OpenAI Published 722 Math Manuscripts, Then Withdrew Three in a Day. What That Says About Checking AI Proofs

On October 6, 2026, OpenAI put 722 mathematics preprints into a public GitHub repository, openai/math, claiming progress on 372 problems. The next day it withdrew three of them because of a sign error. According to Retraction Watch, the error invalidated an argument in one paper and a construction that two other papers depended on. The withdrawal is a small fraction of the release, 3 of 722 or about 0.4%. The interesting part is how it happened, and what it implies about how much of the remaining output has actually been checked.

What was released and what was withdrawn

Most facts here come from Retraction Watch's October 8 report by Alicia Gallegos, supplemented by an AI Weekly summary of OpenAI's version log on GitHub. We have not read the repository ourselves, and OpenAI's claims are attributed to OpenAI throughout.

• October 6: 722 preprints published, covering 372 problems in geometry, computer science, algebra and other fields (Retraction Watch). Counts differ slightly across secondary summaries; we use Retraction Watch's 722 and note 719 remain after the three withdrawals.
• October 7: three manuscripts withdrawn over a sign error. They were titled Algebraicity of Weil classes on split abelian eightfolds (dated September 18), Algebraicity of Kuga-Satake Correspondences for K3 Surfaces (October 3), and The rational Hodge conjecture for products of K3 surfaces (October 4).
• Fourteen other manuscripts were revised, with proof repairs, corrected statements, clearer hypotheses and dependencies, and one citation correction.

OpenAI said, via a spokesperson quoted by Retraction Watch, that it found the errors during an internal audit, described the process as iterative, as with its other research manuscripts, and said it welcomed scrutiny from the mathematical community. Dan Roberts, whom Retraction Watch identified as an OpenAI research lead, said in a post on X that OpenAI would continue to update the repository with new formalizations and any errata it noticed.

How one sign error becomes three withdrawn papers

The key fact is in the dates. The paper dated September 18 contained the sign error. According to the AI Weekly summary, the error invalidated a stabilization-trace cancellation argument. Retraction Watch reported that it also invalidated a construction used by two dependent papers, and AI Weekly named one of those dependents as the October 4 paper on the rational Hodge conjecture for products of K3 surfaces. Because the three withdrawn papers are dated September 18, October 3 and October 4, the two later papers were presumably the dependents, though the sources we read do not say so explicitly.

This is how mathematics normally works: later results cite earlier ones as lemmas, and a flaw in a lemma contaminates everything that relies on it. In a human research program the dependency chain is slow and visible, because a paper is written, refereed and cited over months. When a model produces hundreds of manuscripts in weeks, dependencies accumulate faster than any human can audit them. A single upstream error can quietly undermine a block of downstream results, and the damage is bounded only by how many papers cited the flawed one.

The arithmetic is mild here. Three withdrawals plus fourteen revisions touched 17 of 722 manuscripts, or about 2.4%, within a day of release. It is also incomplete as a measure, since it counts only the errors found so far. Alex Townsend, an associate professor of mathematics at Cornell, told Retraction Watch he suspects more errors will be found.

Lean verification versus human refereeing

Lean, per Retraction Watch, is an open-source programming language used to check mathematical proofs. In practice, a proof written in Lean is checked line by line by a small trusted program, the kernel, which accepts it only if every step follows from the rules. It does not get tired, and it does not skip a step because it looks routine. Peer review works differently: referees read for correctness and significance, rely on their expertise to spot gaps, and often miss errors that are not obvious. A sign error in a long computation is the sort of thing a kernel catches and a tired referee may not.

Lean has a limit that matters for how far to trust a verified label. It checks that a proof proves the statement as written in Lean, not that the Lean statement faithfully captures the claim in the paper. A result can be formally verified and still answer a slightly different question than the abstract suggests. The reverse also holds: an unverified result is not necessarily wrong. It is simply unchecked, and in a corpus of this size the unchecked share is the key quantity.

How much was actually checked? The sources disagree

Retraction Watch quoted an OpenAI spokesperson as saying roughly 50% of the results were released unconfirmed, and gave no exact count of Lean-verified manuscripts. A separate newsletter roundup circulating this week put the Lean-checked share at about 42%. We could not trace that figure to OpenAI or to Retraction Watch, so we do not rely on it. We also cannot reconcile 50% unconfirmed with 42% checked: they could be measuring different things, such as results as opposed to manuscripts, or counting at different times. We are reporting both as stated and not blending them.

Taking OpenAI's own figure at face value, about half of the released results, which would be on the order of 360 if the share applied evenly to manuscripts, had no machine confirmation when published. That rests on an assumption that results and manuscripts map one to one, which they may not. The point is not the exact number but the scale: a human audit of hundreds of research-level papers is not something the mathematical community can complete quickly.

The case for and against release first, formalise later

Retraction Watch reported that the release followed AGMAI recommendations to publish without waiting for full formalization. OpenAI's argument, as relayed by its spokesperson, is that this is an iterative process in which the community's scrutiny is welcome and errors are corrected quickly. Andrew Sutherland, a senior research scientist at MIT, called OpenAI's prompt action after finding the errors the responsible thing to do.

Critics argue the sequencing was wrong. Townsend said, in Retraction Watch's words, that OpenAI should have announced the Lean-verified manuscripts first, and could have released the unverified ones separately while asking for help checking them. The Association for Human Mathematics issued a statement on October 7 saying mathematicians had not asked for the work and that releasing over 700 files at once was not a demonstration of scholarship but a demonstration of power; it urged mathematicians to stop working with OpenAI. Sutherland added that many mathematicians are unhappy with OpenAI's conduct and that it would take a lot more to earn back the trust it has lost.

Context matters here. Retraction Watch noted that OpenAI announced on September 8 that an AI system had solved the Navier-Stokes problem, and that a group of leading mathematicians then criticised that announcement as rushed, without proper writeups or citations to prior work. According to the same report, more than 8,000 researchers have endorsed those concerns. The October release is therefore being read against an existing dispute about how OpenAI communicates mathematical claims.

What a reader should take from this

First, speed of production and speed of verification are different quantities, and an AI lab can currently raise the first much faster than the second. Verification, whether through Lean or expert reading, is the bottleneck, and its cost is borne mostly by people outside the lab. Second, the useful question about any AI-for-science claim is what share is machine-checked, what share is human-read, and what share is neither. A release that cannot answer those three questions is closer to a draft than a result. Third, dependency structure turns small errors into large ones, so the order in which results are published and relied upon matters as much as their count.

None of this shows that the unchecked manuscripts are wrong, and some may prove valuable. It does show that the label of 722 manuscripts overstates what is currently known. The responsible reading for now is that three were wrong enough to withdraw, fourteen needed repair, and the status of the rest is open.