OpenAI publishes 722 math preprints claiming solutions to hundreds of open problems

What was released

OpenAI has published a large batch of mathematical research in a public GitHub repository, at openai/math, containing hundreds of preprint papers dated between September 10 and October 6, 2026. According to The Verge, the release consists of 722 manuscripts grouped into 372 "result families," each family bundling related papers, and the work was produced by an unreleased frontier model.

The Advisory Group on Mathematics and Artificial Intelligence (AGMAI), an independent body of mathematicians formed to help communicate these results responsibly, says the batch includes solutions to "hundreds" of open questions. That figure extends a claim OpenAI made in September, when it said its model had "resolved more than 100 long-standing open problems across most areas of mathematics." The release drew wide attention on Hacker News, where it was discussed as a drop of roughly 700 preprints of proofs and counterexamples.

What's inside

The repository's directory listing reads like a tour of longstanding questions across combinatorics, algebra, operator algebras, geometric group theory, analysis and theoretical computer science. Many titles are explicit counterexamples: to Kaplansky's direct finiteness conjecture in both characteristic two and odd characteristic, to Kurosh's division ring problem, to Ryser's covering conjecture, to Wall's D2 problem, to Hadwiger's conjecture, to Sidorenko's conjecture, and to Naimark's problem in ZFC, among many others.

Other entries are positive results, including a proof of Saxl's conjecture via cyclic polytabloids, a modulus-based proof of Cannon's conjecture, a fully polynomial randomized approximation scheme for perfect matchings in general graphs, and an algorithm for integer multiplication below n log n — the repository provides a standard BibTeX citation for that paper, authored by OpenAI and dated September 23, 2026.

The Verge reports that, alongside the papers, OpenAI included summaries of the model's reasoning, estimates of the compute consumed, and statistics on how many problems were attempted. The company claims the "average result" took the equivalent of three hours of ChatGPT Pro thinking to produce.

The AGMAI guidelines

The release follows the first set of recommendations from AGMAI, published in late September. According to The Verge, the group urged AI labs to release mathematical results promptly and, where possible, through established academic channels, while disclosing the model name, the prompts used and the compute costs involved. It also asked companies to "refrain from treating the release of mathematical results as marketing vehicles to promote their models," arguing that this practice harms the mathematical community.

OpenAI described its process as publishing the results in a GitHub repository with protocols for paper revisions and citations, and said it is exploring other community-hosted alternatives that would meet the committee's guidelines. For future releases, the company said it intends to improve the quality of the papers' citations, exposition and presentation.

Reaction and open questions

Mathematicians had expected results of this kind for weeks, but OpenAI had not previously said which problems were solved or when the papers would appear, as The Verge notes. The full impact will take time to assess, since the community must now verify and digest a body of work far larger than a typical individual research output. The release also adds to a rapidly growing pile of AI-generated mathematics from OpenAI and rival labs such as Anthropic, including results bearing on a Millennium Prize problem.

The pace of these announcements has provoked debate over research ethics and academic conduct, particularly around how AI companies credit the human mathematicians whose prior work their systems build on. Whether this release satisfies AGMAI's guidelines — and how quickly the proofs hold up under scrutiny — will shape how future batches are received.

Why it matters

A single repository claiming resolutions to hundreds of open questions marks a step change in the scale of AI-assisted mathematics, and it arrives before the underlying model is even publicly available. The bottleneck is now shifting from producing proofs to verifying them, which puts new pressure on peer review, citation norms and academic incentives. How the community digests this batch, and whether the AGMAI framework holds, will set precedents for how machine-generated research enters the scientific record.