A Human Audit of OpenAIs AI-Generated Mathematical Proofs

arXiv:2608.14673 · cs.AI, cs.GL, quant-ph · Submitted 2026-08-03 · Read on arXiv

cs.AI, cs.GL, quant-ph

Submitted: 2026-08-03

Updated: 2026-09-09

Comments: 8 pages, 5 references. V2: 11 pages, 8 references. Substantially revised. The polarity error reported in v1 is withdrawn: it resulted from loss of an overbar during PDF text extraction, not from an error in the OpenAI manuscript. The revised paper retains and extends the independent human assessment of Chapter 6. No confirmed mathematical error was found in the examined argument

Code: https://github.com/openai/ten-proofs

License: http://creativecommons.org/licenses/by/4.0/

The gist: We present an independent human assessment of the proof developed in Chapter 6 of OpenAI's Ten Advances in Mathematics and Theoretical Computer Science.

Terminology

Abstract

We present an independent human assessment of the proof developed in Chapter 6 of OpenAI's Ten Advances in Mathematics and Theoretical Computer Science. An initial audit appeared to identify a polarity error in a greedy conditioning lemma. Subsequent examination of the original typeset manuscript showed that this diagnosis resulted from automatic PDF text extraction, which removed an overbar from a mathematical symbol. The alleged error is therefore withdrawn. With the correctly rendered expression restored, we find no confirmed mathematical error in the examined lemma. We retain the broader analysis because it provides an independent reconstruction and assessment of the OpenAI argument and illustrates an important methodological hazard in auditing AI-generated mathematics: errors may arise not only in mathematical reasoning but also in the document-processing pipeline used by human reviewers.

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