OpenAI announced on Monday, October 26, that its internal models have produced three new results that, if they survive expert scrutiny, would rank among the most consequential claims ever attributed to an AI system. In computer science, a model is said to have disproved the Exponential Time Hypothesis, the satisfiability conjecture that underpins hundreds of conditional hardness results. In mathematics, OpenAI claims a proof of the local smoothing conjecture in every dimension, which would also settle the Kakeya and Stein restriction conjectures. In physics, it claims a rigorous existence proof for certain four-dimensional quantum field theories with gauge fields and fermions, including QCD and the Yang-Mills existence problem.

None of the three claims has been peer-reviewed, and OpenAI does not name the model that produced them, referring only to internal systems that are not publicly available. Two of the three results come with Lean formalizations checked by a proof assistant, and the mathematics and computer science materials have been posted publicly on GitHub. The physics artifacts are being withheld for now at the request of the physicists overseeing that result, who are writing it up themselves.

The announcement is as much about process as results. Each claim has been handed to a group of outside experts OpenAI calls 'shepherds', who decide how the material is released, checked and explained: Russell Impagliazzo and Ramamohan Paturi of UC San Diego with Ryan Williams of MIT for the ETH result, and a group led by David Gross for the physics result. OpenAI says the shepherds work under principles of transparency, independence and no academic credit for the lab, and links the effort to a recently announced $5 million contribution to the Simons Foundation for workshops and programs on AI-produced results.