We’re gonna need a lot more mathematicians

我们将需要更多的数学家

When I was an undergraduate student, I remember talking with several students who felt that the pace at which the top students could understand new math concepts was far too fast for them. They, too, could understand the ideas, but it would take them much longer. Eventually, almost all of these students gave up their dream of pursuing research mathematics and found something else to do. 当我还是本科生时，我记得曾与几位同学交谈，他们觉得顶尖学生理解新数学概念的速度对他们来说太快了。他们其实也能理解这些概念，但需要花费更长的时间。最终，这些学生几乎都放弃了从事数学研究的梦想，转而从事其他工作。

I have been thinking about those students a lot in the last few days. The research mathematics community consists largely of those of us who either rarely felt that way, or who felt it and managed to overcome it through hard work. We have had the good fortune to find a place in mathematics where we could make progress. But we are now entering a time for humility: a time when all of us are going to know what it feels like to be unable to keep up. 过去几天里，我经常想起这些学生。数学研究界主要由两类人组成：一类是很少有这种挫败感的人，另一类是虽然有过这种感觉但通过努力克服了它的人。我们很幸运，在数学领域找到了能让自己取得进展的位置。但我们现在正进入一个需要谦卑的时代：一个我们所有人都将体会到“无法跟上节奏”是什么感觉的时代。

The AI systems I have worked with are already producing beautiful new ideas. They are doing far more than impressive calculations or quickly carrying out arguments that a strong human researcher would already understand. And we probably can’t even imagine the wonderful ideas that future systems will be capable of producing. When we feel that we cannot keep up, will we take that as a reason to leave research mathematics, like the students I am remembering? 我所接触的 AI 系统已经能够产生美妙的新思想。它们所做的远不止是令人印象深刻的计算，或是快速执行强人类研究员本就能理解的论证。我们甚至可能无法想象未来系统将能产生多么奇妙的想法。当我们感到无法跟上节奏时，我们会像我记忆中的那些学生一样，以此为由离开数学研究吗？

As more of us experience this, there will undoubtedly be a temptation to draw the same conclusion as they did: If the machines can move so much faster than us, perhaps we should find something else to do. For our community to give up the work of understanding would be a profound abdication of our responsibility to humanity. Each of us is entitled to choose a different life. The responsibility I am talking about belongs to us collectively: to build a future in which humans can understand and contribute to the discoveries that will change our world. A future with meaningful human agency. 随着越来越多的人经历这一点，毫无疑问，人们会倾向于得出与他们相同的结论：如果机器的进步速度远超我们，也许我们应该去做别的事情。但对于我们的群体而言，放弃“理解”这项工作将是对人类责任的严重失职。每个人都有权选择不同的人生，但我所谈论的责任属于我们集体：去构建一个人类能够理解并参与改变世界的发现的未来。一个拥有人类自主权的未来。

Struggle is essential to understanding difficult concepts. Fortunately, this struggle can be shared. I have been blessed to experience this time and time again with my students and collaborators. Imagine a multitude of research groups, each with sustained support, each spending a term or a year trying to understand an extraordinary set of ideas produced by an AI system, with the help of AI systems. This may very well be among the most important mathematical work in the years to come, and we should support and prioritize it accordingly. This enterprise will require a significant expansion in the number of mathematically sophisticated human researchers available world-wide, as major breakthrough ideas accumulate. 挣扎是理解困难概念的必要过程。幸运的是，这种挣扎是可以共同分担的。我有幸与我的学生和合作者们一次又一次地体验过这一点。想象一下，有众多的研究小组，每个小组都得到持续的支持，花费一个学期或一年的时间，在 AI 系统的帮助下，试图理解由 AI 系统产生的一系列非凡思想。这很可能成为未来几年最重要的数学工作之一，我们应该相应地支持并优先考虑它。随着重大突破性思想的积累，这项事业将需要全球范围内具备数学素养的人类研究人员数量大幅增加。

Why should society want this? So far, this might sound like a utopian fantasy for us – a civilization focused on depth of human understanding, awash with mathematicians and physicists and the like. I would certainly love to live in such a world. And indeed there are deep philosophical reasons for society to move in this direction. But I think society has a much more immediate stake in making this possible, too. 社会为什么要这样做？到目前为止，这听起来可能像是一个乌托邦式的幻想——一个专注于人类理解深度、充斥着数学家和物理学家的文明。我当然很乐意生活在这样的世界里。事实上，社会向这个方向发展有着深刻的哲学原因。但我认为，社会实现这一目标还有更直接的利害关系。

Imagine that a future AI system proposes a radically new design for a one terawatt nuclear fusion power plant. It has found a way to sustain and control fusion that no human had conceived of. The design promises abundant, inexpensive, clean electricity. Robots stand ready to manufacture the components and build the plant. A terawatt is an insane amount of electrical power. We would be deciding whether to construct a machine that handles extraordinary flows of energy using principles we have never conceived of, let alone put into practice. 想象一下，未来的 AI 系统提出了一种全新的 1 太瓦（terawatt）核聚变电站设计。它找到了一种人类从未构想过的维持和控制聚变的方法。该设计承诺提供充足、廉价、清洁的电力。机器人已准备好制造组件并建造电站。1 太瓦是一个惊人的电力数值。我们将面临抉择：是否要建造一台利用我们从未构想过、更不用说付诸实践的原理来处理巨大能量流的机器。

We would need to understand how failures can be contained, what happens to energy already stored in the system when it shuts down, how we can be sure that the materials that make up the power plant behave as expected, and what other questions we should ask before proceeding. The very novelty that makes the proposal exciting would mean that we cannot inherit confidence from decades of operating similar plants or experiments. Before approving construction, I would want communities of humans to understand why the design works and what justifies confidence in its safety. I would hope that we all would. 我们需要理解如何控制故障，当系统关闭时已存储的能量会发生什么，我们如何确保构成电站的材料表现如预期，以及在继续之前我们还应该提出哪些问题。这种让提案令人兴奋的“新颖性”本身就意味着，我们无法从过去几十年运行类似电站或实验的经验中获得信心。在批准建设之前，我希望人类群体能够理解该设计为何有效，以及是什么证明了其安全性。我希望我们所有人都能如此。

Human involvement does not automatically improve a technical decision, and I see no reason to insist that humans manually repeat work an AI system might be able to perform more reliably, even including proving mathematical guarantees. But a theorem can only exist within a model. Understanding the guarantee means understanding the model, the experimental evidence for it, and our uncertainties about the accuracy of the model. This is demanding work, and mathematically sophisticated people must be available to engage with it. 人类的参与并不会自动改善技术决策，我看不出有什么理由坚持让人类手动重复 AI 系统可能更可靠地完成的工作，即使是包括证明数学保证在内。但定理只能存在于模型之中。理解这种保证意味着理解模型、相关的实验证据，以及我们对模型准确性的不确定性。这是一项艰巨的工作，必须有具备数学素养的人员参与其中。

One might respond that AI systems should handle those questions too, and ultimately decide whether the plant should be built. That is a serious position. But it asks us to accept a future in which decisions of enormous consequence rest on reasons that no human community understands. I do not want us to arrive at that future simply because we failed to invest in our own capacity to understand. Human agency is a value of fundamental importance. We must retain the ability to meaningfully consider alternatives and decide what kind of world we want to be a part of building. I think it is worth the effort. 有人可能会回应说，AI 系统也应该处理这些问题，并最终决定是否应该建造该电站。这是一个严肃的立场。但它要求我们接受一个未来：即后果重大的决策建立在没有任何人类群体能理解的理由之上。我不希望我们仅仅因为未能投资于自身的理解能力而走向那个未来。人类的自主权具有根本的重要性。我们必须保留有意义地考虑替代方案并决定我们想要参与构建什么样的世界的能力。我认为这值得付出努力。