“I’m Really Terrified”: A Mathematician Grapples With AI’s Recent Breakthroughs

“我真的感到恐惧”：一位数学家对人工智能近期突破的深思

Mathematician and author Steven Strogatz starts to cry when he talks about the artificial-intelligence-driven breakthroughs in his field over the past week. “The science is thrilling,” the Cornell University professor says, “but there’s a lot of human unpleasantness going with it.” 数学家兼作家史蒂文·斯特罗加茨（Steven Strogatz）在谈到过去一周其领域内由人工智能驱动的突破时，不禁潸然泪下。这位康奈尔大学教授表示：“科学进展令人振奋，但随之而来的还有许多令人不快的人际纠纷。”

On Tuesday, OpenAI said it had used tens of thousands of agents to solve a 90-year-old math problem, which had a $1 million prize attached. The solution—which still needs to be independently verified—builds on a strategy developed by Spanish mathematicians Diego Córdoba and Luis Martínez-Zoroa. The announcement was marred by claims from another mathematician, Tristan Buckmaster, who says that OpenAI rushed ahead to solve the problem after learning of his work alongside Anthropic researcher Levent Alpöge. Buckmaster claims OpenAI also tried to influence who got credit for the work. 周二，OpenAI 宣布利用数万个智能体解决了一个困扰数学界 90 年的问题，该问题悬赏 100 万美元。这一解决方案（仍需独立验证）建立在西班牙数学家迭戈·科尔多瓦（Diego Córdoba）和路易斯·马丁内斯-佐罗亚（Luis Martínez-Zoroa）开发的策略之上。然而，这一声明因另一位数学家特里斯坦·巴克马斯特（Tristan Buckmaster）的指控而蒙上阴影。巴克马斯特称，OpenAI 在得知他与 Anthropic 研究员莱文特·阿尔珀格（Levent Alpöge）的研究成果后，抢先一步解决了该问题。巴克马斯特还声称，OpenAI 试图干预该研究成果的署名权归属。

The rupture is a symptom of the rapid changes taking place in the field due to AI advancements and what Strogatz—who cowrote Big Math, a book about how math is slipping away from human understanding that will be out in November—describes as corporate labs’ race to grab headlines ahead of blockbuster IPOs. 这种裂痕是人工智能进步导致该领域发生剧烈变化的缩影。斯特罗加茨即将于 11 月出版新书《大数学》（Big Math），书中探讨了数学如何逐渐脱离人类的理解范畴。他将当前的乱象描述为企业实验室为了在重磅 IPO 前抢占头条而展开的竞赛。

Last week, Anthropic said Claude had proved 29,500 small theorems while formalizing an existing proof of the infamous Fermat’s Last Theorem—a project other mathematicians had been working on for years. In August, OpenAI announced it had made advancements in 10 other long-standing mathematical problems. AI is making mathematical breakthroughs happen faster, Strogatz says, but what it means for the experts who have dedicated their lives to the field is decidedly less clear. 上周，Anthropic 表示其 AI 模型 Claude 在形式化证明著名的“费马大定理”的过程中，顺带证明了 29,500 个小定理——而其他数学家为这一项目已经努力了多年。8 月，OpenAI 宣布在另外 10 个长期未解的数学难题上取得了进展。斯特罗加茨认为，人工智能正在加速数学突破的进程，但对于那些毕生致力于该领域的专家而言，这意味着什么，目前尚不明朗。

“I think the year 2026 is going to be remembered as either an annus mirabilis or annus horribilis for mathematics because so much has happened,” Strogatz tells WIRED, sitting in front of a wall covered in framed university honors. “You will not be able to compete without AI in the future if you want to do breakthrough math,” he adds. “我认为 2026 年将被铭记为数学界的‘奇迹之年’或‘灾难之年’，因为发生了太多的事情，”斯特罗加茨坐在挂满大学荣誉证书的墙前对《连线》（WIRED）杂志说道。“未来，如果你想在数学领域取得突破，没有人工智能将无法参与竞争，”他补充道。

His book collaborator, Alex Townsend, has already been using the technology to accelerate their research. He recently used ChatGPT to help solve a decades-old numerical linear algebra problem. Toward the end of the interview, Townsend walks into Strogatz’s attic. Townsend and his coauthor said that without the technology, the volume of work required and cost-reward ratio would have been unfeasibly high. But while AI has helped his work, it’s also changing how Townsend views the field and his role in it. 他的书籍合著者亚历克斯·汤森德（Alex Townsend）已经开始利用这项技术加速他们的研究。他最近利用 ChatGPT 解决了一个困扰数值线性代数领域数十年的问题。采访临近结束时，汤森德走进了斯特罗加茨的阁楼。汤森德及其合著者表示，如果没有这项技术，所需的工作量以及成本收益比将高到无法实现。虽然人工智能助力了他的工作，但也改变了汤森德对该领域及其自身角色的看法。

“I actually feel kind of upset that I’ve dedicated 15 years of my life to research mathematics, and at a point in my career where I’m very productive and at my peak strength as a mathematician, that peak skill is no longer there. Something is able to surpass me,” he says. “Before, it was so exciting because you’re world-class, doing great research, pushing back the frontier of knowledge, and now I don’t feel like I’m the one at the frontier of knowledge. I’m the one with an AI agent, which feels very different actually. And I feel totally threatened by it.” “我感到很难过，我投入了 15 年的生命去研究数学，正处于职业生涯的高产期，作为数学家的能力也达到了巅峰，但现在这种巅峰技能却不再是独有的了。有东西能够超越我，”他说。“以前，这非常令人兴奋，因为你是世界级的，在做伟大的研究，在拓展知识的边界。而现在，我不觉得我是那个站在知识前沿的人。我只是一个带着 AI 智能体的操作者，这感觉完全不同。我感到自己受到了彻底的威胁。”

For his part, Strogatz likens the current moment for math to a horror movie, as AI, driven by systems that are not well understood, creeps closer and closer. “But we’re not at the end of the movie yet,” Strogatz says. “Instinctively, I’m really terrified.” 就斯特罗加茨而言，他将数学当前的处境比作一部恐怖电影，因为由人类尚未完全理解的系统所驱动的人工智能，正一步步逼近。“但电影还没到结局，”斯特罗加茨说，“出于本能，我真的感到恐惧。”

---

On the significance of solving the Navier-Stokes existence and smoothness problem:

关于解决纳维-斯托克斯（Navier-Stokes）存在性与光滑性问题的意义：

It’s a very theoretical math problem of essentially no interest to a working engineer in civil engineering or aerodynamics. It’s a very, very arcane question. This is a marketing device for them to prove how good their machines are. Nobody cares about the Navier-Stokes singularity problem; only a tiny subset of pure mathematicians care about that. It doesn’t affect anybody except it’s maybe worth a trillion dollars for OpenAI to show they’re better than Anthropic. 这是一个非常理论化的数学问题，对土木工程或空气动力学的在职工程师来说基本没有意义。这是一个非常、非常晦涩的问题。这对他们来说是一种营销手段，用来证明他们的机器有多强大。没人关心纳维-斯托克斯奇点问题；只有极少数纯数学家关心。它不会影响任何人，除了对 OpenAI 来说，证明他们比 Anthropic 更强可能价值万亿美元。

On who deserves the credit for solving the problem, and the million-dollar prize:

关于谁应该获得解决该问题的功劳以及百万美元奖金：

I would love to see Córdoba and Martínez-Zoroa get the money, but let’s be careful here because there’s another pair of people who should be talked about, who are Tristan Buckmaster at New York University and a young mathematician named Levent Alpöge. Arguably, you could say Buckmaster should get the money because Buckmaster posted a couple of days before OpenAI with Levent the solution to three very closely related problems to the Navier-Stokes. They’re slightly easier cases, but they are very serious, important problems in their own right. They were on the trail, and I think they would’ve gotten there, but we don’t know. 我很高兴看到科尔多瓦和马丁内斯-佐罗亚拿到奖金，但我们要谨慎，因为还有另外两个人值得一提，那就是纽约大学的特里斯坦·巴克马斯特和一位名叫莱文特·阿尔珀格的年轻数学家。可以说，巴克马斯特也应该获得奖金，因为他在 OpenAI 发布之前几天，就与阿尔珀格一起发布了三个与纳维-斯托克斯问题密切相关的解决方案。虽然这些情况稍微简单一些，但它们本身就是非常严肃且重要的数学问题。他们当时已经走在正确的道路上，我认为他们本可以解决这个问题，但我们不得而知。

I don’t know Buckmaster, but from what I can see, he is very scrupulous about giving credit. He’s being a real gentleman about it. I have a lot of respect for how he’s been handling it. I feel bad for him that he’s not going to end up getting what he’s devoted his career to. 我不认识巴克马斯特，但从我所见来看，他在署名权问题上非常严谨。他表现得非常有绅士风度。我非常尊重他处理这件事的方式。我为他感到难过，因为他最终可能无法获得他毕生致力于追求的成果。

On whether AI still needs human mathematicians:

关于人工智能是否仍然需要人类数学家：

We need proof digestion, which is explaining it in terms that human beings can understand and appreciate. Right now, the best digestion is still coming from human experts. Is that where we make our last stand? Are we going to be the great interpreters of the things that the machines do? I suspect that will be our role for a little while longer, that we will have that special skill of translating, though I do expect that will be surpassed by machines soon enough, too. 我们需要“证明消化”（proof digestion），即用人类能够理解和欣赏的方式来解释证明过程。目前，最好的“消化”工作仍然来自人类专家。这是我们最后的阵地吗？我们将成为机器所作所为的伟大诠释者吗？我怀疑这在未来一段时间内仍将是我们的角色，我们将拥有这种翻译的特殊技能，尽管我预计这很快也会被机器超越。

Applied math is messy because it deals with the real world. The messier the subject gets, the more resistant it will be to AI. So something like economics or international relations or sociology, these other disciplines, you would think will be relatively safe for a while. 应用数学很混乱，因为它处理的是现实世界。学科越混乱，就越能抵御人工智能。因此，像经济学、国际关系或社会学这些学科，你可能会认为在一段时间内相对安全。

You could do infinitely many things in math, but only some of them will be interesting to human beings. So who will be the arbiter of good mathematical taste? 在数学领域，你可以做无数的事情，但只有其中一些对人类来说是有趣的。那么，谁将成为良好数学品味的仲裁者呢？