Navier-Stokes – Tristan Buckmaster [pdf]
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Tristan 和 Levent Alpoge 发布了三项重要成果，证明了 incompressible porous media equation 、 Boussinesq equations 和 3D incompressible Euler equations 出现 finite-time blowup 的例子。研究通过引入 smooth forcing 实现，所用策略继承并发展了 Diego Córdoba 与 Luis Martínez-Zoroa 最初提出的核心思想。作者们强调，这是一项纯粹的个人合作，独立于他们各自的机构，并在很大程度上依赖多种大型语言模型（包括 Claude 、 Codex 和 Astra）来推进 Córdoba-Martínez-Zoroa program 的完成。
借助 AI 完成这些证明的过程漫长且充满挑战。大部分时间进展缓慢，直到八月中旬出现突破，最终又用 Lean proof assistant 对结果进行了验证。尽管在数学上取得了成功，作者对在巨大压力下发布的预印本的呈现质量表示遗憾。他们认为，这项工作的真正意义在于展现了人在压缩时间内与 AI 协同开展高水平数学研究的可能性——这一点值得学界就培训、署名和人类注意力在科研中的价值等问题进行深入而冷静的讨论。
关于与 OpenAI 的接触，叙述出现了令人不安的转折。据传一款内部 OpenAI 模型也解决了一个重大悬而未决的问题——尤其是 Navier-Stokes 的 forced blowup——Tristan 因此与包括 Sebastien Bubeck 在内的 OpenAI 代表进行了交流。对话中透露，OpenAI 有一个完整团队在攻关，投入了大量算力，而且该内部模型的成果并非像最初所暗示的那样仅靠极少的人为干预。此外，该模型成功的时间点似乎与外界流传的关于作者自身进展的消息相吻合。
讨论中有人建议作者将 Euler 的结果与 OpenAI 关于 Navier-Stokes 证明的公告同时发布，甚至提出因 Levent 在 Anthropic 工作而将其从作者名单中移除。作者拒绝这些提议后，局势变得紧张，并出现可能影响他们职业声誉的暗示性言辞。
作者强调他们并未指控任何具体的不当行为，因为他们并未见过 OpenAI 的证明，也不清楚自己的数据是否被使用。公开此事的目的是维护历史记录的准确性，防止错误叙述流布。研究人员希望将讨论重心重新拉回到数学本身，以及这些工具对更广泛学术界可能带来的变革性影响。
Tristan and Levent Alpoge have released three significant mathematical results concerning finite-time blowup for the incompressible porous media equation, the Boussinesq equations, and the 3D incompressible Euler equations. These findings were achieved using smooth forcing, a strategy building upon foundational ideas originally proposed by Diego Córdoba and Luis Martínez-Zoroa. The researchers highlight that this work was a purely personal collaboration, independent of their respective institutional affiliations, and relied heavily on the use of various large language models, including Claude, Codex, and Astra, to push the Córdoba-Martínez-Zoroa program to completion.
The process of utilizing AI for these proofs was lengthy and challenging. Progress remained slow for much of the year until a breakthrough occurred in mid-August, leading to the verification of the results via the Lean proof assistant. Despite the mathematical success, the authors express regret regarding the presentation quality of their preprints, which were produced under significant pressure. They emphasize that the true significance of this endeavor lies in the capability for humans and AI models to collaborate on high-level mathematical research in a compressed timeframe, a development that warrants a deep, unhurried discussion within the scientific community regarding the future of training, credit, and the value of human attention in research.
The narrative takes a troubling turn regarding interactions with OpenAI. Following rumors that an internal OpenAI model had also solved a major open problem—specifically, forced blowup for Navier-Stokes—Tristan engaged in discussions with representatives from the company, including Sebastien Bubeck. During these conversations, it was revealed that an entire team at OpenAI had been working on the problem, that significant compute resources were deployed, and that the internal model's effort was not the result of minimal human input as initially suggested. Furthermore, the timing of the model's success appeared to coincide with the circulation of news regarding the authors' own progress.
During these discussions, proposals were made to the authors, including suggestions that they post their Euler results alongside an OpenAI announcement of the Navier-Stokes proof, and that Levent be removed from authorship due to his employment at Anthropic. When these offers were declined, the situation grew contentious, with implications made regarding the authors' professional reputations.
The authors maintain that they are not accusing anyone of specific wrongdoing, as they have not seen OpenAI's proof and do not know if their own data was utilized. The purpose of coming forward is to ensure that the historical record remains accurate and to prevent false narratives from taking hold. Ultimately, the researchers express a desire to shift the conversation back toward the mathematics and the transformative potential of these tools for the wider academic community.
829 comments • Comments Link
- 数学家 Tristan Buckmaster 声称 OpenAI 向他施压，要求配合安排一项与 Navier-Stokes 相关重大突破的发表时间，并试图排除他那位就职于 Anthropic 的合作者的署名权。
- 局势升级：据称一名 OpenAI 代表在回应 Tristan Buckmaster 的公开威胁时采取恐吓口吻，质问他为何要"毁掉自己的职业生涯"，并暗示他们不必再对他"客气"。
- 对 OpenAI 流程的质疑主要集中在时间线上：研究团队是在听闻外部研究者取得进展的传言后才转向这一特定数学方法，且后来承认动用了庞大团队和大量算力，这与最初声称仅投入极少人力的说法相矛盾。
- 一个核心担忧是，上传到 AI 工具的敏感研究草稿是否被用于训练或作为查询来源来辅助 OpenAI 内部研发；若属实，这将严重破坏用户信任与职业伦理。
- 有人认为 OpenAI 的竞争手段以及可能利用专有用户工作流进行训练的做法，在大型科技公司中属于常见的激进策略；但也有人坚持，诸如此类的行为从根本上削弱了科学进步所依赖的协作精神。
- 持怀疑态度者提醒不要把单方面陈述当成定论，并指出目前没有确凿证据表明 OpenAI 访问了私有的 Codex 会话数据。
- 这场讨论凸显出对转向"黑箱"式科学发现的日益不安：在这种模式下，突破越来越被视为依靠大量算力的蛮力尝试和模型自动引导的产物，而非源自人类洞察。
- 为 OpenAI 辩护的人认为，模型是基于现有已发表文献独立识别出有前景的研究路径，他们联系 Tristan Buckmaster 可能只是为了公平分配署名，而非恶意抢占成果。
- 观察者指出，这起事件反映了人类直觉与机器驱动发现之间的历史性紧张关系，比如著名的 Kasparov-IBM 对弈，预示着学术界在署名权问题上进入一个充满冲突的新阶段。
- 训练数据缺乏透明度，加之服务条款措辞含糊，让许多用户感觉自己的知识贡献正被用来训练最终可能取代他们的系统。
此事反映了学术野心、高风险企业竞争与 AI 辅助研究进化伦理之间不稳定的交汇。纠纷凸显了精英研究者与 AI 公司之间深刻的信任缺失，源自对大型语言模型被用来"监视"和"挖掘"私人研究突破的担忧。尽管技术细节仍需争论与核实，但总体观点指向一种系统性忧虑：随着前沿模型能力不断提升，"辅助发现"与"知识窃取"之间的界限正变得危险地模糊。归根结底，这场冲突提出了一个关于科学署名权未来的存在性问题：在机器算力往往成为解决棘手问题的决定性因素的时代，我们应如何重新界定署名权？ • Mathematician Tristan Buckmaster alleges that OpenAI pressured him to coordinate on a publication timeline for a Navier-Stokes-related breakthrough, while simultaneously attempting to exclude his collaborator, who is an Anthropic employee, from shared credit.
• The tension escalated when an OpenAI representative allegedly responded to Buckmaster's threat of going public with intimidation, questioning why he would "ruin his career" and suggesting they did not have to remain "nice."
• Suspicion regarding OpenAI's process centers on the timeline: the research team only pivoted to this specific mathematical approach after rumors of the external researchers' progress reached them, and they later admitted the use of a large team and significant compute, contradicting initial claims of minimal human input.
• A central concern is whether sensitive research drafts uploaded to AI tools were used for "training" or "lookups" to inform OpenAI's own internal development, an action that would represent a significant breach of user trust and professional ethics.
• While some argue that OpenAI's competitive behavior and potential use of proprietary user workflows for training are standard, aggressive practices in Big Tech, others maintain that such actions fundamentally undermine the collaborative nature of scientific advancement.
• Skeptics of the allegations caution against accepting a one-sided account as absolute fact, noting that no definitive proof exists of OpenAI accessing private Codex session data.
• The discourse highlights a growing discomfort with the shift toward "black box" scientific discovery, where breakthroughs are increasingly viewed as a function of brute-forcing compute and automated model steering rather than human insight.
• Defenses of OpenAI suggest that these models independently identify promising research paths through existing published literature, and that their reaching out to Buckmaster may have been a genuine attempt at fair credit assignment rather than a hostile takeover of the discovery.
• Observers note that the incident mirrors historical tensions between human intuition and machine-driven discovery, such as the famous Kasparov-IBM match, signaling a new era of conflict over authorship in academia.
• The lack of transparency regarding training data and the "weaselly" nature of terms of service leave many users feeling that their intellectual contributions are being harvested to train systems that may eventually displace them.
The incident reflects a volatile intersection of academic ambition, high-stakes corporate competition, and the evolving ethics of AI-assisted research. The dispute underscores a profound loss of trust between elite researchers and AI firms, driven by fears that large language models are being used to "surveil" and "farm" private breakthroughs. While the technical specifics remain debated and unverified, the overwhelming sentiment points to a systemic concern: as frontier models become increasingly capable, the boundary between "assisted discovery" and "intellectual theft" is becoming dangerously blurred. Ultimately, the conflict raises existential questions about the future of human scientific credit in an age where machine compute is often the decisive factor in solving intractable problems.