OpenAI has posted 722 math manuscripts written by an unreleased internal model, and a few of them go after some of the hardest problems in the field. If they hold up, they would be strong evidence that AI can reason its way to new mathematics rather than recite what it has seen. That's a big if, and OpenAI says so itself in the release notes.
The company put the papers in a public GitHub repository on Tuesday. They're grouped into 372 "families" of related results across number theory, combinatorics, computer science and mathematical physics. According to the repo, the model was given about 4,000 open problems and spent an average of three hours of ChatGPT Pro thinking compute on each result. OpenAI says it widened these tests after its model saturated the company's existing math evaluations, which means it was scoring at or near the top of them.
The two claims everyone will look at
Two results stand out, and OpenAI says neither came out of its standard pipeline. One is work on a zero-free region for the Riemann zeta function. The other is a proof of the Hodge conjecture for a special class of geometric objects called CM abelian varieties. Neither solves a Millennium Prize problem. The Hodge result covers one family of cases. In 2025, mathematician Eyal Markman proved the Hodge conjecture for abelian varieties of dimension 4 and 5, which Totaro called "a monumental piece of work". OpenAI's claim targets a different slice of the problem: the CM class rather than every case in a given dimension.
The zeta claim is the bolder one. The zeros of the zeta function control how prime numbers are spread out, and the repo says the model proved there are none where the real part of the input is greater than 11/12. Since Charles de la Vallée Poussin's work in the 1890s, every proven zero-free region has been a sliver that hugs the line where the real part is 1 and gets thinner the higher you go. The best modern versions, of the Vinogradov and Korobov type, still shrink that way, as in Chiara Bellotti's 2023 explicit bound. A fixed strip at 11/12 that never narrows would go far beyond anything proven so far, though it would still fall well short of the Riemann hypothesis, which puts every nontrivial zero on the line at 1/2. The repo also says people edited this zeta write-up to make it easier to read.
Who has actually checked the work
Fewer than the size of the release might suggest. OpenAI's README says "many, but not all" of the manuscripts come with Lean versions, which is code a machine can check step by step, but it gives no count, so we can't say how many of the 722 have been verified that way. For the rest, OpenAI warns that "some of the unformalized results could have issues". OpenAI took advice on how to release the work from an advisory group at the Institute for Advanced Study, Interesting Engineering reported. No outside referee reports came with the release.
OpenAI's track record here is mixed. Two authors audited the ten results OpenAI announced on Aug. 1 and found no confirmed serious error in the main theorems. Still, one specialist asked for a major revision of some arguments that were too compressed to follow. OpenAI's September claim on the Navier-Stokes equations was still waiting for confirmation more than a week later.
Mathematician Burt Totaro, in a guest post on Terence Tao's blog, wrote that what mathematicians care about "are not so much isolated facts, but rather 'the ideas and inspiration that the search leads to'".
As of Oct. 6, OpenAI had not named an outside review or a Lean formalization effort for the zeta and Hodge papers, and the README does not say either one has been machine-checked. Whether those two get Lean versions, or a named specialist signs off on them, is the next thing to watch.
Sources
- 1.openai/math (repository and README) · OpenAI on GitHub
- 2.OpenAI's largest math release tackles 4,000 problems with Lean proofs · Interesting Engineering
- 3.A Human Audit of OpenAI's AI-Generated Mathematical Proofs · arXiv (Mikołaj Sienicki, Krzysztof Sienicki)
- 4.On the Hodge conjecture (guest post by Burt Totaro) · Terence Tao's blog
- 5.OpenAI may have solved the Navier-Stokes equation, but mathematics is more than $1 million trophy hunts · The Conversation
- 6.Explicit bounds for the Riemann zeta function and a new zero-free region · arXiv (Chiara Bellotti)
Reported by the WattsUpNext desk from the sources linked below. Spot an error? Tell us at corrections@wattsupnext.com.
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