Are all of OpenAI's 722 math manuscripts formally verified?

No. The openai/math README says not all manuscripts have accompanying Lean formalizations, and that some of the unformalized results could have issues. OpenAI says it will keep adding Lean formalizations to the repository as it obtains them, so the share of machine-checked results should grow over time.

Which model produced the OpenAI math results, and can I use it?

The OpenAI math manuscripts were produced by an unreleased internal OpenAI model. It is not available in ChatGPT or the API. The README only says each result used, on average, the equivalent of three hours of ChatGPT Pro thinking compute with that model, which describes effort, not public access.

How will OpenAI handle mistakes in the math manuscripts?

OpenAI says it will preserve the public release history of the openai/math collection. Corrections and revisions will be recorded as new versions, and earlier released versions will stay accessible, so readers can see what changed after review instead of finding results silently edited or removed.

How is this different from OpenAI's earlier math announcements?

OpenAI's August release covered ten claimed advances in one long document. The October 6 openai/math release is far larger: 722 manuscripts in 372 families from about 4,000 posed problems, split into preprints, a Lean library and reasoning traces, under an Apache-2.0 license on GitHub.

OpenAI · 2026-10-06 · major

OpenAI posts 722 math manuscripts — internal model results, some Lean-checked

OpenAI released 722 math manuscripts in 372 families, all from an unreleased internal model that was given about 4,000 open problems. The openai/math GitHub repo holds the papers, Lean proofs and 10 reasoning traces.

GitHub preview card for the openai/math repository

OpenAI's biggest math drop yet: 722 AI-written manuscripts on GitHub, with Lean proofs for many but not all.

Key specs

GitHub stars	3,456
Manuscripts	722

Quick facts

Maker	OpenAI
Manuscripts	722, in 372 families
Problems posed	About 4,000
Compute per result	~3 hours of ChatGPT Pro thinking (average)
Model	Unreleased internal OpenAI model
Repo license	Apache-2.0

What is it?

The openai/math repository is a public collection of 722 mathematical manuscripts, grouped into 372 related families by field. Every result comes from an unreleased internal OpenAI model that OpenAI tests on open research problems. Topics range from number theory and complexity theory to mathematical physics, including the irrationality exponent of π and a relativistic Vlasov–Maxwell system.

How does it work?

Most results came from one fixed procedure: OpenAI posed roughly 4,000 problems to the internal model, and each accepted result used on average three hours of ChatGPT Pro thinking compute. The repo has three parts: preprints/ (PDFs and sources), a lean/ formalization library, and reasoning_traces/ with abridged traces for 10 selected results, such as the symmetric Mahler conjectures and Kaplansky's conjecture.

Why does it matter?

Mathematicians can now check the work instead of trusting a blog post: Lean files are machine-checkable, and corrections will be added as new versions while old ones stay public. OpenAI itself warns that unformalized results may have errors, so the release is also a large test of how fast the field can review AI-produced mathematics.

Who is it for?

mathematicians, theoretical computer scientists, formal-verification researchers

Frequently asked questions

Are all of OpenAI's 722 math manuscripts formally verified?: No. The openai/math README says not all manuscripts have accompanying Lean formalizations, and that some of the unformalized results could have issues. OpenAI says it will keep adding Lean formalizations to the repository as it obtains them, so the share of machine-checked results should grow over time.
Which model produced the OpenAI math results, and can I use it?: The OpenAI math manuscripts were produced by an unreleased internal OpenAI model. It is not available in ChatGPT or the API. The README only says each result used, on average, the equivalent of three hours of ChatGPT Pro thinking compute with that model, which describes effort, not public access.
How will OpenAI handle mistakes in the math manuscripts?: OpenAI says it will preserve the public release history of the openai/math collection. Corrections and revisions will be recorded as new versions, and earlier released versions will stay accessible, so readers can see what changed after review instead of finding results silently edited or removed.
How is this different from OpenAI's earlier math announcements?: OpenAI's August release covered ten claimed advances in one long document. The October 6 openai/math release is far larger: 722 manuscripts in 372 families from about 4,000 posed problems, split into preprints, a Lean library and reasoning traces, under an Apache-2.0 license on GitHub.

Try it

git clone https://github.com/openai/math