OpenAI周一表示，数百篇计算机科学论文所依赖的一个猜想，已被该公司的一个内部模型推翻。同日，OpenAI还公布了另外两项成果，一项属于数学领域，一项属于物理学领域。
Hundreds of computer science papers rest on a conjecture that an internal OpenAI model now claims to have refuted, the company said on Monday. OpenAI announced two more results the same day, one in mathematics and one in physics.
OpenAI在一篇博客文章中表示，指数时间假说（ETH）此前“被广泛认为成立”。该猜想涉及布尔可满足性问题的求解难度，而这一问题与P versus NP密切相关。研究人员一直借助该假说来证明图论、计算生物学、数据库及其他领域中的问题难以快速求解。
In a blog post, OpenAI said the Exponential Time Hypothesis (ETH) has been “widely believed to be true”. The conjecture concerns how hard it is to solve Boolean satisfiability, a problem closely tied to P versus NP. Researchers have used it to show that problems in graph theory, computational biology, databases and other fields are hard to solve quickly.
据OpenAI称，其模型于10月16日找到了这一反证。次日，公司用Lean对这一证明进行了校验，Lean是一种可通过机器验证证明的语言。该公司已将模型的书面说明和Lean证明发布在GitHub上。
According to OpenAI, its model found the disproof on 16 October. The company checked it in Lean, a language that verifies proofs by machine, the next day. It has published the model’s write-up and the Lean proof on GitHub.
提出ETH的科学家将对其进行审查。由加州大学圣迭戈分校的Russell Impagliazzo和Ramamohan Paturi以及麻省理工学院的Ryan Williams领导的一个团队将核查并解释这一结果。Impagliazzo和Paturi曾与Francis Zane共同首次提出ETH。
The scientists who proposed ETH will examine it A group led by Russell Impagliazzo and Ramamohan Paturi of UC San Diego and Ryan Williams of MIT will check and explain the result. Impagliazzo and Paturi first proposed ETH with Francis Zane.
OpenAI的一个内部模型对ETH提出了反证！Russell Impagliazzo、Mohan Paturi和我已受邀协助组织对这一主张进行公开、独立的审查。1/4 Ryan Williams @rrwilliams.bsky.social（@rrwilliams）2026年10月26日。三位研究人员在致其所在领域的公开信中表示，他们的角色并不构成背书。
An internal model at OpenAI has produced a claimed refutation of ETH! Russell Impagliazzo, Mohan Paturi, and I have been asked to help organize an open and independent examination of this claim. 1/4 Ryan Williams @rrwilliams.bsky.social (@rrwilliams) October 26, 2026 In an open letter to their field, the three researchers said their role is not an endorsement.
“我们的参与不应被视为对这一主张的认证。如此重大的结果需要审慎、独立的审查，”Impagliazzo、Paturi和Williams写道。
“Our involvement should not be taken as certification of the claim. A result of this significance requires careful, independent scrutiny,” Impagliazzo, Paturi and Williams wrote.
Williams在X上表示，该团队未签署任何保密协议，也不会获得报酬。该团队要求OpenAI公布其关于ETH结果的全部原始数据，并出资为研究界举办一次会议。据Williams和OpenAI称，OpenAI对这两项要求均表示同意。
Williams said on X that the group signed no non-disclosure agreements and will not be paid. The group asked OpenAI to release all its raw data on the ETH result and to fund a conference for the research community. OpenAI agreed to both, according to Williams and OpenAI.
在数学领域，OpenAI 称其模型在所有维度上证明了 Christopher Sogge 于 1991 年提出的局部平滑猜想。这也将在所有维度上解决 Kakeya 猜想和 Stein 限制猜想。数学家们已于 2019 年在二维情况下证明了局部平滑，并于 2025 年在三维情况下证明了 Kakeya 猜想。OpenAI 发布了模型的撰写稿和 Lean 证明，正如其于 10 月 6 日发布的 722 篇数学论文所做的那样。
A maths proof and a physics proof In mathematics, OpenAI says its models proved the local smoothing conjecture, which Christopher Sogge proposed in 1991, in every dimension. That would also settle the Kakeya conjecture and Stein’s restriction conjecture in all dimensions. Mathematicians had proved local smoothing in two dimensions in 2019 and the Kakeya conjecture in three dimensions in 2025. OpenAI released the model’s write-up and a Lean proof, as it did with the 722 maths papers it published on 6 October.
在物理学领域，OpenAI 称其模型给出了某些量子场论在四维空间中存在的严格证明。这些理论包括量子色动力学，它描述夸克和胶子之间的强相互作用。该工作包含纯杨-米尔斯理论存在的证明，这是克莱数学研究所千禧年大奖难题之一的一部分。OpenAI 曾在 9 月表示，不会就其纳维-斯托克斯方程证明申领奖金。
In physics, OpenAI says its models produced a rigorous proof that certain quantum field theories exist in four dimensions. These include quantum chromodynamics, which describes the strong force between quarks and gluons. The work includes a proof that pure Yang-Mills theory exists, which is part of one of the Clay Mathematics Institute’s Millennium Prize problems. OpenAI said in September it would not claim the prize for its Navier-Stokes proof.
诺贝尔奖得主 David Gross 将领导物理组，成员包括 Michael Douglas、Arthur Jaffe、Igor Klebanov 和 Nikita Nekrasov。该小组目前选择不发布 AI 生成的材料，将自行撰写相关工作。
Nobel laureate David Gross will lead the physics group, with Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov. That group chose not to release the AI-produced material for now and will write up the work itself.
关于署名权 OpenAI 表示，不寻求这些发现的学术署名权。它称，各小组的研究人员应因其撰写的解释性工作获得认可。OpenAI 还向西蒙斯基金会捐赠了 500 万美元，用于举办关于 AI 产出成果的研讨会和会议。
Who gets the credit OpenAI says it does not seek academic credit for the discoveries. It says the researchers in each group should get the recognition for the explanations they write. It has also given $5m to the Simons Foundation for workshops and conferences on AI-produced results.
这三位计算机科学家在信中询问，当 AI 率先发现结果时，署名应如何分配。他们警告说，认可可能会落到最先发表或拥有最强大工具的人手中，而验证和解释工作的贡献得到的认可却较少。数学家们曾在 6 月的《莱顿宣言》中提出过类似担忧。
The three computer scientists ask in their letter how credit should work when AI finds results first. They warn that recognition may go to those who publish first or have the most powerful tools, while checking and explaining the work gets less credit. Mathematicians raised similar concerns in the Leiden declaration in June.
“如果该说法属实，将改变理论计算机科学的一个重要部分，”这三位研究人员写道。
“If the claim is correct, it will change an important part of theoretical computer science,” the three researchers wrote.