OpenAI has published 722 manuscripts containing solutions to hundreds of open mathematical questions. The release follows recommendations from an independent advisory group on AI and mathematics.
OpenAI has released a batch of 722 manuscripts covering 372 result families, which group related mathematical papers. The company states that these documents contain solutions to a number of long-standing mathematics problems produced by an unreleased frontier model. According to AGMAI, the Advisory Group on Mathematics and Artificial Intelligence, the release includes solutions to “hundreds” of open questions.
The results were published in a GitHub repository. OpenAI says the repository includes protocols for paper revisions and citations. The company also shared formalizations of many proofs in Lean, a programming language that allows mathematical proofs to be checked by a computer. OpenAI states it will update the repository with more formalizations as they are obtained.
To promote transparency, OpenAI is publishing additional details about how the results were obtained. These details include 10 summaries of the model’s reasoning, estimations of compute spent in terms of Pro usage on ChatGPT, and statistics about the number of attempted problems. OpenAI claims the “average result” used the equivalent of three hours of ChatGPT Pro thinking.
The release follows public recommendations from AGMAI, an independent advisory group of elite mathematicians formed to work on communicating results responsibly. In late September, AGMAI urged AI labs to release mathematical results promptly and through established academic channels where possible. The group also recommended disclosing details such as the name of the model used, prompts, and compute costs.
AGMAI stated that AI companies should “refrain from treating the release of mathematical results as marketing vehicles to promote their models,” a practice they said inflicts significant harm on the mathematical community. OpenAI’s statement notes that the company has been consulting with AGMAI at the Institute for Advanced Study to develop best practices and has drawn on their advice to inform how it releases these results.
OpenAI says it is continuing to explore other community-hosted alternatives for this release which meet the committee’s guidelines. For future releases, the company states it is committed to further improving the quality of the papers via citations, mathematical exposition, and presentation of the results for better understanding.
The company also announced plans to fund a series of workshops, conferences, and special programs around the understanding of major results produced by AI. OpenAI says it wants to directly empower scientists with state-of-the-art capabilities and is working to responsibly release the model that produced these results.
The release adds to a growing body of mathematical results from AI labs, including OpenAI and rival labs like Anthropic, that the field is still processing. The speed at which AI labs have entered the discipline this year has provoked debate over research practices, ethics, and how companies credit human mathematicians. The full impact of the results will likely take time to be felt as mathematicians assess and digest them.
Sources
This article was drafted with AI assistance and checked against the sources above. Company claims are reported as claims. Cover image is AI-generated.
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Anthropic released four models in four weeks. Opus 5.5 roughly matches Fable 5.1 at lower cost, and Sonnet 5.5, released September 28, comes close to Opus 5.5 for $2/$10 per million tokens.
