OpenAI Math Manuscripts: 722 AI Proofs Spark Skepticism

What OpenAI Released

OpenAI has posted 722 mathematical manuscripts to a public GitHub repository. The company says all of them were produced by an unreleased internal frontier model and that together they report solutions to a large number of open problems.12 The papers are grouped into 372 families of related results and carry an Apache-2.0 license, so anyone can inspect, reuse and build on them.2 The release went up on October 7, a Tuesday.12

The claims are broad. One account highlights proofs that OpenAI says its model produced for the quasi-Riemann Hypothesis, Khot's Unique Games Conjecture and the rational Hodge Conjecture, along with other major results.1 Another account is more cautious. It describes the release, in the words of the advisory group OpenAI consulted, as reporting solutions to "hundreds of open problems" across most areas of mathematics, rather than leading with individual landmark conjectures.2

Both accounts agree on one striking figure: the average result consumed about three hours of compute.12 One source pegs that to the equivalent of three hours of ChatGPT Pro "thinking."2 The model was given roughly 4,000 problems during the evaluation that produced the manuscripts.2 That means the 722 papers are the output of a much larger pool of attempts, not a single targeted campaign.

Verification, With Caveats

The most important detail for mathematicians may be the verification process. Many of the proofs were formalized in Lean, a proof assistant that lets a computer check every logical step mechanically.2 This matters because AI-generated mathematics has long faced a credibility problem: fluent-sounding arguments can hide subtle errors. A Lean-checked proof largely sidesteps that, provided the formal statement actually matches the theorem being claimed.

The record is not perfectly clean, however. Two results fell outside the standard procedure, and one write-up was edited by a human.2 These exceptions are small in number but worth noting. When the headline claim is that a machine solved problems on its own, every departure from the automated pipeline becomes a point of scrutiny.

Why the Math Community Is Pushing Back

The reaction has been described as fury.1 The available reporting points to specific institutional concerns rather than blanket rejection. The Advisory Group on Mathematics and Artificial Intelligence, the body OpenAI itself consulted, urged AI labs not to use mathematical releases as marketing tools.2 The group also said it does not endorse testing advanced problems on models the wider research community cannot access.2

That second point goes to the heart of the dispute. Normally, a proof is published and checked, and the methods behind it are open to anyone who wants to replicate or extend the work. Here, the proofs are public but the system that produced them is not. Researchers can verify the outputs, but they cannot probe the model's failure rate in detail. They cannot run their own problems through it or judge how representative the 722 manuscripts are of its typical performance.

The scale of the drop adds to the tension. Hundreds of papers arriving at once, spanning most of mathematics, is far more than the community's normal review machinery can absorb quickly. Even with Lean formalization, specialists will need to confirm that the formal statements faithfully capture famous conjectures. That is especially true for any result framed as a variant, such as a "quasi" form of the Riemann Hypothesis.

Where the Accounts Diverge

The two reports share the core facts: the manuscript count, the 372 families, the GitHub posting and the three-hour average.12 They differ in emphasis. One foregrounds marquee conjectures and community anger.1 The other foregrounds process: the roughly 4,000-problem evaluation, Lean formalization, the noted exceptions and the advisory group's cautions.2 Read together, they suggest that the significance of individual results is still being sorted out, and that the framing of the release is itself contested.

Our Reading

This looks like a genuine and substantial technical milestone wrapped in a communications choice that undercut it. Releasing proofs under a permissive license, with many of them machine-checked, is the kind of transparency critics usually ask for. But tying those results to an inaccessible model and releasing them all at once invites exactly the criticism the advisory group raised. It makes the release resemble a capability showcase more than a contribution to the field.

The lasting test will not be the count of 722. It will be how many results hold up once experts confirm the formal statements match the intended problems, and whether the most celebrated claims survive that scrutiny. Until then, the fairest description is that OpenAI has made a very large, partly verified claim, and has handed mathematicians a significant amount of homework.