OpenAI Drops 722 Math Manuscripts From an Unreleased Model

On October 6, 2026, OpenAI published 722 mathematical manuscripts — grouped into 372 result families — that it says were produced by an unreleased internal frontier model, covering open problems in mathematics, theoretical computer science, and physics. The company posted them to a public GitHub repository under an Apache-2.0 license with computer-checkable Lean proofs for many results. Within a day it had withdrawn three manuscripts for an error and revised fourteen more, and the release has intensified a dispute among mathematicians over how AI-generated results should be published.

Intermediate

What Was Released

The repository, github.com/openai/math, is organized into 372 families of related results, each classified by discipline; the catalogue now lists 719 manuscripts following the withdrawals. OpenAI says the model was posed roughly 4,000 problems over the course of the evaluation, that reference and citation protocols are included, and that the average result used “the equivalent compute of roughly three hours of ChatGPT Pro thinking.” Roughly 42% of the top-line results ship with Lean formalizations — machine-checkable proofs that verify a result’s logic independently of the English write-up — and the repository also carries ten abridged summaries of the model’s reasoning.

The headline claims span several fields. In mathematics, OpenAI says the model produced a solution to the four-dimensional Kakeya conjecture, progress on the Riemann hypothesis through a “quasi-Riemann hypothesis” and a result ruling out Siegel zeros for the zeta function and related Dirichlet L-functions, Hilbert’s tenth problem over the rationals, Artin’s conjecture on primitive roots, and the Erdős conjecture on arithmetic progressions. In theoretical computer science it reports a new upper bound of ω ≤ 2.25 for matrix multiplication, a derandomization result stated as L = RL = BPL, hardness for the unique games problem, and a sub-n log n Fourier transform. In physics: a nonlinear sigma model result described as a “warm-up” for the Yang–Mills mass gap, and an extension of the Bose–Einstein condensate prediction to interacting gases.

What Mathematicians Are Checking

Lean verification lifts a result close to certain, but it only guarantees that a proof’s steps follow from its stated assumptions — not that the formalized statement is the theorem people think it is. Andrew Sutherland of MIT told Scientific American that “we should expect some of the proofs to contain mistakes, possibly serious ones.” On October 7 OpenAI withdrew three manuscripts after a sign error invalidated an argument in one and the shared construction used by two dependent papers, and it says the errors were found in an internal audit. Alex Townsend of Cornell told Retraction Watch he suspects more will surface, adding that OpenAI “should have announced the manuscripts that were lean verified first.”

The reaction has been mixed. Harvard’s Michael Douglas called it the day “a new era of math and mathematical physics began,” while NYU’s Roland Bauerschmidt described part of the output bluntly: “If I had received these by e-mail from a nobody, I probably would have deleted it, it’s so badly written.” The Association for Human Mathematics, in a statement released October 7, said “releasing over 700 files at once is not a demonstration of scholarship, but a demonstration of power,” and urged mathematicians to stop working with OpenAI. The company says it is following recommendations from the independent Advisory Group on Mathematics and Artificial Intelligence, which advises disclosing the model, the exact prompt, and the compute time behind each result; OpenAI released only the average compute figure and no prompts.

How It Was Produced

A spokesperson told Scientific American that almost every result came from a single prompt given to a single AI agent — a departure from September’s Navier–Stokes claim, which OpenAI said used a swarm of roughly 10,000 coordinating agents over 88 hours. Sutherland’s response to the new claim was direct: “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.” The internal model remains unpublished. OpenAI says it human-edited the write-up of one result for readability, and three manuscripts carry notes describing the gap that led to their withdrawal.

What This Means

For working mathematicians, the practical question is not whether an AI can produce a correct proof but what to do with a pile of them. Daniel Litt of the University of Toronto argued the balance tips toward disclosure — “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.” Terence Tao and others have criticised the sheer pace. The withdrawals are a reminder that a repository of unverified results is not the same as verified knowledge, and that the reading — not the generating — is the bottleneck. A university group, or an undergraduate, can now download the manuscripts and start checking; whether that is a research boon or a flood depends on whether the formalization coverage keeps climbing past 42%.

Related Coverage

• OpenAI Claims a Navier–Stokes Proof, Amid a Dispute Over Credit — the September announcement that first brought this internal model to public attention.
• AI Wins Gold at 2025 International Mathematical Olympiad — the previous marker on this curve, fourteen months earlier.
• OpenAI Releases GPT-6 Sol and Luna at Half the Price — the released models that the unreleased research system is said to considerably outperform.

This post was drafted with AI assistance and reviewed by RITS staff.

Sources

• OpenAI — Sharing AI progress in mathematics (October 6, 2026)
• GitHub — openai/math repository and README
• OpenAI — On the Navier–Stokes Millennium Prize Problem (September 8, 2026)
• Scientific American — OpenAI unleashes hundreds more math results upon a field already in shock (October 6, 2026)
• Scientific American — Mathematicians marvel, and grumble, at OpenAI’s trove of new results (October 8, 2026)
• Scientific American — The most exciting claims from OpenAI’s heap of new proofs (October 8, 2026)
• Retraction Watch — OpenAI withdraws three preprints a day after releasing 722 manuscripts (October 8, 2026)
• Engadget — OpenAI just posted hundreds more results on major math problems (October 7, 2026)
• Advisory Group on Mathematics and Artificial Intelligence (AGMAI)