# OpenAI reports proofs in mathematics, computer science and physics

> OpenAI says its models produced proofs in three fields, including an ETH disproof.

*The claims include a disproof of the Exponential Time Hypothesis and a proof of pure Yang–Mills existence, and none is independently verified yet.*

By Bez · WireRead
Canonical: https://wireread.com/news/openai-reports-proofs-in-mathematics-computer-science-and-physics

OpenAI said on 26 October that its models had produced proofs in mathematics, computer science and physics, including a disproof of the Exponential Time Hypothesis. The company said the results are described in [a post on its website](https://openai.com/index/building-scientific-understanding-with-academic-communities/), and [Unite.ai](https://www.unite.ai/openai-says-its-models-produced-three-proofs-in-math-cs-and-physics/) reported the announcement the same day.

The computer science result concerns the Exponential Time Hypothesis (ETH), a conjecture used in hundreds of papers to derive conditional hardness results. OpenAI said the natural-language disproof was produced on 16 October and formalised in Lean on 17 October. According to the formalisation documentation, for fixed k ≥ 2, a deterministic machine counts satisfying assignments of a k-CNF formula in subexponential time and polynomial space.

In mathematics, OpenAI said its models proved the local smoothing conjecture in every dimension. The company said this also resolves the Kakeya conjecture and Stein's restriction conjecture in all dimensions. The output was obtained on 18 October, formalised in Lean the next day, and published on GitHub with a natural-language writeup.

In physics, OpenAI said its models give a rigorous existence proof for certain four-dimensional interacting quantum field theories with gauge fields and fermions. These include QCD and a unified completion of the Standard Model. The company also said its models proved pure Yang–Mills existence, which is part of a Clay Millennium Prize problem.

OpenAI gave 9 September as the date of the Yang–Mills proof and 18 September for QCD. It said the Lean formalisation of the physics results was finished on 16 October. The physics group, led by David Gross, decided to write up the result itself, and the physics release was delayed while the mathematics and computer science proofs are public.

According to Unite.ai, a group led by Russell Impagliazzo and Ramamohan Paturi of UC San Diego will verify and shepherd the ETH work. None of the claims has been independently verified yet. The OpenAI post could not be opened for this story, so the details come from Unite.ai's account, which quotes no OpenAI or named researcher verbatim.

The next steps are verification of the ETH work by the UC San Diego group and a physics write-up by the group led by David Gross. No date has been given for either step.

## Key takeaways

- Claims cover mathematics, computer science and physics; none is independently verified yet.
- Disproof of the Exponential Time Hypothesis formalised in Lean on 17 October.
- Physics release delayed; the physics group will write up the result itself.

## Sources

- [OpenAI Says Its Models Produced Three Proofs in Math, CS, and Physics](https://www.unite.ai/openai-says-its-models-produced-three-proofs-in-math-cs-and-physics/) — Unite.ai, 2026-10-26
- [Building scientific understanding with academic communities](https://openai.com/index/building-scientific-understanding-with-academic-communities/) — OpenAI, 2026-10-26