OpenAI posts 372 math results from an unreleased AI model, and mathematicians ask for proof of how they were made
OpenAI published hundreds of claimed solutions or advances on open problems in math and theoretical computer science, many with computer-checked proofs. The model that produced them isn’t public, and the results haven’t been peer reviewed.
What happened: OpenAI on Tuesday released 372 results produced by an internal “frontier” model, posting them in a GitHub repository rather than in academic journals, the company said. Each result solves or makes substantial progress on an open question in mathematics or theoretical computer science, OpenAI says, Scientific American reported. Among the claims: a solution to the four-dimensional Kakeya conjecture, improvements to important computer algorithms, and progress related to the Riemann hypothesis.
How it says it did it: An OpenAI spokesperson told Scientific American that nearly every result came from a single prompt given to a single AI agent, though some took multiple attempts. OpenAI says the average result used compute equal to about three hours of ChatGPT Pro “thinking.” That contrasts with the company’s earlier Navier-Stokes result, which took a swarm of 10,000 agents and millions of dollars in computing, The Decoder reported.
How to check it: Many of the proofs come with versions written in Lean, a programming language that lets a computer check every logical step, OpenAI said. A Lean check shows a proof is logically valid; it does not show whether a result is new or important. OpenAI also published 10 summaries of the model’s reasoning and statistics on how many problems it attempted, but not the prompts or per-problem compute.
The pushback: An independent advisory group of mathematicians at the Institute for Advanced Study, which OpenAI consulted, has recommended that companies publish the model, exact prompt and compute time behind each result, Scientific American reported. OpenAI said it takes the guidelines seriously but is not bound by them. “We should ask for receipts,” said MIT mathematician Andrew Sutherland. University of Toronto mathematician Daniel Litt said releasing the results is “going to be a good thing for mathematics.”
What’s next: OpenAI says it is working to release the model “responsibly” and will fund workshops and conferences on understanding AI-produced results. Mathematicians are expected to need months to review the batch.