OpenAI 'Shepherds' Verify and Release Lean Formalization of Yang-Mills Existence Proof

An external expert committee appointed by US-based AI company OpenAI, known as "shepherds," has formally verified and released the AI-generated proof of the existence of quantum Yang-Mills theory. Led by eminent theoretical physicist David Gross, the committee published an explanatory document and the proof's formal verification in the Lean programming language on GitHub on the night of November 10, 2026. This action marks the completion of the first structured independent review of OpenAI's previously announced major scientific breakthroughs.

The Yang-Mills problem is one of seven "Millennium Prize Problems" posed by the Clay Mathematics Institute, concerning the mathematical foundations of the Standard Model of particle physics. In late October 2026, OpenAI claimed its models had solved the first part of the problem—proving the "existence" of pure Yang-Mills theory—though the more difficult "mass gap" remains unresolved. Due to the complexity and length of the AI-generated proof, which is difficult for humans to grasp immediately, OpenAI adopted a "shepherd" model, inviting external experts to supervise the release process to avoid the chaos caused by dumping hundreds of unexplained AI proofs in early October.

While the committee confirmed the logical validity of the proof through machine verification, members admitted they do not yet fully understand the details intuitively, even using OpenAI's Astra model to help digest the Lean code. This approach has drawn criticism from some mathematicians and physicists who argue that this "gatekeeper" mechanism, where AI labs select experts, violates principles of open science. Scott Armstrong, a mathematician at New York University, stated his hope that AI labs would share results more widely in the future to allow the community to review them more efficiently.