On October 6, OpenAI released a batch of mathematical results generated by its internal cutting-edge models, with the manuscripts stored in a public repository. The release method was based on recommendations from the independent advisory group at the Institute for Advanced Study.

The repository currently contains 722 manuscripts, categorized into 372 groups of results. A group may include main results, supporting arguments, inferences, or alternative proofs, classified by mathematical branches. The vast majority of results were generated by the same internal model using a consistent process that has not yet been published. During the evaluation phase, the model was given approximately 4,000 problems, and after filtering by result families and components, these 372 groups were retained. The average computational power used for each result is equivalent to ChatGPT Pro thinking for about 3 hours.

The degree of verification is inconsistent. The repository includes Lean formal proofs and proofreading notes, but it is explicitly stated that not every manuscript has been formalized, and unformalized results may contain errors, which will be corrected as soon as they are discovered, while old versions will be retained. Additionally, 10 summaries of reasoning processes were released, covering topics such as the irrational exponent of π, the Mahler conjecture, the direct finiteness conjecture under Kaplansky's characteristic 2, and free group factor isomorphism. The zero-free region of the Riemann ζ function for real parts greater than 11/12, as well as the Hodge conjecture on CM Abelian varieties, did not follow this fixed process. The text of the ζ function paper has also been manually polished.

This batch of results comes from the same unpublished internal cutting-edge model, which the official sources have linked to previous results related to the Navier-Stokes equations. Model evaluation was intensified after existing mathematical test scores saturated, with some outputs building on earlier results from the model. OpenAI stated that it is advancing the responsible release of this model while continuing to use internal cutting-edge models to evaluate mathematical and other scientific problems.

The release process is another aspect of this event. The advisory group was established at the Institute on September 21, with the first batch of 9 mathematicians not receiving funding from OpenAI, including Timothy Gowers, Edward Witten, and Martin Hairer. The public call for suggestions on September 29 received over 600 responses from the mathematical community, requesting the addition of existing literature, rewriting in formal paper format, inclusion in archives that are not controlled by AI companies and can be cited long-term, public disclosure of model names, prompts, reasoning summaries, and computational costs, as well as funding to support the mathematical community's understanding of these results. The advisory group also stated that they do not support tackling difficult problems using private models that are not accessible to the public and called for a halt to such practices.

OpenAI has first released a public repository, outlined revision and citation rules, and stated that it is still looking for a community-hosting platform that meets the advisory group's standards. It has committed to funding workshops, academic conferences, and special projects to help understand the major results produced by AI, with details to be announced later. It did not accept the suggestion to stop testing private models, but instead stated that it will continue to conduct such evaluations.

This is not a paper trading scenario. Computational resources are spent internally at OpenAI, the manuscripts are publicly available for free, there is no buyer, and the seller is the model output. The event is driven by the controversy over the release following the continuous results from private models. Beneficiaries include mathematicians who can directly verify Lean and read reasoning summaries, as well as competing laboratories that need external benchmarks. Those under pressure include conclusions that have not yet been formalized, the primacy of traditional journals, and research groups that cannot access the model but need to digest these 372 groups of results.

Source: Public Information