OpenAI releases 700+ AI-written maths papers claiming famous open problems

An unreleased model's 722 papers claim, among others, the Unique Games Conjecture, the Mahler conjecture and a zero-free region for the Riemann zeta function above 7/8. About 42% of main results carry Lean proofs; three papers were withdrawn a day later and outside review has just begun.

What happened

On 6 October OpenAI opened a GitHub repository, openai/math, containing mathematical manuscripts produced by an unreleased internal model, together with some formal proofs written in the Lean language and ten summaries of the model’s reasoning. According to the repository:

Manuscripts at release: 722
Grouped into result families: 372
Problems posed to the model: ≈4,000
Main results with formal proofs: ≈42%

Source: openai/math README and revision history, checked 9 October 2026.

According to The Next Web, the model is the same one behind OpenAI’s Navier–Stokes proof in September. OpenAI says each result used, on average, roughly three hours of ChatGPT Pro thinking compute, and nearly all followed the same fixed procedure; OpenAI told Scientific American that almost every paper came from a single prompt to a single AI agent. The two exceptions were a result on the Riemann zeta function and a special case of the Hodge conjecture; the write-up of the 11/12 zeta result was edited by a person for readability.

OpenAI’s research lead Dan Roberts told The New York Times that testing internal models on open problems helps build better tools, and that the proofs were a byproduct (as reported by The Next Web).

How big is this? A few of the claims

722 papers is not 722 problems: some are alternative proofs or consequences of the same result. What stands out is a handful of famous old problems named in the catalogue. “Before” is from Wikipedia and other public sources; “OpenAI claims” is from the repository’s catalogue.

Problem	In plain terms	Before	OpenAI claims
Unique Games Conjecture	Whether a large class of problems is hard even to solve approximately	Posed in 2002; a central open problem in theoretical computer science	Proved (Lean file attached)
Quasi-Riemann hypothesis	Whether the zeta function’s zeros can be kept to the left of some fixed line	Since 1899 we only knew zeros can’t get too close to the line at 1; no fixed zero-free half-plane was known	No zeros with real part above 7/8 (Lean file attached)
Irrationality exponent of π	How well π can be approximated by fractions	Conjectured to be 2; best known upper bound about 7.1	Exactly 2 (Lean file attached)
Mahler conjecture	The smallest possible volume product of a convex shape and its dual	Proved only in two dimensions and the symmetric three-dimensional case	True in every dimension (Lean file attached)
Hodge conjecture (special case)	A Millennium Prize problem; here only for “CM abelian varieties”	Only scattered special cases known for these	True for the whole class (no Lean file)
Free group factors	Whether several basic objects in operator algebras are secretly the same	One of the field’s most famous open problems for decades	They are all isomorphic (Lean file attached)
Kaplansky’s direct-finiteness conjecture	In certain algebras, does a left inverse have to be a right inverse?	Proved only in some cases (such as characteristic zero)	Disproved with a counterexample (Lean file attached)

Why “no zeros above 7/8” would be a big deal

The Riemann hypothesis says every non-trivial zero of the zeta function has real part exactly 1/2. It governs how far the primes stray from their expected count, and it is one of the seven Millennium Prize problems.

OpenAI does not claim to have proved it. It claims a much weaker statement that had still been open for more than a century: that no zero has real part above 7/8. By the classical argument, a zero-free half-plane like that keeps the error in counting primes to roughly x to the power 7/8 — whereas before, mathematicians could not prove any fixed bound below 1.

Put simply: the Riemann hypothesis says everyone stands on the line at 1/2; we used to know only that far away, nobody gets too close to the wall at 1; the new claim is that nobody stands to the right of 7/8.

What is still uncertain

Errors have already turned up. The day after release (7 October) OpenAI withdrew three manuscripts: a sign error in a paper on Weil classes on split abelian eightfolds broke a key argument and two papers that depended on it, one of which claimed the Hodge conjecture for products of K3 surfaces. Fourteen more were revised with proof repairs or corrected statements.

Most results have not been read closely by anyone outside OpenAI. As reported by The Next Web:

New York University mathematician Tristan Buckmaster, who had a credit dispute with OpenAI over the Navier–Stokes problem, told the Times he doubted OpenAI had checked so many results released at once: “I don’t think they’ve done their sort of due diligence at all.”
MIT mathematician Andrew Sutherland told Scientific American to treat the claims as unverified until others can run the model and repeat the results.

Mathematicians object to how it was released. The independent Advisory Group on Mathematics and Artificial Intelligence (AGMAI), hosted by the Institute for Advanced Study, advised OpenAI on the release. Its 29 September guidelines asked AI labs to “stop testing advanced mathematical problems on proprietary models” and to publish the prompts, time and compute behind each result. On 6 October it added that its advisory role “should not be interpreted as a judgment of the impact of these results or an endorsement of the process”, and that “this release is the beginning, not the completion, of the process of human understanding”.

The model is not public. Nobody outside can rerun it, and we don’t know how many of the ~4,000 problems it failed, or how.

How this differs from the Navier–Stokes proof

September’s result was one Millennium problem, one team, about 10,000 agents and 88 hours. This release is the same model answering thousands of problems in bulk, a few hours each. The first was a concentrated assault; this is more like a census, showing how widely the model can produce work that looks like research papers. The sheer volume, which human review cannot keep up with, is also what makes it controversial.

What it means for you

AI research in mathematics now has to be taken seriously. Even if only part of this holds up, a machine produced in weeks a set of candidate results that would represent years of work for many mathematicians.
“Claimed” and “confirmed” are far apart. Maths results are checked line by line by peers, which usually takes months to years. When you see “AI solves famous problem”, ask: is the proof public? Have independent experts checked it? Has anything been withdrawn or revised?
You can’t use this model. OpenAI says it is working on releasing it responsibly but has given no date.

We will follow the independent review of these results and update this article as conclusions emerge.