Artificial Intelligence
OpenAI publishes 372 AI-generated maths proofs
OpenAI put 372 machine-generated mathematical results on GitHub, said they were aimed at open problems, and drew both review-focused support and warnings from mathematicians about the pace and purpose of the work.
- OpenAI published 372 mathematical results generated by an internal frontier model on GitHub.
- The company said the results were intended to solve open problems or advance them, including work on computer algorithms and the Riemann hypothesis.
- OpenAI said nearly all of the results came from one prompt given to one AI agent, and that each one used about three hours of ChatGPT Pro Thinking compute on average.
- Many of the results were accompanied by Lean formalisations, and OpenAI said more formalisations were planned.
- OpenAI said it had consulted the Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study, which included Timothy Gowers.
OpenAI published 372 mathematical results generated by an internal frontier model and placed them in a GitHub repository with revision logs and citations. The company said each result was meant either to solve an open problem or to make substantial progress towards one.
OpenAI said the collection included work on computer algorithms and on the Riemann hypothesis. It also said almost all of the results came from a single prompt to a single AI agent, although some took more than one attempt.
The company said each result used about three hours of ChatGPT Pro Thinking compute on average. It compared this with the Navier-Stokes result it said the model had already produced under formal review, which it said had needed 10,000 agents and millions of dollars in compute.
Many of the proofs were paired with Lean formalisations, and OpenAI said more would follow. It said the aim was to make review more practical because manual checking would be hard to sustain at the volume involved.
OpenAI said it had consulted the Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study and had loosely followed its public recommendations. The company did not publish prompts or per-problem compute figures, and it said it planned workshops and conferences on AI-produced results.
Reaction cited in the article was mixed. In an open letter, 25 Fields Medal winners warned that mass-producing true statements could damage the ground for new ideas, while Timothy Gowers and Terence Tao warned about the growth of unreadable literature and the need to limit AI use in training.
Named in this story
People
- Timothy Gowers
- was named as a member of the advisory group and later warned about the field’s growth
- Terence Tao
- said AI use in training should be tightly limited
Companies
- OpenAI
- published the collection of mathematical results
- GitHub
- hosted the repository containing the results
Organisations
- Institute for Advanced Study
- hosted the advisory group OpenAI consulted
- Advisory Group on Mathematics and Artificial Intelligence
- advised on how the results should be communicated
Products and systems
- ChatGPT Pro Thinking
- supplied the compute measure used to average each result
- Lean
- provided machine-checkable formalizations for some results
How the source tells it
The register is mostly boosterish and confrontational, with OpenAI’s release cast as a challenge to the academy and countered by attributed warnings about overload and loss of understanding.
- boosterish challenge the release is framed as a provocation to academic mathematics and as a sign of progress beyond ordinary publication
- alarm the open letter and commentary warn that mass production of results could damage the field and outstrip human understanding
- urgency the article contrasts the pace of AI output with the slower review capacity of journals and mathematicians