OpenAI Posts 722 AI-Written Math Papers. Three Were Pulled the Next Day.

OpenAI released hundreds of math results made by an unreleased model. A sign error led to three withdrawals, and many proofs are still unchecked.

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한국어 요약
OpenAI는 2026년 10월 6일 미공개 내부 모델이 만들었다는 수학 논문 722편(372개 주제)을 GitHub에 한꺼번에 공개했습니다. 대부분 한 번의 프롬프트로 한 에이전트가 만든 결과이며, 하루 뒤 부호 오류로 3편이 철회되고 14편이 수정되어 719편이 남았습니다. Lean(기계 검증 도구)으로 검증된 비율은 보도마다 달라 약 42%에서 162편까지 엇갈리며, 나머지는 검증되지 않은 주장입니다. 수학자들은 속도를 인정하면서도 검증 부담을 외부 수학자에게 넘겼다고 비판했고, 모델이 비공개라 재현도 어렵습니다. 수치는 대부분 회사 발표와 2차 보도이며 독립 검증이 끝나지 않았습니다.
A wall of small manuscript pages, some with green check marks, and three large pages with red crosses pulled out of the grid
AI-generated illustration (Claude (hand-coded SVG))

On October 6, OpenAI put 722 math manuscripts on GitHub. It says an internal model wrote them. By the next day, three had been withdrawn.

What OpenAI released

According to Nature’s report, the papers claim progress on 372 open problems in geometry, algebra, and computer science. The model is not public. Nature reports it was pointed at roughly 4,000 problems and spent about three hours of thinking time per result. A spokesperson told Scientific American that almost every result came from a single prompt to a single agent. This is different from September’s Navier–Stokes claim, which OpenAI said used about 10,000 agents over 88 hours.

These numbers come from OpenAI and from news reports about it. They have not been independently verified.

What went wrong first

On October 7, OpenAI withdrew three manuscripts. A sign error broke one argument, and two papers that depended on it fell with it. One was titled “The rational Hodge conjecture for products of K3 surfaces.” Fourteen more were revised, and the collection fell to 719 manuscripts.

How much is machine-checked?

Lean is software that checks a proof step by step. Reports disagree on how many results have a Lean proof. Quanta reported about 42%, and rising. AI Weekly counted only 162 of the 722 manuscripts. The differences come from counting papers or results, and from the date of the count. On October 21, OpenAI said results are at different stages of verification and that many, but not all, are formalized. Treat unchecked results as unverified claims.

What mathematicians said

  • Andrew Sutherland (MIT) told Scientific American to expect some proofs to contain mistakes, possibly serious ones. He called the quick withdrawal the responsible thing to do.
  • Michael Harris (Columbia) told Nature he would not spend time on the papers and called the process “illegitimate.”
  • Ursula Martin (Oxford) said the release tosses the community a messy first draft.
  • Daniel Litt (Toronto) argued that sharing the answers is better than keeping them secret.

OpenAI says an advisory group of mathematicians recommended releasing the results before full formalization. According to Nature, the batch did not solve any of the Millennium Prize Problems.

What to watch

Look for independent checks of the Lean proofs, more withdrawals, and whether OpenAI releases the model so others can reproduce the results.

Sources