OpenAI posted 722 math papers from a model nobody outside can test
On 6 October OpenAI put 372 families of new results from an unreleased model on GitHub. Its own README says about 42% of the top-line results have a Lean proof. The rest are waiting for mathematicians.
At 6 p.m. Eastern on 6 October, OpenAI put a folder of mathematics on GitHub. It holds 722 manuscripts written by an internal model the company hasn’t released. They’re grouped into 372 “families”, where each family is one main result plus its companion arguments, consequences or alternative proofs. So 722 counts papers, not solved problems. The repository is licensed Apache 2.0, which means anyone can download it and read every page.
Reading is the easy part. The hard part is judging whether any of it is right, and that’s where the release gets messy.
What OpenAI released
OpenAI says it posed the model roughly 4,000 open problems and kept the outputs it judged significant. The average result used about three hours of ChatGPT Pro thinking. A spokesperson told Scientific American that almost every result came from one prompt to one agent, though some took several attempts. OpenAI also published summaries of the model’s reasoning for 10 of the results and compute estimates. It did not publish the prompts.
The README currently lists 719 manuscripts, not 722. Implicator reports that OpenAI withdrew three papers on 7 October over a sign error. I haven’t seen that withdrawal notice myself, so treat it as their account.
The Wall Street Journal, as summarised by Quartz, reported that the batch touches three of the five Millennium Prize Problems still unsolved, including the Riemann hypothesis. OpenAI’s own page doesn’t put it that way. I’d call the Millennium claim reported, not confirmed, until a mathematician who has read the papers says so.
The Lean number is the one to watch
Lean is a programming language that checks a proof one logical step at a time. If the Lean version compiles, the logic holds, but only if the Lean statement says what the English paper claims. That’s the piece that makes this release different from the September Navier-Stokes claim, which had nothing comparable.
The two sources I could read don’t agree on how much is checked:
| Source | What it says |
|---|---|
| OpenAI’s repo README | About 42% of the top-line results are formalised in Lean |
| Decrypt, reading the same repo | 162 of 722 papers (about 22%) have a computer-checked main result |
I couldn’t reconcile the two. They may count different things, such as top-line results against all papers, or a formal statement against a full proof. Until someone explains the gap, I’d quote the range rather than pick a number. OpenAI’s own page admits the rest might be wrong: the README says “some of the unformalized results could have issues.”
Why mathematicians are angry
Most of the anger is about how the results arrived, not whether they’re right.
The Association for Human Mathematics, which says its 800-plus members agree not to work with commercial AI companies, told mathematicians to stop working with OpenAI. Its statement, quoted by The Independent, called the release “a demonstration of power.” Terence Tao told the same outlet that a real breakthrough usually sets off a wave of follow-up work and excitement in the field. Here the first job is reading 722 papers at once, and many of them come without named human authors.
The Institute for Advanced Study, whose advisory group OpenAI says it consulted, put the core problem in one sentence: AI can now produce mathematical arguments that the person who prompted it may be unable to understand, verify or take responsibility for. Decrypt quoted that statement.
The other side is real too. Rutgers mathematician Alex Kontorovich wrote on X that if a human had produced the Riemann-related result, “it would be an instant Fields Medal, no questions asked.” Some researchers are already working through the papers. MIT’s Andrew Sutherland doesn’t dispute that. His objection is narrower: “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. We should ask for receipts.”
What I think
If even a good share of these Lean-checked results hold, this is a real change in how mathematics gets done, and I’m not going to wave it away. But the format makes judging it hard. The papers are unexplained, the model can’t be tested by outsiders, and OpenAI’s own repository calls part of the work unchecked. That’s a weak way to publish a scientific claim.
The denominator helps a little. The 372 families were picked from about 4,000 attempts, so this release shows what the model produced when OpenAI chose to publish. It doesn’t show how often the model is right.
I’d watch two things. One is whether the Lean share rises, and whether the 42% and 22% figures get reconciled. The other is whether anyone outside OpenAI reproduces one of these results with a published prompt. Right now, neither of those has happened.
For the pattern behind this, see OpenAI shelved GPT-6.1 Astra, where the company also decided what outsiders could see. The sandbox story is in OpenAI’s model got out of its sandbox.
Sources
- OpenAI: Sharing AI progress in mathematics (6 October 2026)
- GitHub: openai/math repository and README
- Scientific American: OpenAI unleashes hundreds more math results upon a field already in shock
- The Independent: Mathematicians are very, very angry at OpenAI. Here’s why
- Decrypt: OpenAI Says a Secret AI Model Cracked Hundreds of Open Math Problems in One Prompt
- Quartz, citing the Wall Street Journal: OpenAI releases 372 math result groups on GitHub
- Implicator: OpenAI’s 372 AI math results leave mathematicians racing