On 6 October 2026, OpenAI published 722 math papers on GitHub, all written by an internal AI model it has not released. The company says each group of results resolves, or makes substantial progress on, an open problem in mathematics or theoretical computer science. Mathematicians have reacted with a mix of awe and anger. Here is what was actually released, what experts say about its quality, and what it means for the bigger question: can AI already do real mathematical research?
What OpenAI released: 722 math manuscripts on GitHub
Everything sits in the public openai/math repository under an Apache 2.0 licence. Based on its documentation and reporting by Scientific American and Quanta Magazine, the key facts are:
- 722 manuscripts grouped into 372 families of results, sorted by mathematical field.
- The model was given roughly 4,000 problems and failed on most of them. OpenAI then applied a significance threshold to decide what to publish.
- Each result used on average about three hours of ChatGPT Pro-equivalent thinking compute.
- A spokesperson told Scientific American that almost every result came from a single prompt to a single agent, though some may have taken several attempts. The repository lists two exceptions, one on the Riemann zeta function and one on the Hodge conjecture, and one write-up edited by a human.
- Only 10 families include summaries of the model's reasoning.
The headline claims include a solution to the four-dimensional Kakeya conjecture, improvements to important algorithms and progress toward the Riemann hypothesis. Read those carefully: progress is not a proof, and none of this work has been peer reviewed yet.
Are the proofs correct? Lean, errors and withdrawals
OpenAI's strongest card is formalisation in Lean, a programming language that checks the logic of a proof step by step. According to the repository's history, 300 of the top-line results (about 42%) have Lean versions, which makes their logic almost certainly sound. The other 58% rely on humans checking them by hand.
Human checking has already found problems. On 7 October, a day after release, OpenAI withdrew three algebraic geometry manuscripts because a sign error broke an argument they depended on, and revised 14 others. That is why the repository now lists 719 manuscripts.
Lean is not a blanket guarantee either. Johan Commelin, director of the Mathlib Initiative, told Quanta that experts still have to read the Lean code, since some formalisations appear to prove weaker statements than the papers claim. And TechCrunch reports that researchers at Cambridge and King's College London found at least two discrepancies between the prose and the Lean code in OpenAI's earlier Navier-Stokes proof.
What mathematicians say about OpenAI's math papers
Opinion is split, sometimes within the same person:
- Excitement: Harvard's Michael Douglas told Scientific American the release marked the start of a new era for mathematics. Jeremy Avigad wrote that it "includes major advances".
- Uneven quality: NYU's Roland Bauerschmidt said that had he received the papers by email from an unknown sender he would probably have deleted them because they are so badly written. Chaim Goodman-Strauss found novel ideas in a tiling paper, but nowhere near publishable form.
- Transparency: MIT's Andrew Sutherland says the single-agent claim should be treated as unverified until the model is released, and that OpenAI should publish its failures too: "You need to report your negative results along with your positive results."
- Sustainability: Terence Tao warned that open problems are being harvested "in an unsustainable fashion", skipping the follow-up work that normally comes with a proof.
- Rejection: the Association for Human Mathematics, a group of more than 800 mathematicians including Fields medallist Peter Scholze, urged colleagues to stop working with OpenAI, calling the mass release "not a demonstration of scholarship, but a demonstration of power".
The context explains the tension. As Scientific American notes, the same internal model had claimed a resolution of the Navier-Stokes problem a month earlier. In late September a nine-member advisory group hosted by the Institute for Advanced Study published guidelines for AI labs, including releasing the model, the exact prompts and the compute behind each result. OpenAI says it is trying to comply, but has released neither the model nor the prompts.
Can AI already do real mathematical research?
The honest answer is: partly, yes, in a way that was still debatable a year ago. Formally verified results on problems experts consider open, at this scale, are new. For the backstory, see our earlier piece AI that solves mathematics: the end of impossible theorems?
But research is more than producing proofs. Harvard's Melanie Wood put it to TechCrunch this way: when a model produces a solution, there is no human understanding of it at the point of release, "and now the work begins." The current limits are clear:
- It is not reproducible: the model is private and the prompts have not been shared.
- Verification falls on humans: hundreds of papers someone has to read, understand and sometimes fix.
- Context is missing: knowing why a result matters and what it opens up is what turns a proof into knowledge.
What it means for science and education
For science, the bottleneck moves from producing results to validating them. Peer review, already under strain, gets a new load; we looked at that in AI in scientific peer review: ally or threat?. Proof assistants like Lean shift from niche tool to core infrastructure, and other fields are watching closely, as with AI used to discover new physics.
For education, the message is less apocalyptic than it sounds. If AI can generate proofs, the valuable skills become reading them, verifying them and choosing which questions are worth asking. Learning to formalise an argument, and to catch the sign error that sinks three papers, becomes more useful, not less. Daniel Litt suggested treating these papers as "raw data" rather than finished results, which is a fair way to see where things stand.
Frequently asked questions
How many math papers did OpenAI publish?
It published 722 manuscripts in 372 result families on 6 October 2026. After withdrawing three over an error, the repository holds 719.
Which OpenAI model wrote the proofs?
An unreleased internal model that OpenAI has not named publicly, so nobody outside the company can reproduce the results.
Did OpenAI's AI solve the Riemann hypothesis?
No. OpenAI claims progress related to the Riemann hypothesis, not a solution.
Are the AI-generated proofs verified?
About 42% have Lean formalisations that check the logic automatically. The rest are not formally verified, and none has been through peer review.
