Yesterday OpenAI released 722 AI maths manuscripts. Today it has withdrawn three of them, over a single wrong sign.
The three retracted papers all touch the Hodge conjecture, one of the Millennium Prize problems. The fault sits in the first: in a key proof, OpenAI recorded a geometric operation’s sign as plus one when its own convention required minus one. A count that should cancel to zero instead became non zero, collapsing a classic theorem’s premise and the construction built on it. The other two borrowed that construction and fell with it.
OpenAI stressed in all three notices that it withdrew the proofs, not the truth of the propositions; the original drafts remain viewable via archive links. The three belonged to result family 032, the most watched Hodge-related cluster. After withdrawal, the family was renamed from Hodge and Kuga-Satake results for all projective K3 surfaces to the rational Hodge conjecture for CM abelian varieties. The erroneous paper was dated 18 September, among the earliest drafts; found and pulled within days of public release.
Beyond the withdrawals, OpenAI revised 14 manuscripts, fixing proofs, narrowing claims or clarifying premises, across statistical physics, complex geometry, symplectic geometry, Navier-Stokes and a BSD formula paper. The update also added six Lean formalisations and five auxiliary results. OpenAI now says 300 of 719 manuscripts have formalised main results, about 42 per cent.
The pattern is clear: almost everything withdrawn or substantively revised sat in sections with no Lean check. It confirms the maths community’s warning that unaudited, unpeer reviewed results are only claimed. The first erratum arrived two days after 700-plus drafts went public, and it will not be the last.
Editor’s note: This is an adapted translation of the original 36Kr report. The full source is at https://36kr.com/p/4017059444330631 (36Kr / Jiqizhixin). It has been trimmed and restructured for readability for an international business audience.