NewsScienceDevelopingNew
Two weeks after OpenAI's 722 math papers, mathematicians are checking the biggest claims
Mathematicians are checking AI-generated proofs OpenAI released on 6 October. Quanta reports broad support for a quasi-Riemann result, but most of the papers have not been reviewed and some were withdrawn.
Evidence: 5 sources · 2 official records · 2 independent reports · 1 research paper · 4 open questions
| Date | Event |
|---|---|
| 6 October 2026 | OpenAI posts 722 manuscripts on GitHub, some with Lean formal proofs |
| 13 October 2026 | Science reports the quasi-Riemann claim, a weaker statement than the Riemann hypothesis |
| 19 October 2026 | Quanta: experts largely back one proof; Tao posts a sketch of the Landau-Siegel argument |
| 20 October 2026 | Tao opens an AI-math challenge; checking continues |
What happened
- On 6 October, OpenAI posted 722 mathematics manuscripts to GitHub that it says were produced by an unreleased internal model.
- The best-known claim is a proof that the Riemann zeta function has no zeros with real part above 7/8, a weaker statement than the full Riemann hypothesis.
- On 19 October, Quanta Magazine reported that number theorists who studied that proof largely agree it is correct.
- On 19 and 20 October, Terence Tao posted a sketch of a separate AI-generated argument against Landau-Siegel zeros and an open challenge to use AI tools to make related bounds explicit.
Why it matters
If the results hold up, this would be one of the largest sets of new mathematics attributed to an AI system. Checking hundreds of unreviewed proofs is slow and falls on human experts.
What is confirmed and what is claimed
Confirmed
- OpenAI published the manuscripts and supporting proof files in a public GitHub repository on 6 October (repository; also reported by Science and Quanta). 2
- The quasi-Riemann result does not prove the Riemann hypothesis itself (Science, Quanta). 2
- Only some of the manuscripts come with formal proofs checked in the Lean proof assistant, and OpenAI's repository warns that unformalized results could contain errors (repository README, as reported by several outlets).
- Some manuscripts have been retracted after outside mathematicians found mistakes (Scientific American).
- Mathematicians including William Banks and Bryce Kerr have posted arXiv preprints reconstructing or simplifying the Landau-Siegel argument (arXiv). 5
Claimed, not independently verified
- OpenAI says an internal model produced the results and that it is working to release that model. 3
- Reports that four independent mathematicians confirmed the Landau-Siegel claim within two weeks come from a single outlet, Tech Times, and we could not confirm that count elsewhere.
On 6 October, OpenAI put 722 mathematics manuscripts on GitHub and said an internal model it has not released wrote them. The papers span number theory, algebra, theoretical computer science, logic, probability and topology. None of them has been through journal peer review.
The claim that drew the most attention is about where the zeros of the Riemann zeta function can lie. The Riemann hypothesis says that all the nontrivial zeros sit on a single line. The AI-generated paper claims something weaker: no zero lies beyond a fixed distance from that line. Many results that were proved assuming the full hypothesis need only a statement of this kind, which is why number theorists care. Quanta reported on 19 October that specialists who have read the proof largely think it is correct. One version comes with a machine-checked Lean proof.
Context
Checking is now the slow part. Terence Tao has written up a human-readable sketch of a separate AI argument, on Landau-Siegel zeros, and on 20 October he invited readers to use AI tools to make one of its key bounds explicit. Other mathematicians have posted preprints that rework the same argument. Some manuscripts in the release have already been retracted over errors.
A formal proof in Lean shows that a theorem follows from its stated assumptions, but someone still has to confirm that the formal statement says what the paper claims. See our guide to reading AI-for-science claims and to preprints and peer review.
What to watch
- Whether any of the results are submitted to, and accepted by, mathematics journals.
- A fuller count of retractions and corrections in the repository.
- Whether OpenAI releases the model, so that others can test how it produces proofs.
What we don’t know yet
- How many of the 722 manuscripts will survive expert review, and how many contain genuinely new mathematics.
- Whether the Landau-Siegel argument will be accepted as a full proof; the follow-up preprints have not been peer reviewed.
- How much human guidance went into choosing the problems and selecting which results to publish.
- Coverage gives slightly different counts for how many results have Lean formalizations, so the exact share is unclear.
Evidence and sources
- Independent reporting AI Proved the Quasi-Riemann Hypothesis. What Happens Now?
- Independent reporting AI edges closer to solving the Riemann hypothesis, one of math's hardest problems
- Primary announcement openai/math (manuscripts and proof artifacts)
- Document or data An experimental AI-math challenge: using tenth discriminant bounds to explore arguments ruling out Siegel zeroes
- Preprint (not peer reviewed) On the OpenAI proof that Landau-Siegel zeros do not exist