News · 2026-10-06 · Reported October 6, 2026; updated October 7
OpenAI releases 722 math manuscripts written by an unreleased AI model
OpenAI posted 722 math manuscripts, grouped into 372 families of related results, produced by an internal AI model it has not released. A day later it withdrew three after a sign error and revised fourteen more. By OpenAI’s own count, 300 of the remaining 719 manuscripts have their main result formalized in Lean (about 42%); the sources here report no outside check of those files. Mathematicians quoted here raised different concerns: one about verification, one about openness.
What happened
- On October 6, 2026, OpenAI published 722 mathematical manuscripts, grouped into 372 families of related results, in a public GitHub repository (openai/math) under the Apache 2.0 license. The model that produced them has not been released.
- OpenAI says the model was posed about 4,000 problems, and that on average each result used "three hours of ChatGPT Pro thinking compute", a unit it does not define further. It says the catalogue came from grouping the output and "requiring an appropriate level of significance". The README does not say how many of the 4,000 problems produced a result.
- On October 7, OpenAI withdrew three manuscripts. A sign error in one, on Weil classes on abelian eightfolds, broke an argument that the other two depended on. The history file does not say whether any of the three had a Lean version. OpenAI also revised 14 other manuscripts with repaired proofs, corrected statements and clearer hypotheses. The repository now lists 719 manuscripts.
- After that update, the repository says 300 of 719 "top-line results", one per manuscript, are formalized in Lean, a programming language for proofs. If a Lean file compiles with no `sorry` placeholders and no extra axioms, a computer has checked every step of the proof, but only of the statement and definitions as written in Lean. OpenAI says the collection includes results at different stages of verification.
- The claimed results include a solution of the four-dimensional Kakeya conjecture, which says that a set containing a line segment pointing in every direction must still have full dimension, however thin it is. They also include a zero-free region for the Riemann zeta function, a statement about where its zeros cannot lie, the kind of result that bears on the Riemann hypothesis. OpenAI says that result was an exception to its fixed procedure and that its write-up was edited by people for readability.
- An OpenAI spokesperson told Scientific American that almost every result came from a single prompt given to a single AI agent. A month earlier, OpenAI’s Navier-Stokes announcement (also on this page) had used a swarm of about 10,000 agents.
- In September, OpenAI formed an advisory group on mathematics and AI, associated with the Institute for Advanced Study, a research institute in Princeton. Terence Tao, a UCLA mathematician widely considered one of the greatest living mathematicians, is a member; he is quoted on AI in mathematics in the Navier-Stokes entry. He wrote that the group’s task included advising OpenAI on how to coordinate the release of a large number of results.
What people said
“Some of the unformalized results could have issues. We will endeavor to fix any such issues quickly.”
“Until and unless they release the model and people can replicate their results, I think you should treat any claims about one-shotting problems with a single agent as unverified. We should ask for receipts.”
“If we want to know the answers to these math questions, I see no reason why we should ask the company to keep them secret from us. To me, it’s going to be a good thing for mathematics.”