Roughly a month before its latest release, OpenAI said an internal model had solved the Navier-Stokes existence and smoothness problem, using up to 10,000 AI agents in parallel over roughly 88 hours at a cost running into the millions of dollars.
The announcement set up a larger strategic choice for the company: whether to keep testing the hardest mathematical questions on systems that outside researchers cannot inspect. The Institute for Advanced Study’s Advisory Group on Mathematics and Artificial Intelligence, which drew on input from more than 600 mathematicians, issued guidelines asking AI labs to stop testing frontier mathematical problems on proprietary models.
OpenAI said it would continue such testing.
On October 7, the company released 722 AI-generated mathematical manuscripts in one batch, organised into 372 groups in a public GitHub repository named openai/math. The papers were produced by an internal model that OpenAI has not released to outside users, and the company said the model had attempted approximately 4,000 problems.
Sam Altman, OpenAI’s leader, wrote on X: “We are entering a new era of discovery now”.
OpenAI says the collection contains 377 new mathematical results across number theory, algebraic geometry, algebra, theoretical computer science, mathematical logic and topology. It includes results bearing on three of the Millennium Prize Problems still unsolved, among them the Riemann hypothesis.
The scale of the release is part of its significance. OpenAI said the average result required the equivalent of roughly three hours of ChatGPT Pro thinking. For researchers, the immediate task is less to absorb the company’s headline claim than to establish which of the manuscripts amount to sound mathematics.
OpenAI has provided some material for that work. Many proofs are accompanied by Lean formalizations, along with 10 summaries of the model’s chain of thought and data on computing resources. Yet the public catalog shows formalization files for 235 of the 372 result families.
The company has acknowledged that proofs without formal verification may contain errors. An OpenAI spokesperson said many of the new results had yet to be fully understood even by the company’s own mathematicians.
That leaves important questions unresolved, including whether any claimed result involving the Millennium Prize Problems is correct, and how many papers have received scrutiny from mathematicians outside OpenAI. The company said the work has not all been reviewed by other experts.
OpenAI worked with the Institute for Advanced Study’s advisory group to shape the release. Lindsay McCallum, an OpenAI spokesperson, said the company was proceeding “responsibly” and had taken the group’s recommendations into account. McCallum also said OpenAI was “not aware” of any promise that it would refrain from releasing all the results at once.
More than two dozen Fields Medal recipients have issued an open letter warning that the industry’s approach threatened to undermine mathematics as a field. Their concerns centre on attribution, publication standards and whether frontier AI companies are moving faster than established academic processes can comfortably accommodate.
The dispute turns on the gap between generating a possible proof and validating one. OpenAI has made a large body of work available, while reserving the use of its proprietary model for further frontier testing. Mathematicians now face the slower task of testing the claims, including those touching some of the field’s most difficult unsolved questions.
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