OpenAI Publishes New Math Results From an Internal Frontier Model

How the results are being shared

According to OpenAI, the release is meant to improve how AI-generated mathematics is shared with the research community. The company says it consulted the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study to develop best practices, and it drew on the group's advice and public recommendations when deciding how to release the results.

For this release, the results are published in a GitHub repository, which includes protocols for paper revisions and citations. OpenAI says it is still exploring community-hosted alternatives that meet the committee's guidelines. For future releases, the company says it is committed to improving the quality of the papers through better citations, mathematical exposition and presentation of results.

Lean proofs and compute details

The repository also contains formalizations of many of the proofs in Lean, a programming language that allows mathematical proofs to be checked by a computer. OpenAI says it will add more formalizations to the repository as it obtains them.

In the name of scientific transparency and openness, the company is publishing further details on how the results were obtained. These include:

• 10 summaries of the model's reasoning
• estimations of compute spent, expressed in terms of Pro usage on ChatGPT
• statistics on the number of attempted problems

According to OpenAI, the average result used the equivalent compute of roughly three hours of ChatGPT Pro thinking.

Funding and plans for the model

OpenAI says it wants the progress to push the frontier of human knowledge and enable further advances in mathematics. It plans to fund a series of workshops, conferences and special programs around understanding major results produced by AI, and says it will share more on this in the near future.

The company also 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. It argues that continuing to evaluate its internal frontier models on mathematics and other sciences is important so that it can accelerate the development of tools for those fields.

What it means for researchers

For mathematicians, the release offers material that can be checked and cited: Lean formalizations allow computer verification of proofs, and the repository's citation and revision protocols give a defined way to refer to the results. The disclosed compute estimates and attempt statistics give some context on how the results were produced.

OpenAI says it will keep acting on community feedback and update its standards for future disclosures of major scientific advancements. The source does not say when the underlying model will be released or what it will cost.