OpenAI's Quasi-Riemann Proof Rests on a 49-Page Paper No Journal Has Checked

OpenAI posted 719 machine-written math manuscripts to a public GitHub repository on October 6, and one of them claims to push every nontrivial zero of the Riemann zeta function into a strip narrower than the one mathematicians have had since 1896. Number theorists who have read the follow-up paper largely agree it is correct, according to Quanta Magazine, though no journal, referee or formal proof checker has signed off on it.

What the quasi-Riemann claim says

The full Riemann hypothesis says every nontrivial zero of the zeta function sits on the line where the real part equals 1/2. The "quasi" version asks for less: that all the zeros lie inside a vertical strip narrower than the known 0-to-1 strip, according to Quanta Magazine's report by Konstantin Kakaes, published October 19.

OpenAI has circulated two versions. They are not the same result.

Version	Zero-free region	Length	Checked by
September 30 preprint	Real part above 7/8	About 199 pages	Lean proof checker
October 5 preprint	Real part above 11/12	About 49 pages	Readers only

Both figures come from Quanta. The 11/12 strip is wider than the 7/8 one, so it is the weaker claim. Quanta does not say why mathematicians have set the Lean-verified 7/8 paper aside and are studying the 11/12 paper instead, and neither does the repository.

What the mathematicians said

Jared Duker Lichtman of Stanford University called it "the most significant AI-for-math achievement so far, by quite a margin," according to Quanta. Maksym Radziwiłł of New York University said "the vast majority of consequences of RH already follow from quasi-RH."

Radziwiłł was also blunt about the writing. He said the papers "are horribly written (in a way that would lead to immediate rejection at any mathematical journal)."

Peter Sarnak of Princeton has repurposed a course this semester to study the 11/12 paper, Quanta reported. He told the magazine he will not call it a theorem until humans have checked and understood every detail.

Will Sawin of Princeton said that even once the methods are absorbed, "we will still feel as far off from the full Riemann hypothesis as we were before."

What OpenAI published and what it did not say

The openai/math repository is licensed Apache-2.0. Its README says the collection holds 719 manuscripts in 372 families, all "produced by an internal OpenAI model." Each result used on average three hours of ChatGPT Pro thinking compute, and the model "was posed approximately 4,000 problems."

The README says results are at "different stages of verification" and that "Some of the unformalized results could have issues." About 42% of top-line results have Lean formalizations.

The counts do not agree across sources. OfficeChai reported 722 manuscripts on October 7. Quanta uses 377 in one place and 722 in another. The repository's own figure is 719.

The 11/12 write-up is the one result in the batch that a person edited, the README says, "for readability." OpenAI has not said who that person is. Quanta quotes the company as saying the work "is the result of work from everyone at OpenAI."

OfficeChai also reported that Sam Altman, OpenAI's chief executive, singled out four results, and that outside mathematicians had not confirmed any of them. The other three claim the Unique Games Conjecture, a special case of the Hodge conjecture, and the isomorphism of free group factors.

Why the Lean proof does not settle it

A Lean proof shows the logic follows from the axioms it was given. Humans still have to confirm the formal statement matches the problem, a point OfficeChai raised about the batch.

The write-ups by outside mathematicians run 7 to 13 pages, Quanta said, and are circulating privately. Sarnak's own course is the first public sign of a check in progress.

Related coverage on this desk: the HybridAgent paper's 10.4% claim and Gemini 4 Argon's launch without a named score.

The mathematicians' own write-ups have not been published. OpenAI has not said when it will correct or version the papers, though OfficeChai reported that corrections will be recorded as new versions.