OpenAI Retracts Three Hodge-Conjecture Papers Over Sign Error, 42% of Results Now Formalized

OpenAI published its first changelog just two days after making the openai/math repository public: 3 manuscripts retracted, 14 revised, and 13 citations updated, bringing the total number of manuscripts down from 722 to 719. The retraction stemmed from a notation error that invalidated a stability-trace cancellation argument, and two other papers relying on that argument were retracted as well; according to 机器之心, all three papers relate to the Hodge conjecture, touching on topics such as the algebraicity of Weil classes and K3 surfaces.

Confirmed

Around October 7, OpenAI retracted 3 papers and revised the other 14 manuscripts.
The repository added 6 Lean formalizations and 19 modifications.
Of the 719 core (headline) results, roughly 300 — about 42% — have been formalized in Lean, and the team says updates will continue.

Why it matters

The episode shows formal verification is becoming a credibility gatekeeper for AI-generated mathematics: the error was exposed by the Lean formalization process, prompting a timely retraction.
A 42% formalization coverage means most results have yet to be machine-verified, so the repository's credibility still depends on ongoing formalization work.

2026-10-08 ~ 2026-10-09 · 5 related posts

Full story(3 episodes)→

Episode 1: Cambridge paper argues Lean verification does not certify proofs, targeting OpenAI's Navier-Stokes claim(2026-10-08, 14 posts)
Episode 2: OpenAI Retracts Three Hodge-Conjecture Papers Over Sign Error, 42% of Results Now Formalized(2026-10-08, 5 posts)
Episode 3: Researchers Improve OpenAI's Math Proof, Verified in Lean(2026-10-08, 2 posts)

Primary sources

OpenAI math repo formalizes ~42% of top-line results, withdraws 3 papers over sign error — danintheory · 2026-10-08 13:20 (UTC+08:00)
OpenAI pulls 3 math papers over sign error; only 42% of 719 results formalized — petrusenko_max · 2026-10-08 23:00 (UTC+08:00)
Sign error forces OpenAI to retract 3 math papers two days after publishing 722 — 机器之心 · 2026-10-08 18:00 (UTC+08:00)

[source] OpenAI math repo formalizes ~42% of top-line results, withdraws 3 papers over sign error — danintheory · 2026-10-08
[source] Sign error forces OpenAI to retract 3 math papers two days after publishing 722 — 机器之心 · 2026-10-08
Tao on AI math repo at ~42% formalized: AI less helpful for fuzzy math tasks than hoped — iskander · 2026-10-08
[source] OpenAI pulls 3 math papers over sign error; only 42% of 719 results formalized — petrusenko_max · 2026-10-08

1 near-duplicate retellings: petrusenko_max