OpenAI math results on GitHub, Lean proofs

On 6 October OpenAI published a repository of new mathematical results produced by an internal frontier model. Many of the proofs come with Lean formalizations that a computer can check step by step. Which model it is, OpenAI does not say; the results are listed in the repository.

In short

6 October 2026: OpenAI published a "broad range" of new mathematical results from an internal model it does not name on GitHub.
Many of the proofs come with formalizations in Lean, a language in which a computer checks every step. OpenAI promises more.
According to OpenAI the average result cost about three hours of ChatGPT Pro thinking. The model is not released yet; the company is working on releasing it responsibly.

Checked on7 October 2026Responsible editorTsvetelin IvanovHow we workMethod · Corrections

Three hours. That is how much ChatGPT Pro thinking the average result of OpenAI's new batch of mathematics cost, according to the company. The number is one of the things you can look at yourself this time.

The facts: on 6 October 2026 OpenAI published "a broad range of new mathematical results" produced by an internal frontier model, which it does not name. The results are in a GitHub repository, with protocols for paper revisions and citations. The company says it consulted the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study and drew on its advice and public recommendations, and that it keeps looking for a community-hosted alternative that meets the committee's guidelines. Many of the proofs in the repository come with formalizations in Lean, and OpenAI will add more. Details of how the results were obtained are also published: 10 summaries of the model's reasoning, estimates of compute spent in terms of ChatGPT Pro usage, and statistics on the number of attempted problems. According to OpenAI the average result used the equivalent of roughly three hours of ChatGPT Pro thinking. The company will fund a series of workshops, conferences and special programs around understanding major results produced by AI, and is working to responsibly release the model that produced them. The repository's README adds: 722 manuscripts in 372 result families, approximately 4,000 problems posed to the model, results at different stages of verification; not all have Lean formalizations, and some of the unformalized results could have issues.

Lean turns checking a proof into a job for a machine: you run the file and it tells you whether every step holds. A second check remains that the machine does not do: whether what is written in Lean is exactly the question mathematicians are asking. That is our reading, not OpenAI's words.

Lean checks the proof. Who checks the question?

The announcement does not list the results or name the model. The repository lists them, 722 manuscripts; it does not name the model either.

The backstory On 8 September OpenAI said an internal model had solved the Navier-Stokes problem, with a proof in Lean; no independent check was cited then. Whether it is in the new repository, the announcement does not say; it is not a separate result in the repository's catalogue, and Navier-Stokes appears there in other work.

What can be checked is now public: the Lean files, the ten reasoning summaries, the compute estimates. The model that produced them is not. OpenAI says it is working on releasing it responsibly, with no date.

The visual is generated code art. No third-party images.

OpenAI put new math results from an internal model on GitHub, and many of the proofs are formalized in Lean

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OpenAI says an internal model solved the Navier-Stokes problem. The page cites no independent verification