AI has proved that a theory underpinning fundamental physics is trustworthy

On October 28, OpenAI submitted a Lean-formalized existence proof for pure quantum Yang-Mills theory to a review group chaired by 2004 Nobel Physics laureate David Gross. The group, which also includes Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov, published its 35-page assessment on November 10, making the full submitted code and validation report public. OpenAI said its models produced a written proof on September 9 and completed the Lean formalisation on October 16. The assessment judges the construction to be Yang-Mills under an existence criterion that does not require precise characterization of the vacuum, calling it a relativistic quantum field theory arising from a four-dimensional Wilson lattice limit with selected-phase reconstruction and short-distance tests. The reviewers said their clean rebuild, axiom audit and other formal checks passed, but added an important caveat: they used OpenAI's Astra to help examine the code and "do not claim to fully understand the proof yet." The result does not solve the full Clay Mathematics Institute Millennium Prize problem, which since 2000 has offered $1 million for a nontrivial quantum Yang-Mills theory on four-dimensional space-time for every compact simple gauge group, together with proof that it has a mass gap. The assessment says the submission "does not prove" the existence of a mass gap — a minimum positive energy separating the vacuum from excited states — and does not prove that the infinite-volume limit is unique. The construction excludes a positive mass gap from its scope and permits refinement in the large-volume limit. The review group's judgment rests on the stronger combined_acceptance target, binding the lattice family, limiting correlations and reconstructed witness together, and specifies a selected scalar stress-trace OS interface, operator content, normalization and leading short-distance law. A separate operator product expansion check has its own witness, which the documentation does not automatically identify with the combined acceptance target. The submitted verification log reports a successful replay of project declarations and lists the axioms used. The group's published procedures describe its review and conflicts rules; OpenAI initially approached Gross, who selected the other members.