OpenAI drops 722 AI-generated math papers, including a result tied to the Riemann hypothesis
An unreleased OpenAI model has produced hundreds of solutions to longstanding mathematical problems — impressing experts while raising hard questions about verification, attribution, and what 'discovery' even means.
A Rutgers University mathematician said on X that one result connected to the Riemann hypothesis — among the most famous unsolved problems in all of mathematics — would warrant an automatic Fields Medal if a human had done the work. The catch: a human didn't.
OpenAI on Tuesday released 722 manuscripts, organized into 372 groups of related findings it calls 'families,' produced by a powerful internal model the company has not publicly released. The papers, posted to a public GitHub repository, cover longstanding problems in mathematics, with many proofs verified in formal systems. OpenAI says the release includes solutions to 'hundreds' of open questions in mathematics.
The release also touches on Millennium Prize problems — a set of seven problems so difficult that a correct solution to any one of them carries a $1 million prize. It follows a September announcement in which OpenAI said its model had 'resolved more than 100 long-standing open problems across most areas of mathematics,' and a separate result released last month.
The scale of the release is without precedent in the field. The reception, according to reporting across multiple outlets, has mixed genuine scientific excitement with unease — both about what the results mean and about how OpenAI has handled them.
OpenAI says the 'average result' in the batch required the equivalent of about three hours of ChatGPT Pro thinking in compute. The papers include some summaries of the model's reasoning and estimates of compute used, along with statistics about the number of problems attempted. The underlying model itself has not been released.
You can discover new math easily. You can make a trillion theorems easily. The problem is most of those theorems are not ones that anybody will care about.— Stephen Wolfram, computer scientist and physicist
Wolfram made the remark at a Tuesday event for the National Museum of Mathematics, capturing a skepticism shared by some in the field: volume alone does not equal significance. Some mathematicians have questioned whether the results represent original breakthroughs or draw heavily from previous human mathematical work, a concern that applies to this release and to the solution OpenAI published last month.
Those concerns have a formal audience. AGMAI — the Advisory Group on Mathematics and Artificial Intelligence, an independent body of elite mathematicians formed to help communicate AI mathematical results responsibly — published its first recommendations in late September. The group urged AI labs to release results promptly and through established academic channels where possible, and to disclose details including the model's name, the prompts used, and compute costs.
Refrain from treating the release of mathematical results as marketing vehicles to promote their models.— AGMAI, Advisory Group on Mathematics and Artificial Intelligence
The group said that practice 'inflicts significant harm on the mathematical community.' For this release, OpenAI published results on GitHub with protocols for paper revisions and citations, and said it is 'continuing to explore other community-hosted alternatives' that meet AGMAI's guidelines. The company also committed to improving citation quality, mathematical exposition, and presentation in future releases.
The speed at which OpenAI and rival labs like Anthropic have moved into mathematics this year has provoked fierce debate over research practices, ethics, and how companies credit the human mathematicians whose work their systems build upon. The full impact of Tuesday's release will likely take time to assess as the community works through the repository — but the pattern it represents is already clear. AI's dominance of competitive programming was once treated as a curiosity. Mathematics, experts now say, may be next.
Why it matters — If AI can reliably solve problems that have stumped human mathematicians for decades, it signals that the technology's impact on expert fields is accelerating — and that mathematics, like competitive programming before it, may be fundamentally changed.
⚠ Not yet confirmed
- A result connected to the Riemann hypothesis would warrant an automatic Fields Medal if a human had done the work
- specific fields covered (algebra, number theory, topology, theoretical computer science) and Lean verification
- quasi-Riemann hypothesis result and progress on the Kakeya conjecture
- Navier-Stokes-related problem
- Many proofs in the release were verified using the Lean formal proof system
Sources differ on Whether the AI results represent original breakthroughs: The results include solutions to hundreds of open mathematical questions, including progress on Millennium Prize problems (openai.com) vs Some mathematicians have questioned whether the results are original or draw heavily from previous human mathematical work (axios.com) vs Generating large numbers of theorems is easy; the question is whether they are ones anyone will care about (axios.com)
Reported by axios.com, thehill.com, theverge.com, openai.com, newscientist.com, nytimes.com, techspot.com
