Committee led by a Nobel laureate says OpenAI's AI proof that Yang–Mills theory exists holds up

Yang–Mills theory is the mathematics behind the strong nuclear force. Physicists rely on it, but nobody had proved it exists as a consistent mathematical object. On 26 October 2026 OpenAI said its AI models had produced such a proof, in four dimensions, and gave it to a committee of five physicists and mathematicians chaired by Nobel laureate David Gross.

The Lean code (a language in which a computer checks every step) and the committee’s assessment are now public on GitHub. The assessment, dated 10 November, says that “in our opinion” the submission constructs a quantum field theory satisfying the Wightman axioms as a limit of four-dimensional lattice gauge theory, for any simple compact gauge group. It does not prove the limit is unique or that there is a mass gap. Gross chose the other members, including Arthur Jaffe, co-author of the official prize problem description.

The submission’s README says Lean’s kernel replayed 100,168 declarations behind 17 headline theorems, using only three standard axioms and no sorry placeholder. A computer can confirm the steps follow, but people must confirm the statement is the right one, and the committee made that its first objective.

The $1 million Millennium Prize problem asks for existence and a mass gap (positive mass for the theory’s particles). The Clay Mathematics Institute still lists it as unsolved.

What it means

If the assessment survives outside scrutiny, an AI system has built the first rigorous version of a theory at the centre of particle physics. It would not win the prize, because the mass gap is unproved.

Caveats

• The 100,168-declaration replay is the submission’s own record, and the group’s assessment is its own opinion. We found no outside party that has rerun the build. The group’s page says posting a submission is not endorsement.
• The Lean statement is what was proved. A reader still has to trust that its definitions say what physicists mean, and the assessment notes that this takes human review.
• OpenAI’s wider claims, such as the theory with quarks, are not part of this assessment.
• This is not peer review. OpenAI approached the chair, who picked the committee. The 1,147-page written proof is not among the files we found in the repositories.
• Nine mathematicians in an advisory group, among them Edward Witten, called on 26 October for release without delay. Peter Woit criticised the secrecy; commenters on his blog asked whether the construction is unique and describes interacting particles.
• OpenAI has not named the model. The committee calls it “OpenAI’s LLM”.