OpenAI 悄然取得数学突破，引发学界寒意

OpenAI 周二宣布，它已经解决了数学界传奇性的千禧年大奖难题之一，这本应是一个值得庆祝的时刻。这一成果既是毋庸置疑的成就，也鲜明展现了AI 正在以多么迅猛的速度改变数学。但甚至在这一突破被正式宣布之前，其背后不同寻常的缘由就令事情变得复杂：在得知其他研究人员正在取得进展后，OpenAI 似乎调集了庞大资源，在最后时刻试图抢先完成这一成果。随之而来的争议引发了关于抢发成果、监视以及公然违反长期学术规范的指控。研究人员担心，这会对整个领域产生寒蝉效应。

伦敦玛丽女王大学数学教授 Abhishek Saha 表示，OpenAI 所做的是“数学家通常不会做的那类事情”。

OpenAI 在周二发布的一篇博客文章中称，其一款尚未发布的模型仅用 88 小时就找到了 Navier-Stokes 问题的解法。这个棘手问题涉及流体的运动。由于解出该问题的人可获得 100 万美元奖金，它是数学界研究最密集的问题之一；但尽管如此，它仍令人类研究人员困扰了近 90 年。OpenAI 表示，其模型通过让大约 1 万个由内部模型驱动的 AI Agent 组成群体专注于这一任务而解决了该问题，并将这一成果称为一个“里程碑”。

“如果你不想让我好好说话，那我也没必要好好说话。”

但这一公告发布的时机引起了质疑。就在前一天，纽约大学数学教授 Tristan Buckmaster 与 OpenAI 最大竞争对手 Anthropic 的研究员 Levent Alpöge，就一个相关问题发布了研究结果（不过，此处 Alpöge 并非代表其雇主开展工作）。Buckmaster 表示，在得知 OpenAI 已经获悉他们的进展后，他联系了 OpenAI，询问该公司何时开始研究这一问题，以及其模型接受过什么数据训练。他说，对话很快变味：当他表示会公开发生的事情时，一名 OpenAI 研究人员问他：“你为什么要毁掉自己的职业生涯？”Buckmaster 说，当他追问公开此事为何会毁掉职业生涯时，得到的回复是：“如果你不想让我好好说话，那我也没必要好好说话。”OpenAI 敦促 Buckmaster 改为发表这项工作，并将 OpenAI 的内部模型列为贡献者，同时将 Alpöge 从共同作者名单中移除。

Buckmaster 表示，他询问 OpenAI 是否访问过自己在解决该问题时使用的 Codex 会话，但 OpenAI 的回答变得越来越闪烁其词，甚至带有敌意。OpenAI 此后发表的声明——包括公布结果的博客文章——断然否认使用过任何特定用户数据。该公司表示：“我们（研究人员和 Agent）在他们公开发布工作之前，没有通过任何方式看到过他们的任何工作——尤其是，为解决这一问题，没有访问任何特定用户数据。”

但 OpenAI 无法明确排除间接影响的可能性。该公司表示：“尽管可能性不大，我们不能排除源自他们使用我们产品的去标识化数据曾帮助改进模型⁠的可能性。”同时，它强调两份证明存在显著差异。OpenAI 研究人员在 X 上的评论也呼应了这些否认。

究竟发生了什么，很难准确判断。时间线相互交织，研究存在重叠，而 AI 生成工作的来源即便在最佳情况下也很难、甚至不可能追溯。不同参与者竞相解决世界上最著名的数学问题之一，尤其是一个附带高额奖金的问题，也并不令人意外。

但 OpenAI 叙述中的一些部分难以解释。按照该公司自己的说法，这是一项仓促且极其昂贵的工作，耗资数百万美元。然而，该公司表示无意申领奖金；而且无论如何，负责管理该奖项的克雷数学研究所尚未授予奖金。OpenAI 称，其唯一目标是“报告我们 AI 模型取得的实质性进展”。该公司似乎在 9 月之前并未为攻克 Navier-Stokes 问题投入太多精力；即使投入过，也没有公开谈论过。

OpenAI 的解释实质上相当于一句响亮的“为什么不呢？”该公司称，它是在听闻其他研究人员正于千禧年大奖难题上取得进展的传言后，才开始研究这一问题。OpenAI 研究员 Sébastien Bubeck 在一场由 Science 报道的新闻发布会上说，这些传言来自“Twitter”。Bubeck 表示：“所以我们想，‘我们有这么强的模型，为什么不也试着解决一个千禧年大奖难题呢？’”

OpenAI 表示，它是后来才意识到这些传言指向 Alpöge 和 Buckmaster。除回应 Buckmaster 关于其数据使用情况的指控外，OpenAI 尚未公开回应他的其他说法；当 The Verge 就此寻求置评时，该公司将其导向自家博客。Buckmaster 在其叙述中点名的 Bubeck 已对其中部分内容提出异议，否认自己曾要求 Buckmaster 将 Alpöge 从共同作者名单中移除。

即便撇开最具爆炸性的指控不谈，OpenAI 已明确承认的一些行为也令数学家震惊。表面上为了抢在其他研究人员之前取得结果而仓促行动，在多数情况下并不是数学研究的惯常方式。Saha 说，抢发成果确实会发生，但并不容易。

他解释说，部分原因在于，前沿研究往往要求极深且高度专业化的专长，因此即使有人想横插一脚，真正具备这种能力的人也很少。

开放是这一学科根深蒂固的价值观。南卡罗来纳大学数学教授、数学计算机辅助推理研究所（ICARM）科学活动副主任 Matthew Ballard 表示：“数学高度依赖一种非正式的信任规范。”他说：“研究人员经常与同事分享尚不完整的想法和正在进行的工作，以打磨自己的思路。这样做的前提是，它不会演变成一场竞争。”

卡内基梅隆大学教授、同时担任 ICARM 主任的 Jeremy Avigad 表示，尽管他无法评论会话日志是否可能被访问，但即便只是“AI 系统可能从我们的查询中窃取想法这种念头，也令人不寒而栗”。数学家习惯于讨论自己的工作，而不必担心被抢发成果。他说：“如今，只要有最微小的提示，就可能足以让拥有充足计算资源的人派出一群 Agent 去解决问题，人们很可能会变得更加谨慎。想到这可能如何改变研究环境，实在令人难过。”

“数学高度依赖一种非正式的信任规范。”

OpenAI 不愿意或无法说明其模型是否受到其他数学家工作的影响，进一步加深了该领域的不安感。布朗大学教授 Brendan Hassett 告诉 The Verge：“这是一个问题。”他补充说，“考虑到 AI 公司未经许可或付费挪用受版权保护作品的历史，人们提出这些问题是很自然的。”他说，这些公司“应当有责任提供”保证，确保聊天记录不会被用于改进模型，其中包括能够证明这一点。

事态接下来究竟会如何发展，目前尚不清楚。伦敦数学科学研究所研究员 Yang-Hui He 在北京参加一场会议时写道，他担心“由大公司主导的数学过于保密”。作为一个自称“始终对 AI 持乐观态度”的人，他承认自己担忧数学可能重新回到过去那种更保密的状态——当时数学研究由美第奇家族等富裕家族的赞助所支撑。

对大多数研究人员而言，情况或许不会有太大变化。Saha 推测，像 OpenAI 及其竞争对手这样的公司，愿意花费如此巨额资金解决的高水平问题毕竟有限。“你不会指望 AI 实验室把一切资源都投入到大多数人研究的问题上，因为它们得不到足够的关注。”

关注度或许正是目的的一部分，这也可能解释了 OpenAI 为何决定追逐一个它知道与 Anthropic 研究人员有关的问题，即使该研究人员当时是独立行动。牛津大学教授 Andras Juhasz 表示：“这显然是 OpenAI 的一次公关胜利。”

但 Juhasz 质疑这种做法能持续多久，并想知道，如今模型已经能够处理一些最重大的问题，这是否可能预示着 AI 公司参与研究数学的终结。人类数学家也会互相抢发成果，他说；但 OpenAI 的做法显示，这种事可以在大得多的规模上发生。“突然之间，1 万名数学家扑向你的问题。”他说。

所有这些都可能让 OpenAI 的公关胜利变成一场得不偿失的胜利。该公司再次证明其模型能够在数学最前沿竞争。但在此过程中，它似乎疏远了那个它一直试图打动的群体。

OpenAI’s announcement Tuesday that it has solved one of mathematics’ legendary Millennium Prize problems should have been a moment of triumph. The result is both an undeniable achievement and a striking demonstration of just how rapidly AI is transforming mathematics. But before it was even formally announced, the breakthrough had been complicated by the unusual circumstances that prompted OpenAI to pursue the problem: After hearing other researchers were making progress, it seems to have thrown its considerable resources into a last-minute effort to beat them to the punch. The ensuing controversy has surfaced allegations of scooping, spying, and flagrant violations of long-standing academic norms that researchers fear could have a chilling effect on the field.

As Abhishek Saha, a mathematics professor at Queen Mary University of London, explains it, OpenAI has engaged in the “kind of things that mathematicians will generally not do.”

In a blog post published Tuesday, OpenAI said it took one of its unreleased models just 88 hours to find a solution to the Navier-Stokes problem, a thorny quandary concerning the movement of fluids. On account of the $1 million bounty available for whoever solves it, the problem is among mathematics’ most heavily researched, but it has nevertheless stumped human researchers for close to 90 years. OpenAI said its model solved the problem by focusing a swarm of roughly 10,000 AI agents powered by its internal model on the task and hailed the achievement as a “milestone.”

“If you don’t want me to be nice, then I don’t have to be nice.”

But the timing of the announcement has raised eyebrows. Just one day earlier, New York University mathematics professor Tristan Buckmaster published findings on a related problem with Levent Alpöge, a researcher at OpenAI’s archrival Anthropic (although Alpöge was not, here, working on behalf of his employer). Buckmaster said he contacted OpenAI after learning the company had become aware of their progress, to ask when it began working on the problem and what data its model had been trained on. The conversation, he said, quickly turned sour, with an OpenAI researcher asking him, “Why would you ruin your career?” when he said he would go public with what happened. When he asked why going public would ruin his career, Buckmaster said he received the following reply: “If you don’t want me to be nice, then I don’t have to be nice.” OpenAI urged Buckmaster to instead publish the work and credit OpenAI’s internal model, dropping Alpöge as coauthor.

Buckmaster said he asked OpenAI whether it had accessed his sessions on Codex, which he had used while tackling the problem, but that OpenAI grew increasingly evasive, even hostile, in its responses. In statements since, including the blog post announcing the result, OpenAI has flatly denied using any specific user data. “We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem,” the company said.

But OpenAI could not conclusively rule out an indirect influence. “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models⁠,” it said, while stressing that the two proofs differ significantly. Comments from OpenAI researchers on X echo those denials.

It is difficult to say exactly what happened. Timelines are tangled, research overlaps, and the provenance of AI-generated work is tough, if not impossible, to identify at the best of times. And it’s hardly a surprise that different players might compete to solve one of the most famous mathematical problems in the world, particularly one attached to a hefty prize.

But aspects of OpenAI’s account are hard to explain. By the company’s own telling, the effort was a hurried and incredibly expensive affair, costing it millions of dollars. Yet the company says it has no intention of claiming the bounty, which, in any case, has yet to be awarded by the Clay Mathematics Institute, which administers it. It said its only goal “is to report on the substantial progress of our AI models.” The company does not appear to have expended much effort on tackling Navier-Stokes before September, or if it has, it hasn’t spoken about it publicly.

OpenAI’s explanation effectively amounts to a thunderous “Why not?” The company said it began working on the problem after hearing rumors that other researchers were making progress on Millennium Prize problems. It found those rumors “on Twitter,” said OpenAI researcher Sébastien Bubeck at a press briefing reported on by Science. “So we thought to ourselves: ‘We have such a strong model. Why don’t we try to solve also a Millennium Prize problem?’” Bubeck said.

OpenAI said it only later realized the rumors concerned Alpöge and Buckmaster. Beyond addressing Buckmaster’s allegations about the use of his data, OpenAI has not publicly responded to his other claims and directed The Verge to its blog when asked for comment. Bubeck, who Buckmaster named in his account, has disputed parts of it, denying he ever asked Buckmaster to remove Alpöge as coauthor.

Even setting aside the most explosive allegations, aspects of OpenAI’s conduct the company has plainly acknowledged have shocked mathematicians. The apparent rush to beat other researchers to a result is simply not how mathematics is done in most cases. Scooping does happen, but it’s not easy, said Saha.

That’s partly because cutting-edge research often requires such deep and specialized expertise that few people are in a position to swoop in even if they wanted to, he explained.

Openness is a deeply embedded virtue in the discipline. “Mathematics depends heavily on an informal norm of trust,” said Matthew Ballard, a professor of mathematics at the University of South Carolina and associate director for scientific activities at the Institute for Computer-Aided Reasoning in Mathematics (ICARM). “Researchers routinely share incomplete ideas and ongoing work with colleagues to sharpen their thoughts. It is done with the expectation that it will not turn into a competition,” he said.

Though unable to comment on whether conversation logs might have been accessed, Carnegie Mellon professor Jeremy Avigad, who is also the director of ICARM, said that even “the thought that AI systems might steal ideas from our queries is chilling.” Mathematicians are accustomed to talking about their work without worrying about being scooped. “Now that even the slightest hint might be enough for someone with sufficient computational resources to set a swarm of agents on solving the problem, people are likely to be more cautious. It’s sad to think about how that might change the research environment.”

“Mathematics depends heavily on an informal norm of trust.”

OpenAI’s unwillingness or inability to say whether its models were informed by the work of other mathematicians compounds the sense of unease in the field. “That is a problem,” Brown University professor Brendan Hassett told The Verge, adding that “given the history of the AI companies appropriating copyrighted work without permission or payment, it is natural for people to ask these questions.” He said companies “should be held accountable to deliver” assurances that chat logs will not be used to improve their models. That includes being able to demonstrate that.

It’s unclear where exactly things go from here. Writing from a conference in Beijing, Yang-Hui He, a fellow at the London Institute for Mathematical Sciences, said he worries that “maths under the big companies is much too secretive.” As someone who says he is “always optimistic about AI,” he admits he is worried mathematics could be reverting to a more secretive state like in the past, when it was funded by patronage from wealthy families like the Medicis.

For most researchers, things may not change that much. There are only so many high-caliber problems companies like OpenAI and its rivals would be willing to spend such vast sums solving, Saha speculated. “You would not expect the AI labs to throw everything at most problems people work on because they just won’t get enough publicity.”

Publicity may have been part of the point, which could help explain why OpenAI decided to race after a problem it knew was connected to a researcher at Anthropic, even if he was acting independently. “This is clearly a PR victory for OpenAI,” said Oxford professor Andras Juhasz.

But Juhasz questioned how sustainable that approach could be, wondering whether this might spell the beginning of the end for AI companies’ involvement in research mathematics now that models can tackle some of the biggest problems. Human mathematicians scoop one another, too, he said, though what OpenAI did has shown that this can happen on a much grander scale. “Suddenly, 10,000 mathematicians jump on your problem,” he said.

All that could make OpenAI’s PR victory a Pyrrhic one. The company has, once again, proven that its models can compete at the very frontier of mathematics. In doing so, it appears to have alienated the very community it has been trying to impress.

Follow topics and authors from this story to see more like this in your personalized homepage feed and to receive email updates.

• Robert Hart

• AI

• OpenAI