TL;DR
- On October 7, OpenAI published a GitHub repository containing 722 mathematical manuscripts from an unreleased internal model, organized into 372 result families. The model itself was not released — only the papers. - Claims include a proof of the quasi-Riemann Hypothesis (all Dirichlet L-functions zero-free in the region where the real part exceeds 7/8, eliminating the Landau-Siegel zeros), the rational Hodge Conjecture for CM abelian varieties in all dimensions, Khot's Unique Games Conjecture, Hilbert's Tenth Problem over the rationals, the Kakeya Conjecture in 3 and 4 dimensions, and irrationality of Catalan's constant. - 162 of 722 papers include Lean formal verification — a computer-checkable proof. The other 560 do not. OpenAI's own repository warns: "some unformalized results could have issues." - Average compute per result: approximately 3 hours of ChatGPT Pro. Most were generated with a single prompt to a single agent. - The Institute for Advanced Study's independent Advisory Group on Mathematics and AI had published recommendations on September 29 — eight days before this release — specifically stating that AI math repositories "should not be controlled by any AI lab." OpenAI published to its own GitHub organization. - Multiple leading mathematicians — including Fields Medalists and IAS faculty — called the move "mafia-like" and accused OpenAI of ignoring explicit requests made at a closed-door August meeting to follow academic norms. The Navier-Stokes controversy from September, in which OpenAI was accused of scooping a collaborative result between an NYU mathematician and an Anthropic researcher, provides the backdrop.
This is not a Sputnik moment for mathematics. It might become one. Right now it is a repository of 722 unreviewed manuscripts from a company that withheld the model that generated them, published to a platform it controls, eight days after an independent advisory group said it should not do that.
The math might be right. Some of it will be wrong. None of it has been checked yet by anyone outside OpenAI. These are not contradictory statements — they are all simultaneously true, and the confusion between them is exactly what the mathematics community is currently furious about.
What the repository contains
The github.com/openai/math repository went live on October 7. It contains 722 PDF manuscripts organized into 372 result families across 17 mathematical disciplines: number theory, algebraic and complex geometry, analysis, theoretical computer science, combinatorics, probability, topology, differential geometry, partial differential equations, and others.
The results fall into three categories: new proofs of open conjectures, extensions of known results, and negative resolutions (proving that something is false or impossible). The most prominent claims:
Result 003, quasi-Riemann Hypothesis: OpenAI's model proved that all Dirichlet L-functions have no zeros in the region where the real part exceeds 7/8. It simultaneously eliminated the "Landau-Siegel zero" — a pathological special case that has haunted analytic number theory for decades. OpenAI notes this result underwent "extremely rigorous human review and readability polishing" — it was not purely automated. The original Riemann Hypothesis (all non-trivial zeros of the Riemann zeta function lie on the critical line) remains unproven. This is a weaker but still significant result.
Result 032, rational Hodge Conjecture for CM abelian varieties: The model proved the rational Hodge Conjecture for every complex abelian variety with complex multiplication (CM), in every dimension and codimension. It also derived the Tate conjecture for all abelian varieties over finite fields and the Hodge standard conjecture in arbitrary characteristic. No Lean formalization has been provided for this result — the most important claim in the repository is also the least verified.
Result 004, Hilbert's Tenth Problem over the rationals: A negative resolution — proving that there is no general algorithm to determine whether a polynomial equation with rational coefficients has a rational solution. This has been an open problem since Matiyasevich resolved the integer version in 1970.
Result 005, irrationality of Catalan's constant: Catalan's constant (approximately 0.9159...) has been suspected irrational since the 18th century. A proof of its irrationality has eluded number theorists for over two centuries.
Result 074, Kakeya Conjecture in 3 and 4 dimensions: The Kakeya problem asks about the minimum space needed to rotate a needle through all directions. Partial results had previously been achieved only up to dimension 2; a 3D result would be a major advance.
Also included: the Unique Games Conjecture (Khot's UGC, which has implications for the approximability of NP-hard problems), the symmetric and general Mahler conjectures in convex geometry, and the Chowla/Elliott conjectures on multiplicative functions.
The verification question
162 of 722 manuscripts include Lean formalization. Lean is a formal proof assistant — it allows a computer to check each logical step of a proof for validity. A Lean-verified proof cannot contain certain classes of logical error. If the Lean formalization is correct and complete, the result is correct.
The other 560 manuscripts have no Lean verification. OpenAI's own README says: "some unformalized results could have issues."
Result 032 — the rational Hodge Conjecture, the most significant claim in the repository — is not Lean-verified. The most important result is also the one that has received the least mechanical checking.
The quasi-Riemann Hypothesis result (003) is Lean-verified, and OpenAI notes it received human expert review. These are the conditions under which the mathematical community can begin to evaluate a claim — not all 372 results meet them.
The distinction matters because the repository was published simultaneously, without differentiation in the press coverage between the verified and unverified claims. A Lean-verified proof and an un-formalized manuscript with an OpenAI warning label are different categories of evidence. They are being discussed as if they are the same thing.
The context that explains the fury
The mathematics community's reaction cannot be understood without two months of backstory.
In August 2026, OpenAI convened a closed-door meeting with approximately 40 leading mathematicians. Multiple attendees told Wired that during this meeting, the mathematical community made explicit requests: follow academic publication norms, coordinate on peer review before release, do not dump results without verification. OpenAI acknowledged the meeting and used the Institute for Advanced Study's independent Advisory Group on Mathematics and AI as a consultation body.
That advisory group published its public recommendations on September 29 — eight days before the repository went live. One of its stated principles: AI math repositories "should not be controlled by any AI lab."
OpenAI published the repository to github.com/openai — its own GitHub organization. The company said it is "exploring community-hosted alternatives." That exploration did not happen before the release.
The Navier-Stokes controversy compounds this. In September, OpenAI published what it called a proof of the Navier-Stokes Millennium Prize problem. NYU mathematician Levent Alpöge and Anthropic researcher Tristan Buckmaster had been collaborating on the same problem — and alleged that their collaborative work had been appropriated or preempted. OpenAI disputed this characterization. The Clay Mathematics Institute review of the Navier-Stokes claim is still pending.
Multiple mathematicians named in Wired's coverage of the October 7 release described OpenAI's conduct as "mafia-like." The named critics include Fields Medalists and IAS faculty. The specific grievance: OpenAI used the closed-door August meeting to gather information about what problems the mathematical community cared about, used it in model training and problem selection, then released 722 manuscripts without following any of the norms it was asked to follow.
The advisory group demanded disclosure of the specific prompts used and full compute costs. OpenAI published average compute figures (approximately 3 hours per result) and did not publish the prompts.
What the model's absence means
OpenAI published the papers. It did not release the model that generated them.
This creates an asymmetry that is unusual in science: the results are public, the methodology is partially described, but the instrument that produced the results cannot be independently reproduced. Standard scientific practice requires that a result be reproducible. If another researcher cannot access the model, they cannot reproduce the result — they can only verify the written proof, which is what Lean formalization provides for the 162 manuscripts that include it.
For the 560 unformalized manuscripts, other mathematicians must read the proofs and evaluate them by hand. This is the process that peer review is designed to organize. Publishing 560 unformalized proofs simultaneously, without peer review, is the equivalent of asking the entire mathematical community to conduct a mass review on no timeline — or to accept the results without review, which is what most press coverage effectively does.
Sébastien Bubeck, who leads Microsoft Research's mathematical reasoning work and has been vocal on AI-math methodology, has argued that the publication method undermines the results' credibility regardless of their mathematical content. The process by which a result is validated is not separate from its scientific status — it is part of what makes it a scientific result.
Why this matters beyond mathematics
The mathematics controversy is, at a larger scale, the same governance dispute that is playing out in AI agent deployment: who decides when an AI system's outputs are ready for use in the real world, and what verification is required before that happens?
For agents, the answer is increasingly: regulators, through the FTC probe and the three-lab safety coordination. For mathematics, there is no equivalent external governance. The mathematical community has norms — peer review, publication in refereed journals, independent verification — but no enforcement mechanism. OpenAI is under no legal obligation to follow them.
The IAS Advisory Group's recommendation that repositories "should not be controlled by any AI lab" was an attempt to create neutral ground for AI-generated mathematics. OpenAI published on its own GitHub eight days later.
This is consistent with a pattern: the company's approach to self-imposed governance constraints, whether in safety research (David Robinson's Atlantic essay), in academic norms (the August mathematician meeting), or in the IAS Advisory Group recommendations, has been to engage, acknowledge, and then proceed on its own timeline.
The mathematical community cannot stop OpenAI from publishing proofs on GitHub. It can decide whether those proofs are accepted as mathematics. That verification process — which will take months for the significant results — is now underway.
Whether the quasi-Riemann Hypothesis result holds will be determined by mathematicians checking the proof, not by the number of papers in the repository. Result 003 has Lean verification and human expert review. That is the result most likely to survive contact with the mathematical community. The other 371 result families are on a longer timeline.
The model that generated them is still unreleased.
