OpenAI publishes 722 math manuscripts with proofs checkable in Lean
An internal model is said to have solved open problems, and anyone can verify the proofs by machine instead of taking the claim on trust.
OpenAI released 722 mathematics manuscripts on October 6, 2026, and their proofs can be checked in the Lean proof assistant. An internal OpenAI model wrote them, and they target problems that were previously open. OpenAI announced the release itself; The Verge and heise online also reported on it.
What is known
According to OpenAI, the manuscripts come from an internal model. The company does not name the model or give a version.
The work draws on a pool of several thousand problems. Solutions now exist for roughly a tenth of them. Most of the pool remains unsolved.
The Verge reports that OpenAI published the material on GitHub. That means the proofs are not just described in a blog post. People can download and inspect them.
heise online calls the release hundreds of additional AI-generated solutions. The wording signals a follow-up, not a first batch.
The key detail is the format. The proofs can be checked in Lean. Lean is a proof assistant: software that tests every step of a proof against formal rules. If the check passes, the proof is correct for the formally stated claim, no matter whether a person or a model wrote it.
Why it matters
Claims that a language model solved a math problem share one weakness. They are hard to verify. A proof written in plain language has to be read line by line by experts, and with hundreds of manuscripts that takes months.
Lean changes who carries that burden. Skeptics do not have to trust OpenAI. They can run the proof through the checker themselves. That is what separates this release from a bare performance claim.
The share also puts the headline number in proportion. 722 manuscripts sounds like a lot, but it covers only about a tenth of the problem pool. The model did not crack open problems at will. It solved a small slice of a large collection.
For mathematicians, that slice still has value. Formally verified proofs can be reused as building blocks for other work, and they give researchers concrete material to study.
What is still unclear
The sources do not name the internal model or say whether OpenAI plans to make it public. They also leave open whether all 722 manuscripts are fully formalized in Lean and whether independent mathematicians have reviewed the results yet. A Lean check only shows that a proof matches its formal statement, not that the statement faithfully captures the original problem.
Dates
- October 6, 2026: OpenAI publishes the 722 math manuscripts
