OpenAI Shares 722 Mathematical Manuscripts from an Undisclosed AI Model on GitHub

OpenAI on Tuesday published 722 manuscripts on GitHub produced by an advanced artificial intelligence model that has not been made publicly available. The materials cover 372 families of results grouping related papers together. Under another counting method, the release contains 377 new mathematical results. The company claims that the model has found solutions to hundreds of open mathematical problems.

The shared materials also include summaries briefly showing how the model arrived at its answers. They also provide statistics on the computing power used and the number of problems examined. According to OpenAI, each result required, on average, resources equivalent to 3 hours of ChatGPT Pro use. Almost all the manuscripts were produced from 1 prompt sent to 1 artificial intelligence agent. However, those prompts and the exact amount of time spent on each problem have not been disclosed.

The main claims include a solution to the 4-dimensional Kakeya conjecture and improvements to important computer algorithms. The model is also said to have made progress on the Riemann hypothesis, considered one of the most difficult open problems in number theory. One of the manuscripts proposes a complete proof of the Birch, Swinnerton and Dyer leading-term formula. However, the result applies only to a limited case of elliptic curves over the rational numbers.

OpenAI says it shared the results in accordance with the recommendations of AGMAI, an independent advisory group on mathematics and artificial intelligence. The group called for the results to be published through academic channels as quickly as possible. The model's name, the prompts sent to it and the computing costs should also be disclosed. AGMAI opposed turning mathematical results into advertising for the model. OpenAI has also established correction and citation guidelines on GitHub and said it would improve the process for sharing future papers.

The same internal model that produced a counterexample for the Navier–Stokes problem about 1 month ago was used for this work. A counterexample shows that a proposed claim is not true in all cases. Navier–Stokes is one of the famous Millennium Prize Problems. It later emerged that OpenAI had completed work that another group of mathematicians using artificial intelligence had been working on. Although AGMAI called for testing such problems on closed models to stop, the new results were again obtained from a model that has not been made publicly available.

Determining the scientific value of the 722 manuscripts will take time. Mathematicians must verify each proof individually. Until the model is made publicly available and the results are replicated by other researchers, claims that solutions were found with 1 prompt cannot be considered confirmed. Work by rival labs such as Anthropic is also increasing the number of results awaiting verification. The discussions are not limited to the proofs. Research ethics, crediting human scientists and how scientific results should be shared are also being discussed.