OpenAI says AI models produced proofs in maths, CS, physics

What happened: OpenAI says its models produced three proofs, in mathematics, computer science and physics. In mathematics, it says the models proved the local smoothing conjecture in every dimension, which also resolves the Kakeya conjecture and Stein's restriction conjecture in all dimensions. In physics, it says the models give a rigorous existence proof for certain four-dimensional interacting quantum field theories, including QCD and a unified completion of the Standard Model.

The numbers: The computer science disproof was produced on 16 October and formalised in Lean on 17 October. The mathematics output was obtained on 18 October, and its Lean formalisation followed the next day. The physics proofs are dated 9 September for pure Yang–Mills existence and 18 September for QCD, with Lean formalisation finished on 16 October.

The context: The Exponential Time Hypothesis (ETH) is a conjecture used in hundreds of papers to derive conditional hardness results. The formalisation documentation states it as follows: for fixed k ≥ 2, a deterministic machine counts satisfying assignments of a k-CNF formula in subexponential time and polynomial space.

The catch: None of the claims has independent verification yet. The details come from Unite.ai's reading of the announcement, and that article quotes no OpenAI or named researcher.

Why it matters: ETH underpins hundreds of papers, so a disproof would bear directly on that body of work.

What's next: A group led by Russell Impagliazzo and Ramamohan Paturi of UC San Diego will verify and shepherd the ETH work. The mathematics and computer science proofs are public, and the mathematics proof is published on GitHub with a natural-language writeup. The physics group, led by David Gross, decided to write up the result itself, and the physics release has been delayed. The full claims are in OpenAI's announcement.