OpenAI 的数学研究团队宣布，其指导的约一万个自主人工智慧代理在先进模型上运行，成功证明了三维纳维-斯托克斯方程式（Navier-Stokes equations）可能出现「奇异点」（即解产生爆炸），从而解决了克雷数学研究所设立的百万美元千禧年大奖难题之一，并已透过 Lean 程式语言完成形式化验证。（关键数字：10,000, 3）

此项突破的核心理论奠基于数学家迭戈·科尔多瓦（Diego Córdoba）与路易斯·马丁内斯-佐罗亚（Luis Martínez-Zoroa）开创的分析方法；他们透过构建无限层级解的串联来寻找奇异点，而 AI 团队则成功克服了维持外力函数平滑性的最后关键瓶颈，揭示出流体在理想模型下极度反直觉的奇异点行为。

在此成果公布的同时，纽约大学的崔斯坦·巴克马斯特（Tristan Buckmaster）与 Anthropic 的莱文特·阿尔珀格（Levent Alpöge）亦宣布利用多种 AI 模型解决了尤拉方程式等相关问题，引发两团队间关于研究优先权及是否涉及成果外泄的激烈竞争与争议，同时也确立了 AI 正式成为攻克顶尖数学难题的关键力量。

Mathematicians at OpenAI announced that approximately 10,000 autonomous AI agents running on an advanced internal model discovered a singularity in the 3D Navier-Stokes equations, resolving one of the Clay Mathematics Institute's million-dollar Millennium Prize Problems with formal verification in Lean.

The breakthrough heavily relied on pioneering analytical frameworks established by Diego Córdoba and Luis Martínez-Zoroa, who used an infinite cascade of solution layers to induce blowups, enabling AI systems to successfully construct a singular solution while maintaining smooth forcing functions.

The announcement coincided with parallel breakthroughs on Euler equations by Tristan Buckmaster and Levent Alpöge using AI models, sparking intense competition, priority debates, and controversy over intellectual timelines, while marking a monumental turning point for artificial intelligence in advanced mathematics.