OpenAI publishes 722 AI-written math papers solving open problems

OpenAI published 722 mathematical manuscripts produced by an unreleased internal frontier model on 6 October, organised into 372 result families that group related papers. The release covers number theory, algebraic geometry, complexity theory, geometry and mathematical physics, and includes solutions to hundreds of long-standing open questions according to AGMAI, the independent advisory group of mathematicians assembled to advise on communicating the results.latent.space

The release matters because it is the largest single batch of machine-generated mathematics to enter the research process, with reproducible records and computer-checkable proofs rather than a single headline claim. It follows an earlier OpenAI announcement in September that its model had resolved more than 100 long-standing open problems across most areas of mathematics, and it lands after a month of tension between AI labs and the mathematical community over how such results are announced.

What the release contains

The collection sits in a public GitHub repository with protocols for paper revisions and citations. OpenAI said it consulted the Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study and drew on its advice. The repository groups related manuscripts into research families and identifies 10 families with abbreviated summaries of the model's reasoning. The papers also include estimates of compute used and statistics on the number of problems attempted.

Lean, a programming language that lets researchers translate mathematical statements and proofs into formal code, provides a verification layer: a computer checks whether each logical step follows from the stated assumptions. Many manuscripts still lack formal Lean versions, and OpenAI says it will add more formalisations as researchers complete the verification work. A computer-checked proof does not automatically establish that every research claim in the collection is correct.

The model attempted roughly 4,000 problems during the research process, and an accepted result consumed about three hours of equivalent ChatGPT Pro thinking compute on average. Coverage of the release contrasts this with an earlier Navier-Stokes result produced in 88 hours with 10,000 agents. An analysis cited in coverage estimates about 20% of the results are disproofs or counterexamples, which would undercut the claim that AI mathematics wins are mostly brute-force search.interestingengineering.com

How the proofs get checked

Among the claimed results, coverage highlights advances related to three of the five remaining Millennium Prize Problems, including the Riemann hypothesis, plus partial progress on Riemann, Hodge and BSD. One result addresses the irrationality exponent of pi, others cover NP-hardness, Mahler conjectures, arithmetic progressions, free group factors, quantum Heisenberg ferromagnets and relativistic Vlasov-Maxwell equations. These individual results are reported by commentators and have not been independently verified.

Reactions split sharply. Levent Alpöge praised the quasi-Riemann and no-Siegel-zeros results and called it "the most significant moment in mathematical history", a line also attributed to a researcher inside Anthropic. Alex Kontorovich, a Rutgers University distinguished professor, wrote that a human producing the Riemann result would earn an instant Fields Medal. Will Depue expects some results will not survive scrutiny and built citedbyagi.com to track which human papers the release cites.

Where the numbers came from

AGMAI published its first recommendations in late September, urging AI labs to release mathematical results promptly through established academic channels and to disclose the model name, prompts and compute costs. The group asked companies to refrain from treating mathematical releases as marketing vehicles. OpenAI adopted most of that advice but declined one request: mathematicians asked labs to stop testing advanced problems on proprietary models, and OpenAI said it must keep evaluating internal frontier models on mathematics.

More than two dozen Fields Medal winners published an open letter titled "A Severe Misalignment of AI in Mathematics", warning the industry's rush threatened the purpose of mathematics. Mathematicians scrambled to publish their own AI-assisted work as rumours of the release spread, fearing they would be scooped. OpenAI plans workshops, conferences and special programmes on the results, with mathematicians' feedback expected to shape future disclosures.