OpenAI's AI-written math papers: 42% checked in Lean, 3 withdrawn

OpenAI has published a GitHub repository, openai/math, of mathematical manuscripts it says were produced by an unreleased internal model, and on 26 October 2026 it added a computer-science result claiming the Exponential Time Hypothesis is false. The part that matters to teams deploying AI is the verification scaffolding around the output, which the company documents in unusual detail. Whether the mathematics holds is for mathematicians to decide; the README itself says it defers to them.

What the repository says it contains

• 721 manuscripts organised into 373 families, per the README's current catalogue.
• A procedure the README describes as largely fixed: the model was posed roughly 4,000 problems, and on average each result used three hours of ChatGPT Pro thinking compute. The README lists exceptions, including a Riemann zeta function zero-free region whose write-up was edited by humans for readability.
• Lean formalizations for about 42% of top-line results. Lean is a programming language in which a computer checks every step of a proof.

How OpenAI labels what it cannot vouch for

The README says the collection includes "results at different stages of verification" and that some unformalized results "could have issues". It calls the manuscripts "raw research data" rather than polished papers. The change history shows the policy in use. On 7 October OpenAI withdrew three manuscripts after a sign error invalidated an argument that two of them depended on, and said it had revised 14 others with proof repairs. Withdrawn papers carry notices that link to the archived versions.

For the Exponential Time Hypothesis paper, the history says an independent working group led by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams will examine and explain the proof, and that OpenAI published the materials immediately at the group's request. The Decoder reports that OpenAI asked outside experts to act as "shepherds" for the three announced results and is handling each field differently.

The limits of the check

The Decoder notes that a Lean proof is not a guarantee of correctness: Lean checks that a proof establishes the statement as written in Lean, and experts still have to judge whether that statement captures the intended problem. In practice, a machine check removes one class of error and leaves another, which is the same shape as a test suite that passes against a wrong specification.

The Hacker News thread on the announcement (item 50251344, about 1,040 points) shows the sharpest objection. A commenter, rickdeckard, objected to "the bicycle manufacturer announcing its achievements in bicycle racing": the lab that built the model is also the one reporting what it achieved. Another commenter credited OpenAI for involving domain experts before publishing, though they expected accusations of favouritism over which experts were chosen.

What we do not know

• Whether the headline results survive the outside review; no review outcome has been published yet.
• What fraction of the roughly 4,000 problems produced nothing usable. The README reports how many results were kept, not how many attempts failed.
• The cost per kept result, beyond the three-hours-of-compute average.

What to do

• If an AI system produces reports, code or analyses that others will rely on, tag each output with its check status (machine-verified, human-reviewed, or unchecked) the way this repository does.
• Name who reviews high-stakes output and let them see it before it is final; OpenAI's approach here is to bring in outside groups and publish at their request.
• Keep a withdrawal log. Three retracted manuscripts and 14 revisions, listed in public, are why the rest of the catalogue is easier to trust.