OpenAI Posts 722 Math Papers From an Unreleased Model, Including a Claimed Quasi-Riemann Hypothesis Proof
OpenAI posted 722 manuscripts from an unreleased internal model on GitHub, claiming results on zeta zeros, the Hodge conjecture and matrix multiplication. Only 162 have a Lean-checked main result.
OpenAI has put 722 mathematics manuscripts written by an unreleased internal model into a public GitHub repository. The company groups them into 372 “result families,” and the list reads like a syllabus of famous open problems: a zero-free half-plane for the Riemann zeta function, the Hodge conjecture for CM abelian varieties, a 9/4 bound on the matrix multiplication exponent.
The catch sits in the repo’s own files. Its Lean formalization catalogue lists 162 papers whose main result has been machine-checked, and that catalogue’s review field reads “unchecked.” OpenAI’s README says plainly that “some of the unformalized results could have issues.”
The release went live at 6 p.m. EDT on October 6 (3:30 a.m. IST on October 7), according to Scientific American, alongside an OpenAI post titled Sharing AI progress in mathematics. “OpenAI mathematics” is now a trending US search on Google, and the release is a top AI story on X.
What OpenAI actually released
The repository is licensed Apache 2.0 and holds PDFs, source files, a Lean library and per-paper citation instructions. According to the README, the work came out of model evaluations on open research problems, which OpenAI expanded “after performance on our existing mathematical evaluations saturated.”
OpenAI says the model was posed about 4,000 problems. It grouped the output into families, applied what it calls “an appropriate level of significance,” and ended up with the 722 papers. On average, each result used about three hours of ChatGPT Pro thinking compute with the internal model.
The preprints are dated between September 10 and October 6, 2026, with most of them dated in the last week of September or on October 5. Family numbers in the manuscript map run up to 377 because five numbers are skipped, which is why 372 is the actual count.
| Item | What the repo says |
|---|---|
| Manuscripts | 722, grouped into 372 result families |
| Problems posed to the model | About 4,000 |
| Average compute per result | About 3 hours of ChatGPT Pro thinking |
| Papers with a formalized main result | 162 in the Lean catalogue |
| Families linking to a Lean scope page | 235 of 372 |
| Abridged reasoning summaries | 10 |
| License | Apache 2.0 |
| Model name, price or API access | Not disclosed |
The headline claims, and which have Lean behind them
Each family gets a one-paragraph summary in the repository’s manuscript map. Here is a sample of the biggest claims, with whether the family links to a Lean scope page.
| Family | Claim, as OpenAI states it | Lean page? |
|---|---|---|
| 003 | Every Dirichlet L-function, including zeta, has no zeros where the real part exceeds 7/8 (the “quasi-Riemann hypothesis”) | Yes |
| 017 | The irrationality exponent of pi is exactly 2 | Yes |
| 107 | The matrix multiplication exponent over the complex numbers is at most 9/4 | Yes |
| 159 | Erdős’s conjecture that any set with a divergent reciprocal sum contains arithmetic progressions of every length | Yes |
| 287 | The free group factors are all isomorphic | Yes |
| 004 | Hilbert’s tenth problem over the rationals has a negative answer | No |
| 032 | The rational Hodge conjecture holds for every complex CM abelian variety | No |
| 074 | The Kakeya maximal conjecture in three dimensions and the dimension conjecture in four | No |
A Lean link does not mean the whole paper is checked. The scope page for the pi result says the formalization proves the exponent is two, but the paper’s consequence for the Flint-Hills series “is outside this selected statement.” Each scope page is the real boundary of what a computer has verified.
OpenAI also flags exceptions to its own process. The README says the zeta zero-free work and the Hodge proof for CM abelian varieties did not follow the fixed procedure used for most results. The write-up for a separate zero-free region, at real part above 11/12, “was human edited for readability.”
One mathematician’s reaction went viral
The zeta result drew the loudest response. “Quasi-RH?!?!???! Are you kidding me? If a human did this, it would be an instant Fields Medal, no questions asked,” Rutgers mathematician Alex Kontorovich posted on X. That post had passed 570,000 views by Wednesday afternoon IST.
Kontorovich is not a neutral bystander on the tooling. His PrimeNumberTheoremAnd Lean project is listed as one of the libraries the formalizations build on. In a follow-up he added “no Siegel zeros either,” pointing to a companion paper on excluding Landau-Siegel zeros that the Lean scope page for family 003 also covers.
Why many mathematicians are not celebrating yet
Scientific American reported that an OpenAI spokesperson said the model produced almost every result from a single prompt given to a single agent. The magazine contrasts that with OpenAI’s earlier Navier-Stokes result, which it says came from a swarm of 10,000 agents and cost millions of dollars in compute. The spokesperson also said some results might have taken multiple attempts.
“Until and unless they release the model and people can replicate their results, I think you should treat any claims about one-shotting problems with a single agent as unverified,” Andrew Sutherland of MIT told the magazine. “We should ask for receipts.”
Daniel Litt of the University of Toronto took the other side. “If we want to know the answers to these math questions, I see no reason why we should ask the company to keep them secret from us,” he said. The magazine also noted that Terence Tao has criticized the “insane” pace of AI-generated results, and reported that many of the new results are not yet understood by OpenAI’s own mathematicians.
OpenAI followed some advice, not all of it
OpenAI says it consulted the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study. Its nine members include Timothy Gowers, Martin Hairer and Edward Witten. The group says it formed after OpenAI approached some of its members, takes no payment and has no decision-making power at any company.
Its September 29 guidelines, according to Scientific American, ask labs to disclose the model, exact prompt and compute time behind each result. OpenAI shared average compute, some statistics and no prompts. The spokesperson said the company takes the guidelines seriously but is not bound by them.
The group’s October 6 statement is careful. Its role “should not be interpreted as a judgment of the impact of these results or an endorsement of the process,” it wrote, adding that “this release is the beginning, not the completion, of the process of human understanding.”
| Disclosure | In this release? |
|---|---|
| Papers and source files | Yes |
| Lean formalizations | For many results, not all |
| Reasoning summaries | 10 abridged summaries |
| Compute per result | Average only |
| Exact prompts | No |
| The model itself | No, OpenAI says it is working to release it responsibly |
| Community-hosted repository | Not yet, OpenAI says it is exploring options |
OpenAI says it will keep every released version accessible, record corrections as new versions, and fund “a series of workshops, conferences, and special programs” on AI-produced results. It has not said how much money that involves. As The Verge notes, OpenAI said in September that its model had “resolved more than 100 long-standing open problems,” so this is the long-promised receipt, at least in part.
What it means for developers
The matrix multiplication claim will get engineers’ attention, so precision matters. The Lean scope page bounds the exponent at 9/4 and says the result “concerns arithmetic complexity, rather than bit complexity or practical crossover sizes.” Past record bounds in this range only paid off, on paper, at matrix sizes far beyond any real workload. Your GPU kernels will not change.
The bigger shift is in tooling. OpenAI leans on Lean and comparator files so outsiders can check claims without trusting the company, much like test suites anchor AI coding tools. We saw smaller versions of this when Meta said Muse Spark helped answer five open math questions, and when OpenAI said Astra solved 10 long-open problems.
What it means for Indian developers
India has a deep pool of mathematics and theoretical computer science talent, and the skill this release rewards is checking, not raw problem solving. People who can read a Lean statement, compare it with a paper’s claim and spot the gap are suddenly useful to every lab doing this work.
There is a caution for researchers too. As our report on AI writing in US STEM PhD dissertations showed, AI is already changing how academic work gets produced. Citing an unformalized result from this repository carries real risk until humans or Lean have checked it.
FAQ
How many math papers did OpenAI release?
722 manuscripts grouped into 372 result families, published in the openai/math GitHub repository on October 6, 2026 (US time).
Are the results verified?
Partly. The formalization catalogue lists 162 papers with a Lean-checked main result. OpenAI says some unformalized results could have issues, and these are preprints, not peer-reviewed journal papers.
Which model produced the papers?
An unreleased internal OpenAI model. The company has not named it, priced it or made it available in ChatGPT or the API.
Did OpenAI release the prompts?
No. It shared average compute per result, the number of problems attempted and 10 reasoning summaries, but not the prompts its advisory group asked for.
Does the matrix multiplication result make AI training faster?
No. OpenAI’s own Lean notes say the bound concerns arithmetic complexity, not practical speed, so it does not change real-world GPU or CPU performance.