Between conjectures and protocols: OpenAI's foray into the hard sciences

On 26 October 2026 OpenAI announced that its internal models had produced three major theoretical results: a refutation of the Exponential Time Hypothesis (ETH) in computer science, a proof of the local smoothing conjecture in mathematics, and rigorous existence proofs for certain interacting quantum field theories in four dimensions, including QCD and pure Yang-Mills theory. Even if confirmed, the results have clear limits: refuting ETH does not settle P versus NP or yield polynomial-time algorithms, and OpenAI does not claim to have solved the Clay Institute's Millennium Problem on Yang-Mills, because the mass gap part remains open.

Beyond their theoretical reach, what makes this news is how the results are being released. The company has taken three distinct paths: immediate publication with a Lean formalization for the mathematics; release alongside an independent check for the computer science, entrusted to the hypothesis's originators Russell Impagliazzo and Ramamohan Paturi of UC San Diego and to Ryan Williams of MIT; and advance delivery to a group of physicists led by Nobel laureate David Gross. According to ForkLog, the group made clear that taking part in the review does not amount to endorsing OpenAI's conclusion, and announced a verification open to the community. As the same outlet reported, OpenAI said it intends to “give the material to the experts first, who will then decide how it is published”. The Advisory Group on Mathematics and Artificial Intelligence (AGMAI) has asked OpenAI to publish the Yang-Mills paper: “there is no scientific reason to delay any further”. According to Scientific American, the approach chosen for two of the three results runs counter to the group's recommendations, including on how the experts were appointed.

Significant methodological reservations remain. None of the three results has yet been peer-reviewed or independently confirmed. The Yang-Mills paper is not public, so for now it cannot be checked. In the ETH case, the documentation in OpenAI's GitHub repository notes that the statement formalized in Lean carries a weaker analytic bound than the one claimed in the manuscript, and it has not been verified whether the formalized statement exactly matches the manuscript's claim. Moreover, because this is a proprietary model whose prompts, compute time and reasoning chains are not disclosed, the scientific community is left scrutinizing texts that OpenAI itself calls raw research data: the output of a system whose logical components are out of reach.

The announcements arrive before the checks, and checks take time: the value of artificial intelligence in theoretical research will also be measured by the transparency of its methods. — Olya