must check. OpenAI also admits that choosing the first shepherds shapes who gets involved and creates an imbalance of information.
None of the three results has been peer reviewed, and the physics material is not public at all. Claims on this scale have collapsed before under expert reading. The sensible course is to wait for the working groups' verdicts before treating any of them as settled.