OpenAI publishes 719 mathematical manuscripts from a not-yet-released AI model

On 6 October OpenAI made public a large series of mathematical results produced by an internal frontier model that has not yet been released. The catalogue contains 719 manuscripts, grouped into 372 so-called result families: clusters of related papers on the same problem. Originally there were 722, but a day after the release OpenAI withdrew three of them, because a single calculation error made the proof in those papers invalid. According to AGMAI, the release contains solutions to 'hundreds' of open questions. OpenAI is not disclosing the name of the model.

AGMAI stands for Advisory Group on Mathematics and Artificial Intelligence. The group was announced on 21 September and is hosted by the Institute for Advanced Study in Princeton. The initiative came from OpenAI, which approached several mathematicians about an external advisory board; they chose to set up an independent group instead. The nine members, including Fields Medal winners Timothy Gowers and Martin Hairer and physicist Edward Witten, are not paid.

What has been released?

The results had been expected for weeks. On 21 September OpenAI said the model had solved 'more than 100 long-standing open problems' 'in most areas of mathematics', without saying which problems they were or when publication would follow.

The manuscripts are in the GitHub repository openai/math, under an Apache 2.0 licence. According to OpenAI, the model was given about 4,000 problems. On average, one result cost computing power comparable to three hours of 'thinking' by ChatGPT Pro with this internal model. There are also abridged summaries of the model's reasoning for ten of the 372 families, and aggregate statistics.

For some of the results a formal proof in the proof assistant Lean is included, but not for all. OpenAI itself acknowledges in the repository that 'some non-formalised results may contain problems'. Corrections appear as new versions, with earlier versions remaining visible. The company also says it is looking at alternatives hosted by the mathematical community, and promises to improve the quality of future papers, including citations, mathematical explanation and presentation.

Guidelines and debate

AGMAI published its first recommendations at the end of September. AI laboratories should release mathematical results quickly, where possible through established academic channels, and report which model was used, with which prompts and at what computing cost. The group also called on companies not to use such releases as a marketing tool for their models, because according to AGMAI this does considerable damage to the mathematical community.

OpenAI does not fully follow these recommendations: it states the average computing use and the number of problems attempted, but does not publish the prompts or the computing cost per problem. AGMAI itself stresses that its advisory role should not be taken as a judgement on the significance of the results.

How big the impact is will only become clear once mathematicians have assessed the manuscripts; none of the results has yet been reviewed by peers. The release adds to a fast-growing stream of mathematical claims from OpenAI and competitors such as Anthropic. In early September, for example, OpenAI claimed a proposed solution to the Navier-Stokes problem, one of the Millennium Prize Problems; that claim has not yet been confirmed either. The speed with which AI companies have entered mathematics this year, and especially the way they make announcements, is leading to heated debate about research practices, ethics and the recognition of the human mathematicians on whose work the systems build.

What mathematicians think of the most important results can be read in our background article. At the end of October OpenAI reported three new results, this time with well-known scientists guiding the checking from the start.

What does this mean for the road to the singularity?

Mathematics is one of the few fields where a result can, in principle, be checked conclusively. If a model really solves hundreds of open questions, it shows that AI can independently deliver high-level research: a step towards systems that speed up science, and eventually their own development. For now that remains a big 'if', because the assessment by mathematicians is still to come. The news does expose a bottleneck: the production of results is growing faster than the ability of people to check, cite and properly attribute them. Formal proofs in Lean can take over part of that work, but only if the formal statement really says what the human version claims, and a human has to check that too.

What is the technological singularity? Read the explanation →