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OpenAI says its internal models produced results in mathematics, computer science, and physics, and that these manuscripts are best read as raw research data. External experts are acting as academic shepherds to organize understanding and writeups. Per OpenAI’s research blog, the claims remain AI outputs pending community verification—not peer-reviewed proofs or prize wins.

What OpenAI announced

OpenAI’s post is dated October 26, 2026. It says the company reached out to external experts and followed three shepherd-advised release strategies:

  1. Math — release the AI output so researchers can organize their own explanations.
  2. Computer science — form an external group to explain the result, while publishing the AI output immediately.
  3. Physics — form an external group and defer release of the AI-produced materials.

Four principles guide the collaborations: transparency (no NDAs), no academic credit sought by OpenAI for the model outputs, recognition for the shepherds’ understanding and writeups, and independence (voluntary, unpaid; groups do not speak for OpenAI).

Mathematics: local smoothing and Kakeya (AI output public)

OpenAI says its models produced a proof of the local smoothing conjecture in every dimension, and therefore also cover the Kakeya and Stein restriction conjectures in all dimensions, via a novel auxiliary PDE. It says the AI natural-language writeup and a Lean formalization are in the public GitHub repository openai/math. Those files are AI raw output awaiting community verification—not a peer-reviewed journal result.

Computer science: ETH claim (AI output public)

OpenAI says its system produced a proof that the Exponential Time Hypothesis (ETH) is false, later formalized in Lean. Shepherds named in the post include Russell Impagliazzo, Ramamohan Paturi (UC San Diego), and Ryan Williams (MIT). Natural-language writeup and Lean are on public GitHub. Those files are OpenAI’s AI raw output awaiting community verification—ETH is not established as overturned.

Physics: QFT／Yang–Mills materials deferred

OpenAI says models produced natural-language arguments for existence of certain four-dimensional gauge＋fermion QFTs (including QCD and a Standard Model completion), with pure Yang–Mills existence as a subproblem tied to the Clay Millennium problem. David Gross leads a shepherd group that includes Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov. The group is holding off on releasing the AI-produced artifacts and writing them up themselves. The post does not give public Lean or manuscript URLs for this physics track; none have been seen on this site.

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