OpenAI's AI-Written Math Papers: Unique Games Claim and Lean Proofs

A repository of papers nobody had refereed

On the afternoon of October 6, 2026, Pacific time, OpenAI published a public GitHub repository of mathematical manuscripts and proof artifacts "produced by an internal OpenAI model." Its catalogue lists 719 manuscripts grouped into 372 families, each a principal result with companion papers, consequences or alternative proofs, classified by discipline. The repository includes an overview of every family, the papers' PDFs and sources, a Lean library, abridged summaries of the model's reasoning for ten results, and an Apache-2.0 license. [1][3]

OpenAI said it began evaluating models on open research problems after its existing mathematical evaluations saturated. Most results came from one fixed procedure using an unreleased model, averaging three hours of ChatGPT Pro thinking compute per result. The model was posed about 4,000 problems, and the output was grouped and filtered for significance to produce the catalogue. A Riemann zeta zero-free region and the Hodge conjecture for CM abelian varieties were produced outside that procedure, and one zeta writeup was edited by a human for readability. [1]

The release followed OpenAI's September claim to have settled the Navier-Stokes Millennium Prize problem and, before that, a model's solution to an Erdős problem in January. The difference here is volume: hundreds of claimed results in a single drop, rather than one problem at a time. [1][2]

The claims at the top of the list

The overview's entries include a proof of Subhash Khot's Unique Games Conjecture, together with direct NP-hardness reductions for Max-Cut and vertex cover that do not go through it; a resolution of the Kakeya maximal conjecture in three dimensions and the Hausdorff-dimension conjecture in four; a bound of at most 9/4 for the matrix multiplication exponent over the complex numbers; and the rational Hodge conjecture for every complex CM abelian variety. [3]

Scott Aaronson, writing the next day, said the 372 results were released on the recommendation of an OpenAI advisory group that included Timothy Gowers and Edward Witten. He called October 6 "surely one of the biggest days in mathematical history," and added a qualification: "we're pretty sure that it's a proof!" [2]

Lean certificates for some, nothing yet for the rest

The README warns that the collection is at "different stages of verification" and that "some of the unformalized results could have issues." After an update on October 7, OpenAI put the share of top-line results with Lean formalizations at 300 of 719, about 42 percent. The formalization catalogue includes an entry for "The Unique Games Theorem" with instructions for independently checking it. [1][4][5]

The same October 7 update withdrew three manuscripts on Hodge-type questions for abelian eightfolds and K3 surfaces, after OpenAI found that a sign error invalidated a cancellation argument in one paper and the construction two others depended on. Fourteen more manuscripts were revised with proof repairs, corrected statements and clearer hypotheses. OpenAI said earlier versions would remain accessible. [4]

A Lean certificate shows that a formal statement follows from its axioms; it does not show that the formal statement says what the conjecture says, or that anyone understands why it is true. For the unformalized majority, the withdrawals within a day are the clearest evidence that the catalogue still needs human refereeing. [4][5][2]

Mathematicians start reading

Aaronson's wife, the complexity theorist Dana Moshkovitz, had worked toward proving the Unique Games Conjecture for as long as he had known her. He wrote that "no human has understood just about any of these proofs yet; the race to do so has just started," and quoted her texts from the first night: the paper was "so horribly written that it's impossible to read it without AI help," and its proof "invents a completely new bizarre code with a noise test." [2]

In an update on October 9, Aaronson reported that a group calling itself the Association for Human Mathematics had condemned OpenAI for the release, including the line "Mathematicians did not ask for this work to be done." He said he knew of no direct practical implications of the results and argued that keeping human understanding at the center of mathematics was the reason to engage with them. [2]