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Is ETH false? OpenAI shares three AI-generated results in math, CS and physics

OpenAI News ★★★ View Markdown
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This one is a research announcement that's exciting just to read. OpenAI says it will work with academic communities on three results in mathematics, computer science and physics.

What was announced?

OpenAI News presented three results produced by OpenAI's models. OpenAI calls the manuscripts "raw research data" and says external experts will help turn them into scientific understanding.

Why it matters

The way researchers verify, release and credit AI-produced results is itself an open question. It's interesting that experts acting as "shepherds" advised three different release strategies.

What changes

Researchers can check the released natural-language proofs and Lean formalizations themselves and build on them. These are OpenAI's claims, and outside verification is still to come.

Dive Deep

First, the release approaches:

  • Math: release the AI output and let researchers organize their own explanations
  • Computer science: form an external collaboration to explain the result, and make the AI output public for anyone to examine
  • Physics: form an external collaboration and defer to it on what gets released

The collaborations follow four principles:

  • Transparency (no nondisclosure agreements)
  • No academic credit for OpenAI's internal models
  • Recognition for the external groups' work
  • Independence (voluntary, unpaid participation, and members don't speak for OpenAI)

Now the three results:

  • Mathematics (local smoothing and the Kakeya conjecture): OpenAI says its models produced a proof of local smoothing in every dimension, which would also resolve the Kakeya and Stein's restriction conjectures in all dimensions. The proof uses a novel auxiliary partial differential equation. The output was obtained on October 18, 2026 and formalized in Lean the next day. The writeup and Lean proof are on GitHub
  • Computer science (ETH): OpenAI says its system disproved the Exponential Time Hypothesis on October 16, 2026, verified in Lean on October 17. The collaboration is led by Russell Impagliazzo and Ramamohan Paturi (UC San Diego) and Ryan Williams (MIT). They asked for all raw data to be public, OpenAI agreed, and it will fund a conference on the implications. The proof and Lean formalization are on GitHub
  • Physics (existence of QCD and Standard Model completions): a mathematically rigorous existence proof for certain four-dimensional interacting quantum field theories, including QCD and a unified completion of the Standard Model, plus pure Yang-Mills existence, part of the Clay Millennium Prize problem. The Yang-Mills natural-language proof came on September 9, QCD on September 18, and the Yang-Mills Lean formalization was completed on October 16. The group led by David Gross decided to hold off releasing the AI-produced artifacts and write up the work itself

To support scientists, OpenAI is contributing $5 million to the Simons Foundation, which will manage and award funding for workshops, conferences and programs on understanding and building on AI-produced results.

Wrap-up

  • Three results will be verified and released together with outside researchers
  • Release approaches differ by field (math: release output; CS: collaboration plus release; physics: defer to the collaboration)
  • The claims, such as disproving ETH, are big, and verification is still ahead
  • $5 million to the Simons Foundation supports researchers

If you're into theoretical CS or mathematical physics, or curious how AI and science will work together, this one is for you!

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