OpenAI Releases 722 Math Papers from Unreleased Model, Drawing Skepticism from Mathematicians

The manuscripts are grouped into 372 sets of results. OpenAI said the model attempted about 4,000 research questions, and the average compute for each result was roughly equivalent to ChatGPT Pro thinking for three hours. The GitHub repository includes 10 inference summaries. Most results were produced by the same unreleased internal model following a fixed pipeline, but two exceptions are noted: the zero-free region of the Riemann zeta function and the Hodge conjecture for abelian varieties with complex multiplication. One paper on the Riemann zeta function for real part greater than 11/12 was manually edited for readability, and the repository states that verification levels vary, with some results lacking Lean formalization.

Among the highlighted results, one group claims that the Riemann zeta function and all Dirichlet L-functions have no zeros in the region where the real part is greater than 7/8. A separate proof in the same group gives a version for real part greater than 11/12 while also excluding Siegel zeros. Another group addresses Hilbert's tenth problem over the rationals, claiming that no general algorithm exists to decide whether a polynomial with integer coefficients has a rational solution. The integer version was solved in 1970 by Soviet mathematician Yuri Matiyasevich, but the rational version had remained open for over half a century. For the BSD conjecture, OpenAI claims a complete formula for elliptic curves satisfying conditions such as Selmer corank 0 or 1, covering most quadratic twists of each elliptic curve over the rationals by density when combined with another result in the repository. For the Hodge conjecture, the manuscripts treat abelian varieties with complex multiplication and products of K3 surfaces, with one paper claiming coverage of all dimensions and codimensions for CM abelian varieties, though not the full generality of the conjecture.

Other claims include that the irrationality exponent of pi is exactly 2, improving on a previous bound of about 7.1, and that Catalan's constant is irrational. In theoretical computer science, a group claims to prove the Unique Games Conjecture, proposed by Khot in 2002, with implications for approximation hardness of problems such as Max Cut and Vertex Cover. The repository also lists results on sparse spin glasses, the Mezard-Parisi formula, spontaneous magnetization in quantum Heisenberg ferromagnets, free group factors, and global smooth solutions to the relativistic Vlasov-Maxwell equations in three dimensions.

The release drew immediate skepticism. A nine-member independent mathematics and AI advisory group, which includes Fields medalists Timothy Gowers and Martin Hairer as well as theoretical physicist Edward Witten, issued a statement saying that while the release is a significant event for mathematics, the group's prior advice to OpenAI does not mean it endorses the results or OpenAI's process. The group said mathematicians in relevant fields must verify the proofs and assess their usefulness.

Before the release, Francesco Maggi, a mathematician at the University of Texas at Austin, asked on social media who would have the energy to read hundreds of papers, noting that experts were still studying a fluid dynamics proof from September and wondering what new methods or problems might emerge. Maggi said he does not oppose using AI in mathematics but worries that results are being produced faster than humans can understand, leaving mathematicians chasing the AI. According to WIRED, OpenAI convened about 40 mathematicians in August to discuss how to release the results. Bryna Kra of Northwestern University and others wanted clear papers that peers could read and cite. Some attendees said they thought OpenAI would not release all results at once, while an OpenAI spokesperson said the company was not aware of such a promise.

Tensions were already high after a September controversy over fluid dynamics. NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpoege published three proofs of fluid equation blow-up with Lean formalization. Around the same time, OpenAI released a Navier-Stokes proof. Buckmaster said he had wanted more time to make the proof readable but released it early due to external pressure. A dispute followed over research progress and credit, with both sides presenting similar or identical results, and OpenAI denying that Buckmaster's earlier use of Codex with certain prompts influenced its model. Terence Tao, who has often promoted AI tools, said in a September talk at Caltech that the pace of AI development is too fast. Fields medalist Cedric Villani also expressed shock at OpenAI's claimed Navier-Stokes result.

For this release, OpenAI posted papers, some Lean proofs, and inference summaries in the repository, and said it would fund workshops to help the mathematics community study the results. The advisory group responded that the materials are now public and that mathematicians should check and explain them before deciding which results enter mathematical research.

Separately, OpenAI's 28-day challenge reached Day 2. The company released four updates, including Auto-review, which lets another AI agent check actions Codex is about to take during long tasks, now available without consuming plan credits for users logged in through ChatGPT accounts. Other updates include simplifying API paid tiers from five to three, a Meetings plugin that turns meetings into notes and action items, and a public beta of a Decisions API for developers.