# OpenAI's 722 machine-written math manuscripts land on mathematicians to verify as Terence Tao warns of a rush to "flatten" open problems

According to the repository's own catalogue, Lean formalizations cover the main result of only 162 of the 722 papers, and the Clay Mathematics Institute still lists Navier-Stokes as an open problem.

- Published: 2026-10-08T06:25:29.519Z
- Canonical: https://polylog.news/ai/2026-10-08/openai-s-722-machine-written-math-manuscripts-land-on-mathem
- Publisher: Polylog (AI desk)
- Section: tech
- Sources: [Hacker News / Mathstodon (Terence Tao)](https://mathstodon.xyz/@tao/117395269325940185), [What's new (Terence Tao blog)](https://terrytao.wordpress.com/2026/10/07/ahm-statement-on-openais-october-6-release-of-mathematical-documents/), [Tech Insider](https://tech-insider.org/openai-722-math-claims-mathematician-scrutiny-2026/), [Gadget Review](https://www.gadgetreview.com/openai-drops-722-ai-math-manuscripts-on-github-experts-must-now-verify-them), [Unite.AI](https://www.unite.ai/openai-releases-722-math-manuscripts-from-an-unreleased-ai-model/), [Futurism](https://futurism.com/artificial-intelligence/drama-openai-supposed-mathematical-breakthrough), [Decrypt](https://decrypt.co/377818/ai-math-best-problems-terence-tao)

On October 6, OpenAI published [722 mathematical manuscripts, grouped into 372 families of related results](https://tech-insider.org/openai-722-math-claims-mathematician-scrutiny-2026/), in a public GitHub repository called openai/math. All of them were produced by an internal frontier model that the company has not released. OpenAI says the same model generated its earlier claimed solution to the Navier-Stokes existence and smoothness problem. OpenAI has published neither the model nor the exact prompts, so outside researchers can check the outputs but cannot reproduce how they were made.

Formal verification covers only part of the release. The repository's formalization catalogue shows [Lean proofs for the main result of 162 of the 722 papers](https://www.unite.ai/openai-releases-722-math-manuscripts-from-an-unreleased-ai-model/) (Lean is a computer program that checks mathematical proofs step by step), and 235 of the 372 families link to a Lean page. The README itself warns that some unformalized results could contain errors. A machine-checked proof also has a limit: it does not show that the formal statement matches the theorem a mathematician cares about. [Gadget Review reports](https://www.gadgetreview.com/openai-drops-722-ai-math-manuscripts-on-github-experts-must-now-verify-them) that the Clay Mathematics Institute still lists Navier-Stokes as active. Tristan Buckmaster, a mathematician at New York University, and Andrew Sutherland have both questioned whether OpenAI vetted the results and want the claims treated as unverified until someone reproduces them independently.

Terence Tao, the Fields Medalist who sits on the advisory group OpenAI set up to coordinate these releases, responded on Mastodon. He wrote that "[even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it](https://decrypt.co/377818/ai-math-best-problems-terence-tao) before the original research project has time to reach its full potential." On October 7, [Tao's blog published a statement on the release](https://terrytao.wordpress.com/2026/10/07/ahm-statement-on-openais-october-6-release-of-mathematical-documents/). Tao's warning points to a specific case. OpenAI has said its Navier-Stokes work began after it heard that Buckmaster and Levent Alpöge had made progress on a related problem. Buckmaster [says OpenAI's proof follows a path suspiciously close to his own](https://futurism.com/artificial-intelligence/drama-openai-supposed-mathematical-breakthrough). He also says he had used OpenAI's Codex to check his work. Sébastien Bubeck of OpenAI denies that he ever asked for Alpöge to be removed from authorship.

Without the model, OpenAI's capability claim cannot be tested in the usual way. No benchmark, held-out problem set, or third-party evaluation accompanies it. The only available evidence is the outputs themselves, and checking them takes a great deal of expert labor, most of it unpaid.

## What this means

OpenAI is using a large set of results that are hard to check as evidence for a model nobody outside the company can test. That strengthens OpenAI's case to investors and job candidates, while academic mathematicians bear the cost of checking the work. Good precedents exist. Grigori Perelman posted his Poincaré proof on arXiv in 2002 and 2003, and independent teams needed until 2006 to confirm it. Shinichi Mochizuki's 2012 abc proof is still disputed. Most commentary treats "722 papers" as a measure of capability. It is better read as a measure of how much verification work OpenAI has shifted onto others. The desk's read is that over the coming months, the Lean-formalized results in narrower areas will mostly hold up and be cited. The Navier-Stokes claim is likely to stay formally unresolved for a year or longer, because the people able to referee it include the researchers who are disputing its origin. Journals and arXiv are likely to adopt AI-provenance disclosure rules within months. That forecast depends on OpenAI continuing to withhold the model. Two things would prove it wrong: a substantive error found in a headline Lean-formalized result, or a quick favorable review by the Clay Institute. For investors, the release supports private valuations of OpenAI and its partner Microsoft as long as no retractions follow.

## What to watch

- Whether errata or retractions appear in the openai/math repository. A visible error rate on the unformalized papers would indicate how reliable the formalized subset is by comparison.
- Any change in how the Clay Mathematics Institute lists Navier-Stokes, because that is the only body whose decision settles the Millennium Prize claim.
- Whether OpenAI releases the model, or the prompts and compute used. Without them, the claim rests on outputs alone and cannot be reproduced.
- Whether Google DeepMind or another lab responds with its own large release of formalized results, which would make mathematics a recurring venue for capability marketing.