CADE METZ2026年9月9日纳维-斯托克斯存在性与光滑性问题与一组流体力学方程相关，长期以来一直被视为数学领域中尚未解决的重大难题之一。 Philippe Plailly/Science SourceOpenAI said on Tuesday that its newest artificial intelligence technology had solved one of the “Millennium Problems,” a collection of important unanswered math questions meant to push the world’s leading mathematicians to new heights.OpenAI周二表示，其最新的人工智能技术解开了一道“千禧年大奖难题”。这是一组重要的未解数学难题，旨在推动世界顶尖数学家迈向新的高度。The announcement is another clear sign that A.I. is fundamentally changing the upper reaches of mathematics, which have long been viewed as a pinnacle of human achievement. The change has excited some mathematicians, while stirring concern among others.这一声明再次清晰地表明，人工智能正在从根本上改变数学的最高领域，该领域长期以来被视为人类成就的巅峰。这一变化让一些数学家感到振奋，同时也引发了另一些人的担忧。Over the past year, A.I. systems successfully solved a wide range of problems that have bedeviled mathematicians for decades. But these problems were not as complex, nor as closely watched, as the one that OpenAI’s technology has solved over the past several days. The Millennium Problems are among the most heavily researched in the field.过去一年里，人工智能系统成功解决了一系列困扰数学家数十年的难题。但这些难题的复杂程度和受关注程度都不及OpenAI技术在过去几天里解决的那一个。千禧年大奖难题是该领域研究最为密集的课题。“This is a spectacular culmination of the arc we have seen over the past twelve months,” OpenAI researcher Sébastien Bubeck said of the company’s new solution.“这是我们过去12个月所看到的发展轨迹的一个壮观顶点，”OpenAI研究员塞巴斯蒂安·布贝克在谈到该公司的新解法时说。The company announced that one of its latest models, which has not yet been released to the public, needed just 88 hours to solve what mathematicians call “the Navier–Stokes existence and smoothness problem.” This problem involves a series of equations that are often used to predict the weather.该公司宣布，其尚未向公众发布的最新模型之一仅用88小时就解决了数学家所称的“纳维-斯托克斯存在性与光滑性问题”。这个问题涉及一组常用于预测天气的方程。The equations describe the movement of water and other fluids. The Navier-Stokes problem, which has no clear practical value, asks whether these equations completely break down in certain situations. OpenAI’s proof claims to have defined just such a situation.这些方程描述水和其他流体的运动。纳维-斯托克斯难题没有明确的实用价值，它探讨的是这些方程在某些情况下是否会完全失效。OpenAI的证明声称已经定义了这样一种情况。This would imply, at least theoretically, that the laws of physics themselves would break down under certain conditions: that, for example, water could be made to spontaneously explode. But mathematicians and physicists do not believe that this mathematical breakdown could really lead to such an outcome in the physical world.这意味着，至少在理论上，物理定律本身在某些条件下会失效：例如，水可能被引发自行爆破。但数学家和物理学家并不认为这种数学上的失效真的会在物理世界中导致这样的结果。The Navier-Stokes problem was one of seven “Millennium Problems” selected by the Clay Mathematics Institute in the year 2000 as a way of tracking the progress of mathematics in the new millennium. The institute, founded by an American businessman named Landon T. Clay, offered a million dollars for the first correct solution to each problem. Before OpenAI’s announcement, only one of the problems had been solved.纳维-斯托克斯难题是克莱数学研究所在2000年选定的七个“千禧年大奖难题”之一，目的是追踪数学在新千年的进展。该研究所由美国商人兰登·克莱创立，为每个难题的首个正确解答提供100万美元奖金。在OpenAI宣布之前，七个难题中只有一个被解决。OpenAI研究员塞巴斯蒂安·布贝克。 Meron Tekie Menghistab for The New York Times“These questions are lighthouses,” said Terence Tao, a professor at the University of California, Los Angeles, who is regarded by many as the finest mathematician of his generation. “They are great focus points that attract the efforts of human scientists.”“这些难题是灯塔，”加州大学洛杉矶分校教授陶哲轩说。他被许多人视为同代人中最杰出的数学家。“它们是吸引人类科学家努力的绝佳焦点。”Dr. Tao is among the many mathematicians who have publicly warned that the latest A.I. systems could end up damaging the field of mathematics. If A.I. technologies can solve the most difficult problems with little input from human mathematicians, he says, they could weaken human understanding of the field.陶哲轩是众多公开警告最新人工智能系统可能最终损害数学领域的数学家之一。他说，如果人工智能技术几乎不需要人类数学家的参与就能解决难度最大的问题，它们可能会削弱人类对这一领域的理解。“The effort needed to solve problems is often very instructive. It teaches you something. It’s like going to the gym and having a goal to lift a weight a hundred times,” he explained. “Now, A.I. can solve questions without really getting any value out of them. It’s like having machines that can lift weights for you at the gym.”“解决难题所需的努力往往非常有教育意义。它能教会你一些东西。就像去健身房，设定一个举重一百次的目标，”他解释道。“现在，人工智能可以解决难题，却无法从中真正获得任何价值。这就像在健身房里有机器代替你举重一样。”But as he and others point out, mathematicians still provide a helping hand as A.I. systems work through these problems. OpenAI said that it deployed vast teams of “A.I. agents” to solve the Navier-Stokes problem and that its researchers passed key ideas between these teams.但正如他和其他人所指出的，在人工智能系统处理这些难题时，数学家仍然提供了帮助。OpenAI表示，它部署了庞大的“AI智能体”团队来解决纳维-斯托克斯难题，其研究人员在这些团队之间传递关键想法。“Our role was like a bumble bee cross-pollinating across different groups and delivering different bits of information,” said OpenAI researcher Dan Roberts.“我们的角色就像一只大黄蜂，在不同群体之间交叉授粉，传递不同的信息片段，”OpenAI研究员丹·罗伯茨说。Companies like OpenAI build their A.I. technologies using what scientists call neural networks, systems that learn skills by analyzing vast amounts of digital data. About two years ago, such companies started to hone these systems using another technique called reinforcement learning. Through this process, A.I. systems can learn additional behavior through extensive trial and error.像OpenAI这样的公司使用科学家所称的神经网络来构建其人工智能技术，这些系统通过分析海量数字数据来学习技能。大约两年前，这类公司开始使用另一种名为强化学习的技术来完善这些系统。通过这一过程，人工智能系统可以通过大量的试错来学习额外的行为。By working through thousands of math problems, for instance, they can learn which methods lead to the right answer and which do not. Researchers inside labs like OpenAI develop complex feedback mechanisms that show the system when it has done something right and when it has done something wrong.例如，通过处理数千道数学题，它们可以了解哪些方法能得出正确答案，哪些不能。OpenAI等实验室的内部研究人员开发了复杂的反馈机制，让系统知道什么时候做对了，什么时候做错了。(The New York Times has sued OpenAI and Microsoft, claiming copyright infringement of news content related to A.I. systems. The two companies have denied the suit’s claims.)（《纽约时报》已起诉OpenAI和微软，指控其人工智能系统侵犯了新闻内容的版权。两家公司否认了相关指控。）Reinforcement learning is difficult to perfect in areas like creative writing, philosophy and ethics, where the question of which answers are right or wrong is hard to define objectively. But the technique is ideally suited to mathematics.强化学习在创意写作、哲学和伦理等领域难以完善，因为在这些领域，哪些答案是对是错很难客观定义。但这项技术非常适合数学领域。Through this process, A.I. systems can learn to prove mathematical theorems using a computer programming language called Lean. The language was originally designed as a tool for human mathematicians. But now that A.I. systems are skillful enough to generate their own computer code, they, too, can use Lean to generate their own math proofs.通过这一过程，人工智能系统可以学会使用一种名为Lean的计算机编程语言来证明数学定理。该语言最初是为人类数学家的工具而设计的。但现在，既然人工智能系统已经足够熟练，能够生成自己的计算机代码，它们也可以使用Lean来生成自己的数学证明。OpenAI said that it solved the Navier-Stokes problem using as many as 10,000 “A.I. agents” working in concert. Running such a large number of A.I. systems is likely to have cost millions of dollars, a result of the enormous amounts of electrical power needed to operate the specialized chips that drive A.I. technologies.OpenAI表示，它使用多达1万个协同工作的“AI智能体”解决了纳维-斯托克斯难题。运行如此大量的人工智能系统很可能花费了数百万美元，这是因为驱动人工智能技术的专用芯片需要消耗大量电力。OpenAI research scientist Noam Brown called this a “very expensive process,” before adding that the costs of running A.I. technologies tend to drop as companies like OpenAI improve their efficiency.OpenAI研究科学家诺姆·布朗称这是一个“非常昂贵的过程”，但他补充说，随着OpenAI等公司提高效率，运行人工智能技术的成本往往会下降。On Tuesday, the company released a paper describing its solution, including a Lean proof, allowing outside mathematicians to see how its agents cracked the problem. But to Dr. Tao, it is still a poor substitute for humans solving the problem on their own. He compared OpenAI to a wilderness guide who finds a path to a hidden waterfall.周二，该公司发布了一篇论文，描述了其解决方案，包括Lean证明，让外部数学家得以了解其智能体是如何攻克这一难题的。但对陶哲轩博士来说，这仍然无法替代人类自己解决问题。他将OpenAI比作一位找到通往隐秘瀑布之路的野外向导。“This has some value,” he said. “But once someone shows a specific path to the waterfall, people just take that path. They don’t spend as much time looking for other paths.”“这有一定价值，”他说。“但一旦有人展示了一条通往瀑布的特定路径，人们就会直接走那条路。他们不会花那么多时间寻找其他路径。”Cade Metz是时报记者，撰写有关人工智能、无人驾驶汽车、机器人、虚拟现实和其他新兴技术领域的报道。翻译：晋其角、杜然点击查看本文英文版。