FRIDAY, OCTOBER 9, 2026|No. 18065

Technology · AI Research

OpenAI Retracts Three Mathematical Proofs Amidst Ongoing Formalization Efforts

OpenAI has withdrawn three mathematical research papers, citing the need for further verification as part of its ongoing efforts to formalize mathematical proofs using software.

News AutomationCompiled 11:05 UTC · 1 min read

An abstract representation of mathematical equations and code. — An abstract representation of mathematical equations and code. · Photo by Saad Ahmad on Unsplash

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We've updated our GitHub math repo with 6 new Lean formalizations, 19 modifications, and 3 withdrawals. The repo now has ~42% top-line results formalized. We will continue to update the repo with new formalizations and with any errata we notice.

https://github.com/openai/math/blob/main/history.md

proofs are shipping like software now

Respectfully why did you not check these before releasing them?

To save you a click:

As a result, we have withdrawn the following three manuscripts:

Algebraicity of Weil classes on split abelian eightfolds
Algebraicity of Kuga–Satake Correspondences for K3 Surfaces
The rational Hodge conjecture for products of K3 surfaces

PAN's pipeline reviewed approximately 1 open sources for this article. No human editor reviewed this article before publication.

Three independent reads. One synthesis. PAN generates a positive, neutral, and negative interpretation of every event, then merges them. The article you are reading is the merged output. Below: the underlying reads, weighted by source coverage.

＋ POSITIVE40%

OpenAI is demonstrating a strong commitment to scientific rigor by proactively withdrawing three mathematical results that require further formalization. This move underscores their dedication to ensuring the highest standards of accuracy in their research. By updating their GitHub math repository with new Lean formalizations and modifications, OpenAI is advancing the frontier of software-shipped proofs.

Source weight: ~2 documents

＝ NEUTRAL50%

OpenAI has withdrawn three mathematical manuscripts from public record. The company updated its GitHub math repository, noting the withdrawal of "Algebraicity of Weil classes on split abelian eightfolds," "Algebraicity of Kuga–Satake Correspondences for K3 Surfaces," and "The rational Hodge conjecture for products of K3 surfaces." The repository now contains approximately 42% of top-line results formalized.

Source weight: ~2 documents

− NEGATIVE10%

OpenAI has been forced to retract three of its published mathematical results, raising questions about the initial vetting process for these complex proofs. The withdrawal of papers on topics such as the algebraicity of Weil classes and the rational Hodge conjecture suggests a premature release of research that had not undergone sufficient verification.

Source weight: ~2 documents

→ Synthesis · Published Read

OpenAI has withdrawn three mathematical manuscripts from public record. The company updated its GitHub math repository, noting the withdrawal of "Algebraicity of Weil classes on split abelian eightfolds," "Algebraicity of Kuga–Satake Correspondences for K3 Surfaces," and "The rational Hodge conjecture for products of K3 surfaces." The repository now contains approximately 42% of top-line results formalized.

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Synthesis · final pass1

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