OpenAI publishes 722 AI math manuscripts on GitHub, and mathematicians ask for receipts

OpenAI has opened the floodgates on AI mathematics. Late on 6 October 2026, US Eastern time, the company published a public GitHub repository called openai/math with 722 mathematical manuscripts that were produced by an unreleased internal model. The papers are grouped into 372 "result families", and according to OpenAI each family resolves or makes substantial progress on an open question in mathematics or theoretical computer science. The list of claimed results reads like a wish list of the last few decades: the quasi Riemann hypothesis, the Kakeya problem in three and four dimensions, the Unique Games Conjecture, and a way to multiply huge integers faster than a bound that was believed to be optimal since 1971.

The reaction from mathematicians was immediate and mixed. Some welcome the results as a gift to the field. Others say OpenAI ignored the advice it asked for, and that a company which keeps its model and its prompts private cannot expect to be taken at its word. As MIT mathematician Andrew Sutherland put it to Scientific American: "We should ask for receipts."

What OpenAI actually released

Here is what is on the record in the repository itself and in OpenAI's announcement post, "Sharing AI progress in mathematics".

• 722 manuscripts in 372 families. A family groups related papers: a main result, companion arguments, consequences or alternative proofs. Every family is classified by discipline in an overview PDF, and a manuscript map lists every paper with its abstract.
• One internal model. OpenAI says the vast majority of results came from the same procedure with an unreleased internal model. According to an OpenAI spokesperson quoted by WIRED, the company began training this model on 28 August, and it is the same model that resolved the Navier-Stokes Millennium Prize problem last month.
• About 4,000 problems. Over the course of the evaluation, the model was posed roughly 4,000 problems. OpenAI then grouped the output into families and kept only results it considered significant enough.
• About three hours per result. On average, each result used the equivalent of three hours of ChatGPT Pro thinking with that model. OpenAI did not publish the compute for each individual result.
• Lean proofs, but not for everything. Many manuscripts come with formal proofs in Lean, a programming language that checks every logical step. The repository's formalization catalogue lists 162 papers with a formalized main result, and in the manuscript map 235 of the 372 families link to Lean documentation. OpenAI says some of the unformalized results "could have issues" and promises to fix them quickly.
• Ten reasoning summaries. For ten families, including the irrationality exponent of pi, the Mahler conjectures and Kaplansky's direct finiteness conjecture in characteristic two, OpenAI published abridged summaries of how the model reasoned.
• Exceptions. Not everything came from the fixed procedure. The README names work on a zero free region for the Riemann zeta function and a proof of the Hodge conjecture for CM abelian varieties as exceptions, and says one write up was edited by humans for readability.
• License and versions. The repository is published under the Apache 2.0 license. Corrections will appear as new versions, and older versions stay accessible so that citations keep working.

Every corner of mathematics

What makes this release different from earlier AI math news is the breadth. These are not ten puzzle style problems from one area. The overview groups the 372 families into 17 fields, and no field is left out.

Theoretical computer science leads with 40 families, followed by combinatorics with 37, algebraic and complex geometry with 36 and number theory with 31. Even the smallest group, mathematical logic, still has six families. A few of the headline claims, in plain words:

• The quasi Riemann hypothesis. The Riemann hypothesis says that the nontrivial zeros of the zeta function all sit on one line. The weaker "quasi" version asks for a zero free strip of positive width. Family 003 claims that every Dirichlet L function, including the zeta function, has no zeros where the real part is greater than 7/8. That would not prove the Riemann hypothesis, but it would be real progress on the most famous open problem in mathematics.
• Kakeya in three and four dimensions. How small can a set be that contains a line segment pointing in every direction? Family 074 claims the maximal conjecture in three dimensions and the dimension conjecture in four.
• The Unique Games Conjecture. Family 102 claims a proof of Subhash Khot's conjecture, which would settle the limits of efficient approximation for many optimization problems, such as Max Cut.
• The irrationality exponent of pi is 2. Family 017 claims that pi cannot be approximated by fractions much better than a typical number can.
• Integer multiplication below n log n. Family 109 claims a deterministic algorithm that multiplies two n bit numbers in time O(n (log n) to the power of 1 minus kappa), with kappa equal to 2 to the power of minus 182, on a multitape Turing machine. Schonhage and Strassen conjectured in 1971 that n log n is the best possible, and Harvey and van der Hoeven only reached n log n in 2019. The gain here is purely theoretical, because kappa is absurdly small, but it would disprove a 55 year old belief.

All of these are claims by OpenAI. Some have Lean proofs that a computer can check, others do not. None of them have been through peer review yet.

Two weeks, 722 papers

The dates on the manuscripts tell their own story. Every paper folder in the repository carries a date in its name, and almost all of them fall within two weeks.

More than half of all papers are dated 23 or 24 September, and another 112 are dated 5 October, one day before the release. This is the speed that worries people. Human mathematicians might publish a handful of papers a year. Here, a single system produced hundreds within days, and OpenAI told Scientific American that many of the new results are not yet understood by the company's own mathematicians.

How we got here

This release did not come out of nowhere. In September, OpenAI announced that its model had resolved the Navier-Stokes problem, one of the Millennium Prize problems. According to Scientific American, that solution came from a swarm of around 10,000 AI agents and cost millions of dollars in compute. The release was controversial: WIRED reports that NYU mathematician Tristan Buckmaster accused OpenAI of front running unpublished work he had done with an Anthropic employee, and that the talks over credit became tense. OpenAI researcher Sebastien Bubeck pointed WIRED to an earlier public statement in which he denied asking for that employee to be left off the paper.

In August, OpenAI had already met with around 40 mathematicians to discuss what to do if AI outpaces humans in the field. According to WIRED, the group asked the company to publish real papers that explain the work, rather than results in a blog post or a tweet. Northwestern mathematician Bryna Kra told WIRED: "Apparently, that input was ignored." On 21 September, OpenAI announced that it was assembling an independent advisory group of mathematicians, the Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study, which has since published recommendations for releasing AI generated results.

The difference this time is the method. An OpenAI spokesperson told Scientific American that almost every result came from a single prompt given to a single AI agent, although some may have needed multiple attempts. If that holds up, the expensive swarm is no longer needed, and this kind of mathematical power could become accessible to anyone with access to the model.

The receipts problem

The advisory group's recommendations call for companies to publish the model, the exact prompt and the compute time behind each result. This release only partly meets that bar.

OpenAI publishes the papers, many Lean proofs, ten reasoning summaries and an average compute figure. It does not publish the prompts, and the model itself is not available. The spokesperson told Scientific American that OpenAI takes the guidelines seriously but is not bound by them, and that the company is working to release the model "as quickly and responsibly as possible". In its own post, OpenAI says it is still exploring community hosted alternatives to GitHub and will fund workshops, conferences and special programs around understanding major AI results.

The criticism is not only about transparency. NYU visiting professor Nestor Guillen told WIRED that "there's a perception of mobster behavior" from AI companies among mathematicians, which OpenAI rejects. Terence Tao has criticized the "insane" pace of AI generated results from frontier labs. On the other side, University of Toronto mathematician Daniel Litt told Scientific American that he sees no reason to keep the answers secret: "To me, it's going to be a good thing for mathematics."

Why it matters

First, this is the clearest sign yet that frontier AI models can do research level mathematics at scale. OpenAI says it expanded these open problem evaluations because its models had saturated the existing math benchmarks. When a test suite is too easy, the next test is the real frontier of human knowledge, and that is where the model is now being measured.

Second, verification becomes the bottleneck. Producing a proof is now cheap for whoever owns the model. Checking it is still expensive for everybody else. Lean formalizations help a lot, because a machine checked proof is all but certain to be correct, but only if the formal statement really matches the claimed theorem. For the families without Lean proofs, the community has to read the papers the old way, and Scientific American expects that to take months.

Third, it changes the incentives in science. If one company can resolve hundreds of open problems in two weeks and release them on its own terms, questions about credit, priority and peer review get much harder. Mathematicians who spent years on some of these problems may now find them answered in a GitHub folder with "OpenAI" as the author. That is why the debate about prompts and model access is not a technicality. It decides whether other people can build on this work or only consume it.

Finally, it matters for the AI race. OpenAI says these math problems are an indispensable test to show that its models are really getting smarter. Expect Anthropic, Google DeepMind and others to answer with their own results, and expect more releases like this before the end of the year.

Dany's take

I find this release both impressive and a bit uncomfortable. Impressive, because even if only a part of these 372 families holds up, it would be one of the biggest bursts of mathematical progress ever. And the Lean proofs are a big step in the right direction: a machine checked proof does not care who wrote it or how famous the author is.

Uncomfortable, because OpenAI asked mathematicians for advice and then followed it only where it was convenient. Publishing the average compute instead of the prompts is not transparency, it is marketing with footnotes. If the model really solves these problems with a single prompt, then publishing the prompts costs OpenAI very little and would let everyone test the claim.

What I will watch next: how many of the unformalized results survive a close reading in the coming weeks, whether the first correction versions appear in the repository, whether OpenAI really releases the model to researchers, and how Anthropic and Google respond. Until then, I treat this as a huge set of claims with partial proof attached. That is still big news, just not the end of mathematics.

Sources

• OpenAI on GitHub: openai/math repository (README, overview PDF and manuscript map, 6 October 2026)
• OpenAI: Sharing AI progress in mathematics (6 October 2026)
• Scientific American: OpenAI unleashes hundreds more math results upon a field already in shock (6 October 2026)
• WIRED: OpenAI is pissing off a bunch of mathematicians, again (6 October 2026)
• The Verge: OpenAI drops another batch of mathematical breakthroughs (6 October 2026)