What OpenAI’s latest controversy tells us about the future of math
What OpenAI’s latest controversy tells us about the future of math
OpenAI 的最新争议揭示了数学的未来
EXECUTIVE SUMMARY OpenAI’s latest mathematical milestone has quickly become mired in controversy. Today, the company announced that its agents have solved one of the Millennium Prize Problems, some of the most important open problems in mathematics. Under normal circumstances, that solution would be a huge feather in OpenAI’s cap. But the announcement has been overshadowed by accusations that OpenAI used NYU mathematician Tristan Buckmaster’s and Anthropic employee Levent Alpöge’s AI-assisted work on the problem as a jumping-off point and failed to credit them. OpenAI has denied the accusations.
执行摘要 OpenAI 的最新数学里程碑事件迅速陷入了争议之中。今天，该公司宣布其智能体（agents）已经解决了“千禧年大奖难题”（Millennium Prize Problems）之一，这是数学界最重要的几个未解难题。在正常情况下，这一解决方案本应是 OpenAI 的一大功绩。但该公告被指控所掩盖——有人称 OpenAI 将纽约大学数学家 Tristan Buckmaster 和 Anthropic 员工 Levent Alpöge 在该问题上的 AI 辅助研究作为起点，却未给予他们应有的署名。OpenAI 否认了这些指控。
It remains uncertain if OpenAI’s models made use of the work completed by Buckmaster and Alpöge, though Sébastien Bubeck, a member of the technical staff at OpenAI, said in a press briefing that the team was inspired to pursue the problem after hearing a rumor about Buckmaster and Alpöge’s efforts. But whether or not OpenAI’s models took advantage of Buckmaster and Alpöge’s research, this episode may mark a turning point in the history of mathematics. AI models now seem essential for making progress on the most important mathematical problems of our time, and solving them may demand resources only available at a couple of frontier AI companies, which often defy the norms of academic collaboration that undergird most mathematical progress. If that’s the future we are headed for, it is unclear how human mathematicians will fit into it.
目前尚不确定 OpenAI 的模型是否使用了 Buckmaster 和 Alpöge 完成的研究成果，尽管 OpenAI 技术人员 Sébastien Bubeck 在新闻发布会上表示，团队是在听到关于 Buckmaster 和 Alpöge 研究工作的传闻后，才受到启发去攻克这一难题的。但无论 OpenAI 的模型是否利用了他们的研究，这一事件都可能成为数学史上的一个转折点。AI 模型似乎已成为推动当代最重要数学问题取得进展的关键，而解决这些问题可能需要只有少数几家前沿 AI 公司才具备的资源，这些公司往往违背了支撑大多数数学进步的学术合作规范。如果这就是我们所走向的未来，那么人类数学家将如何自处尚不明确。
The problem that OpenAI claims to have solved is known as the Navier–Stokes existence and smoothness problem. It is one of seven Millennium Prize Problems selected by the Clay Mathematics Institute in 2000. Solutions come with a one million dollar prize; before today, only one other Millennium Prize Problem had been solved. The Navier–Stokes problem concerns a set of equations that describes how fluids, such as water and air, flow over time. The equations are widely used in the field of fluid dynamics, and they have proven powerful, but physicists and mathematicians didn’t understand them completely. In particular, it was unknown until today whether the equations might, under some conditions, break down and predict an impossible state of affairs—such as a fluid having infinite velocity.
OpenAI 声称解决的问题被称为“纳维-斯托克斯存在性与光滑性问题”（Navier–Stokes existence and smoothness problem）。它是克雷数学研究所（Clay Mathematics Institute）于 2000 年选出的七个“千禧年大奖难题”之一。解决该问题可获得一百万美元奖金；在今天之前，只有另外一个千禧年大奖难题被解决。纳维-斯托克斯问题涉及一组描述流体（如水和空气）随时间流动的方程。这些方程在流体力学领域被广泛使用，且已被证明非常强大，但物理学家和数学家并未完全理解它们。特别是直到今天，人们仍不清楚这些方程在某些条件下是否会失效，并预测出一种不可能的状态——例如流体具有无限大的速度。
On Monday, NYU’s Buckmaster posted a proof on the social media site Mastodon showing that a simplified version of the Navier–Stokes equations can indeed break down—a major step forward on the Millennium Problem. He and Alpöge had worked on the problem for almost a year, using publicly available models from both OpenAI and Anthropic. Then today, OpenAI presented a proof showing that the full Navier–Stokes equations can break down as well. The proof was obtained using an internal model that dramatically outperforms the already-impressive Astra model, which was only released last week. The company says it does not plan to claim the million-dollar prize for solving the problem.
周一，纽约大学的 Buckmaster 在社交媒体平台 Mastodon 上发布了一项证明，表明纳维-斯托克斯方程的简化版本确实会失效——这是在解决该千禧年难题上迈出的重要一步。他和 Alpöge 使用 OpenAI 和 Anthropic 公开的模型，针对该问题研究了近一年。随后在今天，OpenAI 展示了一项证明，表明完整的纳维-斯托克斯方程同样会失效。该证明是使用一个内部模型获得的，其性能远超上周才发布、表现已十分惊人的 Astra 模型。该公司表示，不打算领取解决该问题的一百万美元奖金。
These mathematical achievements are indisputably impressive, but they have attracted far less attention than the controversy about their origins. Along with the proof, Buckmaster posted a document detailing his interactions with OpenAI employees after he heard rumors about their work and reached out to one of them. According to him, OpenAI employees presented two possibilities to him: Either he and Alpöge could post their work and OpenAI would post their Navier-Stokes solution the following day, or he could work with OpenAI on a Navier-Stokes paper that excluded Alpöge from authorship, due to his affiliation with Anthropic, OpenAI’s biggest rival.
这些数学成就无疑令人印象深刻，但它们所引发的关注远不及关于其来源的争议。除了证明本身，Buckmaster 还发布了一份文件，详细记录了他与 OpenAI 员工的互动过程——此前他听到了关于他们工作的传闻，并联系了其中一人。据他所述，OpenAI 员工向他提出了两种可能性：要么他和 Alpöge 发布他们的研究成果，而 OpenAI 将在次日发布他们的纳维-斯托克斯解决方案；要么他与 OpenAI 合作撰写一篇纳维-斯托克斯论文，但由于 Alpöge 隶属于 OpenAI 的最大竞争对手 Anthropic，他将被排除在作者名单之外。
Buckmaster also wrote that he asked the employees whether the agents had obtained access to transcripts of the work that he and Alpöge had done with OpenAI models, which they denied; and whether OpenAI models had been trained on those transcripts, to which they offered no response. MIT Technology Review reached out to Buckmaster for comment, but didn’t hear back before publication.
Buckmaster 还写道，他曾询问这些员工，智能体是否获取了他和 Alpöge 使用 OpenAI 模型进行研究时的对话记录，对方予以否认；当他询问 OpenAI 的模型是否曾基于这些记录进行训练时，对方则未作回应。《麻省理工科技评论》联系了 Buckmaster 请求置评，但在截稿前未收到回复。
The clear implication of the document is that OpenAI’s models somehow made use of Buckmaster and Alpöge’s work. That scenario is plausible on its face. The Buckmaster/Alpöge and OpenAI proofs both make use of an approach to the Navier-Stokes problem pioneered by the mathematicians Diego Córdoba and Luis Martínez-Zoroa. According to Javier Gómez-Serrano, a mathematics professor at Brown University, this approach was one of several that was thought to hold promise for solving the Navier-Stokes problem. So, while it’s by no means impossible that both teams could have arrived at this approach independently, it’s also conceivable that Buckmaster and Alpöge’s work could have influenced OpenAI’s.
该文件明确暗示 OpenAI 的模型在某种程度上利用了 Buckmaster 和 Alpöge 的工作成果。从表面上看，这种情况是合理的。Buckmaster/Alpöge 和 OpenAI 的证明都采用了由数学家 Diego Córdoba 和 Luis Martínez-Zoroa 开创的纳维-斯托克斯问题研究方法。据布朗大学数学教授 Javier Gómez-Serrano 称，这种方法是被认为有望解决纳维-斯托克斯问题的几种方法之一。因此，虽然两个团队完全有可能独立得出这种方法，但 Buckmaster 和 Alpöge 的工作影响了 OpenAI 的研究也是可以想象的。
In the press briefing, Mark Chen, OpenAI’s chief research officer, again denied that any agents or OpenAI employees accessed Buckmaster and Alpöge’s transcripts—but given what has been revealed about the Hugging Face hack, it’s clear that OpenAI is not always entirely aware of what its agents are doing. If OpenAI’s models did train on Buckmaster and Alpöge’s work, or if its agents somehow gained access to it, then the company’s failure to track down the truth and assign those researchers appropriate credit reflects poorly on it.
在新闻发布会上，OpenAI 首席研究官 Mark Chen 再次否认任何智能体或 OpenAI 员工访问过 Buckmaster 和 Alpöge 的对话记录——但考虑到此前关于 Hugging Face 被黑事件的披露，很明显 OpenAI 并不总是完全清楚其智能体在做什么。如果 OpenAI 的模型确实基于 Buckmaster 和 Alpöge 的工作进行了训练，或者其智能体以某种方式获取了这些内容，那么该公司未能查明真相并给予这些研究人员应有的署名，反映出其管理上的不足。
But there might be a thin silver lining to that version of the story for mathematicians, because it would suggest that the hard work of two humans, one of whom is a prominent expert on Navier-Stokes, was essential to the agents’ ability to solve the Millennium Problem. Experts have long identified “research taste,” or the ability to choose promising research questions and directions, as a major obstacle for AI in science and mathematics. If the OpenAI agents did indeed choose to follow the Córdoba–Martínez-Zoroa approach because Buckmaster and Alpöge had done the same, then human research taste played an essential role in OpenAI’s success. Even so, the bigger picture here is sobering. The progress that Buckmaster and Alpöge made over almost a year of collaboration with publicly availa…
但对于数学家来说，这个版本的叙事可能有一线希望，因为它表明两名人类（其中一位是纳维-斯托克斯领域的杰出专家）的辛勤工作，对于智能体解决这一千禧年难题至关重要。专家们长期以来一直认为，“研究品味”（research taste），即选择有前景的研究问题和方向的能力，是 AI 在科学和数学领域面临的主要障碍。如果 OpenAI 的智能体确实是因为 Buckmaster 和 Alpöge 选择了 Córdoba–Martínez-Zoroa 方法而跟随了这一路径，那么人类的研究品味在 OpenAI 的成功中发挥了至关重要的作用。即便如此，从大局来看，情况依然令人清醒。Buckmaster 和 Alpöge 在近一年的合作中利用公开可用的模型所取得的进展……