OpenAI Math: 722 Mathematical Manuscripts from an Internal AI Model

Three hours. According to OpenAI, that is the average computation spent by its internal model for one mathematical result, equivalent to three hours of "thinking" by ChatGPT Pro. 

At that scale, OpenAI uploaded 722 mathematical manuscripts to GitHub on October 6, 2026 in a release called OpenAI Math. It contains research results claimed to come from an AI model not yet released to the public, and now awaits examination by mathematicians.

Key Takeaways

• OpenAI released 722 manuscripts in 372 result families in the openai/math repository, licensed Apache-2.0.
• Many proofs include Lean formalization that computers can check, but not all. OpenAI itself warns that unformalized results may be problematic.
• Independent verification by the mathematics community is still ongoing, and some parties question the release method.

What OpenAI Released in the Math Repository

According to OpenAI, this release contains various new mathematical results produced by an "internal frontier model." All were uploaded to the GitHub repository openai/math. 

Unite.AI details the contents: 722 manuscripts grouped into 372 families. One family contains related papers, for example the main result, companion arguments, consequences, or alternative proofs.

Each family is classified by branch of mathematics. The preprint directory stores PDFs, source files, and citation instructions, while the formalization catalog explains the available formal proofs. The entire collection is released under the Apache-2.0 license.

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Among all those results, two are specifically mentioned by the repository README. First, work on the zero-free region for the Riemann zeta function. Second, a proof of the Hodge Conjecture for CM abelian varieties.

It is important to note that this result on the Riemann zeta function is not a proof of the famous Riemann hypothesis. According to Gadget Review, the claim concerns the zero-free region, which is weaker than the classical hypothesis.

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How the OpenAI Math Results Were Made

The vast majority of results were obtained using the same procedure, according to the README cited by Unite.AI. During evaluation, the model was given about 4,000 problems. On average, one result used computation equivalent to three hours of ChatGPT Pro.

OpenAI says it expanded this evaluation after performance on existing mathematics evaluations reached saturation. Some outputs were also built on previous results from the same model.

For transparency, the repository contains three additional things:

• 10 model reasoning summaries.
• Computation estimates in ChatGPT Pro usage units.
• Statistics on the number of problems attempted.

The ten reasoning summaries touch on diverse topics, from the irrationality exponent of π to the spin glass formula and the relativistic Vlasov–Maxwell system. The paper on the zero-free region of the zeta function is also said to have been human-edited to make it easier to read.

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Lean Proofs and the Limits of Verification

Lean is a programming language that allows mathematical proofs to be checked by computer. Many manuscripts in the repository have companion formalizations in Lean, and OpenAI promises to add formalizations over time.

Not all results have been formalized. The README warns that some that have not been formalized may have issues, and OpenAI states it will fix them quickly. Fixes are recorded as new versions, while old versions remain accessible.

So, Lean formalization helps prove that the logical steps are valid. However, results without formalization still depend on human review, and that is where the biggest work awaits.

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Recommendations from the IAS Advisory Group

Before release, OpenAI says it consulted with the Advisory Group on Mathematics and Artificial Intelligence (AGMAI) at the Institute for Advanced Study. 

The group published responsible release recommendations on September 29, 2026, after receiving more than 600 responses from the mathematics community, according to Unite.AI.

The contents of the recommendations are quite firm. Results should be stored in a scientific repository not controlled by any AI lab and should not be used as a model marketing tool. 

For each result, laboratories are asked to disclose the model name, prompt, reasoning summary, processing time, and estimated computation cost. Mass releases also need a document explaining how many equivalent problems were attempted but failed to be solved.

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OpenAI said it used the group's advice as a reference. Nevertheless, this release has not met all of it. The repository is still on OpenAI's GitHub, and OpenAI itself says it is still looking for a community-managed hosting alternative. 

Reasoning summaries are also available for only 10 results, while the full model and prompts have not been published. Gadget Review noted that this release did not fully adopt those recommendations.

Background: From Navier–Stokes to 722 Manuscripts

The phrase "internal frontier model" in this announcement refers to OpenAI's announcement on September 8, 2026. 

At that time, OpenAI stated that its model produced a proof, complete with Lean formalization, that smooth three-dimensional fluid flow according to the Navier–Stokes equations can form a singularity in finite time. 

This problem is one of the Seven Millennium Prize Problems, and OpenAI stated it did not intend to claim the prize, according to Unite.AI.

A claim that big sparked debate about how to verify and give credit for AI-generated proofs. The release of 722 manuscripts came after that debate, according to Inside AI.

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Concerns from the Mathematics Community

A release this big makes experts cautious. IBTimes reported that mathematicians question the giving of credit for AI results, how to verify such a large volume, and the possibility that a flood of AI papers could burden the peer review system.

According to Gadget Review, broad verification by the mathematics community has not yet formed, and the absence of access to the exact model and prompts makes examination difficult. Therefore, for now, OpenAI's claims should be read as "according to OpenAI," not as problems that have already been confirmed solved.

OpenAI says it will fund workshops, conferences, and special programs to understand large AI-generated results, and is working to release the model responsibly. Details will be announced later.

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Conclusion

OpenAI Math is the release of 722 manuscripts in 372 result families from OpenAI's internal AI model. The results are claimed to touch open research problems, with Lean formalization on many proofs and a number of reasoning summaries.

Despite its size, its scientific value can only be determined after the mathematics community examines it. Results without formalization still require human review, and the release method is not fully aligned with AGMAI recommendations. Monitor verification developments from official sources and trusted coverage.

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FAQ

1. What is OpenAI Math?
OpenAI Math is the GitHub repository openai/math containing 722 mathematical manuscripts in 372 result families. All were produced by OpenAI's unreleased internal AI model.

2. Has OpenAI already solved a major mathematical problem?
OpenAI claims some results touch open research problems, but broad verification by the mathematics community has not yet formed. These claims should be read as "according to OpenAI."

3. How long did the model work on each result?
On average, one result used computation equivalent to about three hours of ChatGPT Pro "thinking." This figure comes from OpenAI.

4. What is a Lean proof?
Lean is a programming language that allows mathematical proofs to be checked by computer. Many manuscripts in the repository have one, but not all.

5. Are all the results verified?
Not yet. The repository README warns that results that have not been formalized may have issues.

6. Is this the same as proving the Riemann hypothesis?
No. The result mentioned concerns the zero-free region of the zeta function, which is weaker than the classical Riemann hypothesis.

7. Who is AGMAI?
AGMAI is an independent advisory group for mathematics and AI at the Institute for Advanced Study. It published recommendations for releasing AI results on September 29, 2026.

8. Where can the results be accessed?
All manuscripts are available in the GitHub repository openai/math under the Apache-2.0 license.