Live from ICM 2026: What Is Math For in the Age of AI?

Mathematicians are witnessing a profound shift in their field.

数学家们正在见证他们的领域发生的深刻转变。

AI systems are now producing proofs, spotting connections between distant fields, and, in a few cases, solving problems that had stumped mathematicians for decades.

人工智能系统现在正在提供证明，发现遥远领域之间的联系，并在某些情况下解决困扰数学家数十年的问题。

The pace of progress over the past several months has raised challenging questions: What can AI systems actually do?

过去几个月的进展速度提出了具有挑战性的问题：人工智能系统实际上能做什么？

And what happens to the more human, creative aspects of the field once machines can match – or exceed – people at problem-solving?

一旦机器在解决问题方面能够与人类相匹配或超过人类，那么该领域中更人性化、更具创造性的方面会发生什么？

In this special live episode of The Joy of Why , recorded at the International Congress of Mathematicians in Philadelphia on July 26, 2026, hosts Janna Levin and Steven Strogatz are joined by three mathematicians responding to the rise of AI in math: Akshay Venkatesh at the Institute for Advanced Study; Ravi Vakil at Stanford University and president of the American Mathematical Society ; and Alex Kontorovich at Rutgers University.

在 2026 年 7 月 26 日在费城举行的国际数学家大会上录制的《The Joy of Why》特别现场节目中，主持人 Janna Levin 和 Steven Strogatz 与三位数学家共同应对人工智能在数学领域的兴起：高等研究院的 Akshay Venkatesh； Ravi Vakil 斯坦福大学教授、美国数学会主席；和罗格斯大学的亚历克斯·康托罗维奇。

Together they discuss what recent AI-generated proofs really demonstrate, what will be gained and lost as mathematics becomes more machine-assisted at the frontier, and what this means for the next generation of mathematicians.

他们一起讨论了最近人工智能生成的证明真正证明了什么，随着数学在前沿变得更加机器辅助，将会获得什么和失去什么，以及这对下一代数学家意味着什么。

The conversation turns to a deeper question: What do mathematicians value about doing mathematics in the first place?

谈话转向一个更深层次的问题：数学家首先看重数学的什么？

The answer involves grappling with what proof and understanding really mean, and the surprising importance of storytelling.

答案包括理解证明和理解的真正含义，以及讲故事的惊人重要性。

Listen on Apple Podcasts , Spotify , TuneIn or your favorite podcasting app, or you can stream it from Quanta .

在 Apple 播客、Spotify、TuneIn 或您最喜爱的播客应用程序上收听，或者您也可以从 Quanta 进行流式传输。

It really does feel like a historic moment.

这确实感觉像是一个历史性的时刻。

The stakes are pretty high for the future of math.

对于数学的未来来说，赌注相当高。

And we’ve had a good run for three, four thousand years doing this on our own.

三、四千年来，我们靠自己的努力已经取得了良好的成绩。

But there’s a new kid in town — artificial intelligence.

但镇上出现了一个新事物——人工智能。

And it’s starting to play with us, and our field.

它开始影响我们和我们的领域。

And so we’re excited to hear what our panelists have to say about the interaction between math and artificial intelligence, now and in the short term and maybe in the longer term.

因此，我们很高兴听到我们的小组成员对数学和人工智能之间的相互作用的看法，无论是现在、短期还是长期。

So let me introduce our distinguished panel here.

让我在这里介绍一下我们尊敬的小组。

First up, I see Akshay Venkatesh from the Institute for Advanced Study.

首先，我见到了来自高等研究院的 Akshay Venkatesh。

And next to him, we’ve got Ravi Vakil from Stanford University.

在他旁边的是斯坦福大学的拉维·瓦基尔 (Ravi Vakil)。

And rounding out the panel, there’s Alex Kontorovich from Rutgers.

来自罗格斯大学的 Alex Kontorovich 是小组的最后成员。

All right, Janna, do you wanna get us launched in our discussion?

好吧，詹娜，你想让我们开始讨论吗？

I first want to ask before we get into exactly how it was done, how many of you participated in the International Mathematical Olympiads back in your day?

在我们具体讨论它是如何完成之前，我首先想问一下，你们中有多少人参加过国际数学奥林匹克竞赛？

You did?

你做到了吗？

You did?

你做到了吗？

And will you tell people about it?

你会告诉人们这件事吗？

’Cause some of our audience might not know it’s, six problems, nine hours, two days, and high-school-aged competitors.

因为我们的一些观众可能不知道这是六个问题、九小时、两天和高中年龄的竞争对手。

Tell us what it was like.

告诉我们那是什么样的。

Uh, the important thing about the competition isn’t the six people or the problems, it’s how it encourages millions and millions of kids to hone their minds.

呃，比赛重要的不是六个人或者问题，而是它如何鼓励数以百万计的孩子磨练他们的思想。

So, it was wonderful when the models did well.

所以，当模型表现出色时真是太棒了。

It was really a proof of concept.

这确实是一个概念验证。

I think it was extremely interesting, and I think it can both be an amazing milestone reached, while also I think perhaps people might have misinterpreted it.

我认为这非常有趣，我认为这既可以是一个令人惊奇的里程碑，同时我也认为人们可能会误解它。

So, the first time a model answers a question, it’s exciting.

因此，模型第一次回答问题是令人兴奋的。

A milestone is reached.

达到了一个里程碑。

The first time a student answers a question, it’s exciting for a different reason, because they’ve learned how to think.

学生第一次回答问题时，会因为不同的原因而感到兴奋，因为他们学会了如何思考。

And the seventh time a model answers a question, it’s far less interesting, and the seventh time a student answers the same question is far less interesting, for similar reasons.

出于类似的原因，模型第七次回答一个问题时，它就不再那么有趣了，而学生第七次回答同一个问题时，它也不再那么有趣了。

So, it was exciting, and I, I see it as only a good thing, but it did not represent, uh, superhuman intelligence or anything crazy like that.

所以，这很令人兴奋，我，我认为这只是一件好事，但它并不代表，呃，超人智慧或任何类似的疯狂事物。

But let me go back to your question about these Erdős Problems.

但让我回到你关于这些埃尔多斯问题的问题。

Okay, so we have problems that we’re working on, and as Akshay said, solving problems is just one small component of what mathematicians do.

好的，我们正在解决一些问题，正如阿克谢所说，解决问题只是数学家工作的一小部分。

We find definitions, we find new structures we’re interested in, we create new questions and new problems all the time.

我们找到定义，找到我们感兴趣的新结构，我们一直在创造新问题和新问题。

One person who just loved to ask questions and didn’t mind writing them down whether he was right or wrong, uh, was Erdős, and he wrote down thousands of them.

有一个人就是爱问问题，而且不介意把问题写下来，不管他是对还是错，呃，就是埃尔多斯，他写下了数千个问题。

And, thankfully, Tom Bloom, for whatever reason, several years ago decided to collect these into a database.

值得庆幸的是，汤姆·布鲁姆（Tom Bloom）无论出于何种原因，几年前决定将这些数据收集到数据库中。

The first time a model answers a question, it’s exciting.

模型第一次回答问题是令人兴奋的。

The seventh time a model answers a question, it’s far less interesting.

模型第七次回答问题时，就不再那么有趣了。

And what happens sometimes in mathematics, in fact, it happens with some frequency, is that problems that we thought were difficult end up being not nearly as difficult as we thought and doable by existing techniques if you only bothered to look at that problem and, uh, had the background necessary to apply the techniques that end up cracking it and making it easy.

在数学中有时会发生什么，事实上，它以一定的频率发生，就是我们认为困难的问题最终并不像我们想象的那么困难，并且可以通过现有技术解决，如果你只费心去研究这个问题，并且，呃，有必要的背景来应用最终破解它并使其变得容易的技术。

And so what AI is amazing at is: you give it 1,000 problems, and maybe it has a 1% hit rate, and that’s 10 good papers a year, which is a fantastic, uh, career in mathematics.

所以人工智能的神奇之处在于：你给它 1000 个问题，也许它的命中率只有 1%，那就是每年 10 篇好论文，这是一个非常棒的数学职业。

So, right now we’re seeing every day more and more of these Erdős, uh, style problems being announced.

所以，现在我们每天都看到越来越多的 Erdős，呃，风格问题被宣布。

How many of them are actual solutions as opposed to maybe partial progress or complete abject nonsense ’cause it’s just LLMs saying things, is one thing.

其中有多少是实际的解决方案，而不是部分进展或完全无意义的废话，因为这只是法学硕士在说的话，是一回事。

I think what you’re referring to is the Erdős unit distance conjecture, which is something that quite a lot of people knew, quite a lot of people worked on.

我想你指的是Erdős单位距离猜想，这是很多人都知道、很多人研究过的东西。

There was very significant, progress trying to, you know, get this constant to the conjectured value.

你知道，在尝试让这个常数达到推测值方面取得了非常重大的进展。

And, it turns out that the conjectured value is just wrong.

而且，事实证明，推测的值是错误的。

And, autonomously, uh, GPT found a counterexample, you know, constructed a solution where this exponent is not satisfied.

而且，呃，GPT 自主地找到了一个反例，你知道，构建了一个不满足该指数的解决方案。

What to me is most interesting about that, I mean, first of all, it’s brilliant.

对我来说最有趣的是，我的意思是，首先，它太棒了。

It’s fantastic.

太棒了。

This would be a really great contribution if it was a human being that came up with this counterexample.

如果是人类想出了这个反例，这将是一个非常伟大的贡献。

Um, the most fun thing about this is, a week later, a completely unrelated problem called the sum-product problem was also solved in the negative by human beings who were applying the ideas, the techniques that were exposed to us from this AI solution.

嗯，最有趣的是，一周后，一个完全不相关的问题，称为和积问题，也被应用从这个人工智能解决方案中向我们展示的想法和技术的人类以否定的方式解决了。

So I don’t think theorems have intrinsic value in the universe.

所以我不认为定理在宇宙中具有内在价值。

Mathematicians value them, and right now, AI companies value them because they’re great at marketing.

数学家重视他们，而现在，人工智能公司也重视他们，因为他们擅长营销。

They’re a great way for them to say, “Hey, my tool is better than the previous tool and all the other tools out there.” And it is very effective in that sense, and I think pretty soon AI companies will need other, you know, things that actually bring value to the world, which theorems do not, except for to mathematicians.

这是他们说“嘿，我的工具比以前的工具和所有其他工具更好”的好方法。从这个意义上讲，它非常有效，我认为人工智能公司很快就会需要其他真正为世界带来价值的东西，而定理则不会，除了数学家。

So but in their wake, they’ll leave us a fantastic tool to learn lots of amazing facts.

因此，在他们之后，他们将为我们留下一个很棒的工具来了解许多令人惊奇的事实。

Do any of you find yourself lured by the attraction of checking some of these proofs?

你们中有人发现自己被检查其中一些证据的吸引力所吸引吗？

I mean, some of our very prestigious colleagues have done that, right, have offered their services.

我的意思是，我们的一些非常有声望的同事已经做到了，是的，已经提供了他们的服务。

Would you ever do it, Akshay?

阿克谢，你会这么做吗？

To referee like Terry Tao did.

像陶渊明一样担任裁判。

I don’t think theorems have intrinsic value in the universe.

我不认为定理在宇宙中具有内在价值。

Mathematicians value them, and right now, AI companies value them because they’re great at marketing.

数学家重视他们，而现在，人工智能公司也重视他们，因为他们擅长营销。

That’s, you know, something that we should be thinking about.

你知道，这是我们应该考虑的事情。

Like, should we define this discipline by proofs?

比如，我们应该通过证明来定义这个学科吗？

And of course, we have done so, but I’m not sure it really matches with what we value and what we’re doing.

当然，我们已经这样做了，但我不确定它是否真的符合我们的价值观和我们正在做的事情。

But human understanding and the storytelling, My graduate students, they’re brilliant already.

但是人类的理解和讲故事，我的研究生，他们已经很出色了。

What I teach them, it’s the storytelling.

我教他们的是讲故事。

Learning how to do mathematics, is when you write a paper, you have to understand the human understanding and the conveying of the understanding.

学习如何做数学，就是当你写论文时，你必须了解人类的理解和理解的传达。

I claim this is what we’ve always wanted.

我声称这是我们一直想要的。

There have been brilliant mathematicians who’ve had ideas that went nowhere because they could not convince people of them.

曾经有一些杰出的数学家，他们的想法没有任何进展，因为他们无法说服人们相信这些想法。

And there are other people who’ve really changed fields who’ve just been excellent.

还有其他一些真正改变了领域的人，他们表现得非常出色。

Erdős is a good example of someone who’s changed mathematics, or there even, on a very different level, Martin Gardner is someone who probably has advanced mathematics much more than most people because of what he’s managed to do by storytelling.

埃尔多斯是改变数学的一个很好的例子，甚至在一个非常不同的层面上，马丁·加德纳可能比大多数人拥有更多的高等数学，因为他通过讲故事成功做到了这一点。

And there’s no question what the developments from the 19th century have led to in technology and science and in our standards of living.

毫无疑问，19 世纪的发展给技术和科学以及我们的生活水平带来了怎样的影响。

But it’s because people were curiosity-driven and so Fermat led to the development of a good chunk.

但这是因为人们是好奇心驱动的，所以费马带动了一大块的发展。

Well, not alone.

嗯，并不孤单。

It’s part of a grander story.

这是一个更宏大故事的一部分。

And then the final proof, it was way better the way it turned out because it required the building of a far more interesting story with dramatic bridges that had no right to be there between one way of thinking and completely different way of thinking.

然后是最终的证明，结果比结果要好得多，因为它需要构建一个更有趣的故事，并在一种思维方式和完全不同的思维方式之间建立戏剧性的桥梁，而这种桥梁没有权利存在。

And they were completely out of reach until they weren’t.

他们完全遥不可及，直到他们无法到达为止。

Until you had dramatic leaps of thought.

直到你有了戏剧性的思想飞跃。

There were cliffhangers.

其中有悬念。

There were examples where it looked like we were all done, and then, uh-oh, we weren’t.

有一些例子，看起来我们已经完成了，然后，呃哦，我们还没有。

And then the story is not over.

然后故事还没有结束。

Once you finish the book, you put the book down, and the best theorems are the ones where you’re waiting for the next volume.

一旦你读完这本书，你就把书放下，最好的定理就是你等待下一卷的定理。

And everyone is talking about it around the world to try to think of how the story continues.

世界各地的每个人都在谈论这件事，试图思考这个故事如何继续下去。

It’s hard to think of an example where things do not fit this.

很难想出一个与此不符的例子。

I wanna question the assumption that proof is the central activity.

我想质疑证据是核心活动的假设。

If I think about if I’m doing a piece of math, I probably think of it more akin to storytelling.

如果我考虑我是否在做数学题，我可能会认为它更类似于讲故事。

But, uh, it’s something about that, that when you talk about a story, you mean something about the coherence of the subject, I think.

但是，呃，我认为，当你谈论一个故事时，你指的是主题的连贯性。

Uh, but I don’t know.

呃，但我不知道。

You wanna try to unpack that better than I just just did, Alex?

你想尝试比我刚才更好地解开这个谜团吗，亚历克斯？

But I, I think that question led to a series of other absolutely amazing breakthrough discoveries.

但我，我认为这个问题导致了一系列其他绝对惊人的突破性发现。

From the very beginning of that question, it led to the understanding of non-uniqueness of factorization in number fields, and the fact that we have to understand number fields as their own entities and so that one question, if all you think about is, “I wonder if that’s true or not,” for no reason whatsoever, and you just follow the thread of that story from one breakthrough to another, you get all the way down to, you know, this, uh, massive Taniyama-Shimura and, and so on, and Taylor-Wiles breakthrough.

从这个问题的一开始，它就导致了对数域中因式分解的非唯一性的理解，以及我们必须将数域理解为它们自己的实体这一事实，因此，如果你无缘无故地只想到“我不知道这是不是真的”，然后你只是沿着这个故事的线索从一个突破到另一个突破，你就会一路走到，你知道，这个，呃，巨大的谷山志村等等，泰勒-怀尔斯的突破。

So that’s a beautiful arching, overarching story, and we have many of these in mathematics.

所以这是一个美丽的、包罗万象的故事，我们在数学中有很多这样的故事。

Just to give one more, you know, the question of whether the parallel postulate, this fifth postulate in Euclid’s elements, can or can’t be proved from the other four.

再举一个问题，你知道，平行公设（欧几里得几何原理中的第五个公设）是否可以从其他四个公设中得到证明。

Seems like the most esoteric, useless thing.

似乎是最深奥、最无用的东西。

Who the hell cares, uh, if the fifth postulate can or can’t be proved from the other four?

谁在乎第五个公设能否从其他四个公设中得到证明？

It’s not like, we’re not even arguing about whether the fifth postulate is true or not.

这并不是说，我们甚至没有争论第五条假设是否正确。

We’re saying, you know, should it be a theorem or should it be an axiom in the theory?

我们说，你知道，它应该是一个定理还是理论中的公理？

And you follow the thread of that question 2,000 years all the way to Einstein’s general theory of relativity.

2000 年来，你沿着这个问题的线索一直到爱因斯坦的广义相对论。

I mean, the fact that so many of us are using AI in different ways as part of our regular research, I I think it shows you the practice of mathematics is in flux.

我的意思是，事实上，我们很多人都在以不同的方式使用人工智能作为我们常规研究的一部分，我认为这表明数学实践正在不断变化。

My graduate students, they’re brilliant already.

我的研究生，他们已经很出色了。

What I teach them, it’s the storytelling.

我教他们的是讲故事。

Learning how to do mathematics…

学习如何做数学...

the human understanding and the conveying of the understanding.

人类的理解和理解的传达。

I do think there are things we should be very worried about.

我确实认为有些事情我们应该非常担心。

I’m worried about younger mathematicians, I think.

我认为我担心年轻的数学家。

And the good thing is the community, at least uniformly, seems to realize the danger to the profession comes from the threat to younger mathematicians.

好消息是，整个社会，至少一致地，似乎意识到这个职业面临的危险来自于对年轻数学家的威胁。

But the threat isn’t the obvious one.

但威胁并不明显。

First, I need to say in practice, the evidence so far is that technology has always accelerated science in history.

首先，我需要在实践中说，迄今为止的证据是，技术在历史上总是加速科学的发展。

I can’t think a single time in history when it’s been disastrous for science.

我想不出历史上有哪一次对科学造成过灾难性的影响。

And currently the evidence is that it’s been positive.

目前的证据表明这是积极的。

We’re in a period of great transition, and the error bars are huge, and I make no guarantees for the future.

我们正处于一个伟大的转型时期，误差线很大，我对未来不做任何保证。

And so there’s uncertainty and anxiety, and also opportunity.

因此存在不确定性和焦虑，但也存在机会。

But that’s not what I’m worried about.

但这不是我担心的。

What I’m worried about is, is this is being used as a pretext, as a Trojan horse for anti-intellectualism, which is that people are coming with pitchforks and torches to burn down the library.

我担心的是，这是否会被用作反智主义的借口，作为反智主义的特洛伊木马，人们拿着干草叉和火把来烧毁图书馆。

And we worry that maybe in a few years, what if this leads to disastrous cuts.

我们担心，也许几年后，这会导致灾难性的削减怎么办？

You could imagine in five years, graduate programs might be cut by huge amounts.

你可以想象五年后，研究生课程可能会大幅削减。

Funding for science might be cut.

科学经费可能会被削减。

But that’s actually happening right now.

但这确实正在发生。

And the pretexts for it don’t make sense.

而且其借口毫无意义。

So when people say it’s because of AI that we have to cut funding for graduate students, reduce jobs, cut REUs, that we don’t no longer need to teach kids how to think mathematically because they can just Google it, they no longer need to understand science because they could just ask a model.

因此，当人们说，由于人工智能，我们必须削减研究生经费、减少工作岗位、削减 REU，我们不再需要教孩子们如何进行数学思考，因为他们可以通过谷歌搜索，他们不再需要理解科学，因为他们可以只问一个模型。

So the danger is that it’s a Trojan horse for anti-intellectualism, and it’s already happening.

所以危险在于它是反智主义的特洛伊木马，而且它已经发生了。

And we’re fighting the cuts right now.

我们现在正在努力削减开支。

So that’s, that’s my first real danger and so, yeah, I mean, it makes no sense.

所以，这是我面临的第一个真正的危险，所以，是的，我的意思是，这是没有意义的。

So the second thing I’m worried about is students learning.

所以我担心的第二件事是学生的学习。

We talked about earlier, just fighting with a problem over weeks and maybe never solving it.

我们之前谈到过，只是与一个问题斗争了数周，而且可能永远无法解决它。

And there’s a reason why you don’t want all the answers to be the back of the book, and now you have the temptation.

你不希望所有的答案都出现在书的后面是有原因的，而现在你面临着诱惑。

The danger is that some of the tools, the problem sets to think over a week, now we have to really trust students to work on their own, and the purpose of it is not to get the answer.

危险在于，有些工具、问题需要思考一周以上，现在我们必须真正信任学生自己完成工作，而其目的不是得到答案。

It was never to get the answer on a test.

从来不是为了在考试中得到答案。

It was to train your mind.

这是为了训练你的头脑。

The best students, and I don’t mean the smartest, but the wisest students are gonna be accelerated.

最好的学生，我不是指最聪明的学生，而是最聪明的学生将会加速进步。

They will learn faster because it will give them clues as to how they should struggle with problems for longer.

他们会学得更快，因为这会给他们提供线索，告诉他们应该如何更长时间地与问题作斗争。

But I worry that a large number of people will think they understand something.

但我担心很多人会认为他们理解了一些东西。

That will lose a large number of very bright students who will think less clearly because of the existence of…

这将失去大量非常聪明的学生，他们会因为……的存在而思考不那么清晰。

But you know, it’s interesting, we mathematicians should have the longest time horizon over which to understand how education interacts with technology, because pocket calculators have been around for 70 years or something, and we all know educators who tell their own students, “You don’t have to know your times tables ‘cause a calculator will do it.”

但你知道，这很有趣，我们数学家应该有最长的时间跨度来理解教育如何与技术相互作用，因为袖珍计算器已经存在了 70 年左右，我们都知道教育工作者告诉自己的学生，“你不必知道你的乘法表，因为计算器可以做到这一点。”

What AI is amazing at is: you give it 1,000 problems, and maybe it has a 1% hit rate, and that’s 10 good papers a year, which is a fantastic career in mathematics.

AI 的神奇之处在于：你给它 1000 个问题，也许它的命中率只有 1%，那就是一年 10 篇好论文，这在数学领域是一个很棒的职业。

So we don’t consider the problem to be solved by the supercomputer.

所以我们不考虑超级计算机要解决的问题。

It’s the human who adapts it in a way that, as you said, as human beings, we’re able to appreciate it, understand it, and integrate it into the larger sphere of knowledge.

正如你所说，是人类以某种方式适应它，作为人类，我们能够欣赏它、理解它，并将其整合到更大的知识领域。

And we’re not computer scientists, of course.

当然，我们不是计算机科学家。

You’re not a computer scientist.

你不是计算机科学家。

But just wonder if at any point, do we think the AI will understand?

但只是想知道，在任何时候，我们认为人工智能会理解吗？

And will that understanding be completely different than the way in which human beings understand?

这种理解会不会与人类的理解方式完全不同？

Presumably we looked at birds and dreamed up such a thing.

想必我们看着鸟类并梦想了这样的事情。

And, um, maybe in the same way, you know, uh, depending on what our goals are, we’ll, we invent technology that doesn’t look exactly the way nature figured out to solve that problem, but solves it slightly differently.

而且，嗯，也许以同样的方式，你知道，呃，取决于我们的目标是什么，我们发明的技术看起来并不完全符合大自然解决这个问题的方式，但解决方式略有不同。

And so that’s kind of what LLMs have become, is this alternative mechanism by which we can do a small part of what mathematical practice strives for.

这就是法学硕士已经成为的样子，是一种替代机制，通过它我们可以完成数学实践所追求的一小部分。

Does it mean that it understands?

意思是明白了吗？

I don’t know what the word understands means in this context.

我不知道这个词在这种情况下意味着什么。

So in the same way, maybe I’m even more pragmatic about it.

所以同样的，也许我对此更加务实。

Is the AI useful to me in what my goals are?

人工智能对我实现目标有用吗？

My goals are to understand mathematics.

我的目标是理解数学。

I wanna learn new math every single day.

我想每天学习新的数学。

Is using AI helping that goal or not?

使用人工智能是否有助于实现这一目标？

To the extent that it’s helping, I’m gonna use it, and to the extent that it’s not, I’m gonna stop and go for a walk and, you know, play ball with my kids, or something.

如果它有帮助，我就会使用它，如果没有帮助，我就会停下来去散步，你知道，和我的孩子们一起打球，或者其他什么。

But the part that I feel is, back to my list of taboo questions, is what happens when they’re not useful to us because they could do everything that we could do except much, much better.

但我觉得，回到我的禁忌问题清单，当它们对我们没有用处时会发生什么，因为它们可以做我们能做的一切，除了更好得多。

So I, I will stipulate, but maybe you won’t agree.

所以我,我会规定,但是也许你不会同意。

But I think it’s obvious that not only will they be able to solve problems better than us, they’ll be able to ask questions that we will find interesting.

但我认为很明显，他们不仅能够比我们更好地解决问题，而且能够提出我们感兴趣的问题。

They’ll be able to do exposition better than Martin Gardner and the whole thing.

他们将能够比马丁·加德纳和整个事情做得更好。

Will it still be fun for us to do math?

我们做数学仍然很有趣吗？

Should we define this discipline by proofs?

我们应该通过证明来定义这个学科吗？

Of course, we have done so, but I’m not sure it really matches with what we value and what we’re doing.

当然，我们已经这样做了，但我不确定这是否真的符合我们的价值观和我们正在做的事情。

But then you said things that were very reasonable because they were precise, and they were statements about evidence of, they will be able to write things that will be interesting.

但后来你说了一些非常合理的事情，因为它们很精确，而且它们是关于证据的陈述，他们将能够写出有趣的东西。

And those things were already here.

而那些东西已经在这里了。

That time has already come, and I think they are already telling us.

那个时刻已经到来，我想他们已经告诉我们了。

So, is someone gonna predict that a Pulitzer Prize-winning novel will be written by an AI within three years?

那么，有人会预测三年内人工智能会写出普利策奖获奖小说吗？

I’ll put $20 against you on this.

我将为此向你赔 20 美元。

And people have made bets like this in the past, and they’ve lost those bets every single time.

人们过去也曾做过这样的赌注，但他们每次都输掉了这些赌注。

We were supposed to be on Mars by today if you listen to certain very wealthy people 10 years ago.

如果你听十年前某些非常富有的人的话，我们应该在今天到达火星。

So, absolutely large quantities of acceptable material I expect to be very useful.

因此，我认为绝对大量可接受的材料将非常有用。

And I’m not belittling it.

我并不是贬低它。

This will change everything, uh, will happen.

这将改变一切，呃，将会发生。

But I think the way things are currently happening is outstanding things are going to happen, and AI is involved, and humans are involved.

但我认为目前事情发生的方式是，杰出的事情将会发生，人工智能和人类都会参与其中。

And, uh, I guess people are claiming that a time will come when there’ll be no more humans, but they need some evidence.

而且，呃，我猜人们声称有一天将不再有人类，但他们需要一些证据。

You know, like when I arrived at grad school, right?

你知道，就像我刚到研究生院时一样，对吗？

I met all these people who were just much better at math than I was.

我遇到了所有这些人，他们的数学比我好得多。

And at that time, I was like, “I’m never gonna be as good at math as these people.” But this is great.

那时，我想，“我永远不会像这些人那样擅长数学。”但这很棒。

I get to study this field.

我要研究这个领域。

It’s a beautiful field.

这是一个美丽的领域。

I’m not gonna be the best at it.

我不会是最擅长的。

I’m happy to spend my life this way.” So I, I think you know, yes, we will still do math because it has some basic value to us as human beings.

我很高兴这样度过我的一生。”所以我，我想你知道，是的，我们仍然会做数学，因为它对我们作为人类有一些基本价值。

Vignette number one, uh, you have some heavy pallets and you need to move them onto a truck.

第一个小插图，呃，你有一些很重的托盘，你需要把它们搬到卡车上。

So you get a forklift, you drive it over, you lift the pallets, you put them on the truck, end of story.

所以你找了一辆叉车，把它开过来，抬起托盘，把它们放在卡车上，故事结束。

Okay?

好吧？

What I’m worried about is this is being used as a pretext, as a Trojan horse, for anti-intellectualism, which is that people are coming with pitchforks and torches to burn down the library.

我担心的是，这被用作反智主义的借口、特洛伊木马，即人们拿着干草叉和火把来烧毁图书馆。

Scenario number two, you’re trying to learn how to use a forklift.

第二个场景，您正在尝试学习如何使用叉车。

So you get in the forklift and you move some pallets, not because they need to be moved from point A to point B, but because you’re learning how to operate a forklift.

因此，您坐上叉车并移动一些托盘，不是因为它们需要从 A 点移动到 B 点，而是因为您正在学习如何操作叉车。

Okay, scenario three, you decide you wanna get a, a little workout in.

好的，场景三，你决定要进行一点锻炼。

You go to the gym, you put 200 pounds on the bench press.

你去健身房，在卧推上举起 200 磅的重量。

You get in your forklift, you drive over, and you do 10 reps with the forklift.

您坐上叉车，开过去，然后用叉车重复 10 次。

One of these is the wrong use of technology.

其中之一是技术的错误使用。

Okay?

好吧？

So if you just explain to students, why are you here?

所以如果你只是向学生解释一下，你为什么来这里？

What are you…

你是什么……

You know, if I don’t need to know the answer to this real analysis homework.

你知道，如果我不需要知道这个真实分析作业的答案的话。

I know how to do this.

我知道该怎么做。

It’s in the back of the book.

它在书的后面。

Before AI, you could Google the answers.

在人工智能出现之前，你可以通过谷歌搜索答案。

Okay?

好吧？

So, uh, what is the purpose of this operation?

那么，呃，这个操作的目的是什么？

Is it for you to learn how to use that technology, to learn how to prompt AI to solve real analysis problem?

是让你学习如何使用该技术，学习如何促使人工智能解决实际分析问题吗？

Is it that I want the solution to the problem, or is it that you’re supposed to sit there being frustrated and get the stamina for frustration that it takes to do any kind of difficult thing that human beings want to do?

是我想要问题的解决方案，还是你应该坐在那里感到沮丧，并获得做人类想做的任何困难事情所需的挫折耐力？

If that’s what the goal of this exercise is, then either sign up voluntarily to do the exercise the way it’s designed, or drop this course ’cause that’s, that’s what I’m trying to teach.

如果这就是本练习的目标，那么要么自愿注册按照设计的方式进行练习，要么放弃这门课程，因为这就是我想要教的内容。

I don’t like that defense of geometry.

我不喜欢这种对几何学的辩护。

Geometry is a magnificent creation of humanity, and this is like, you know, you could play soccer because you wanna exercise your leg, or because it’s the beautiful game, you know?

几何是人类的伟大创造，这就像，你知道，你可以踢足球，因为你想锻炼你的腿，或者因为这是一项美丽的运动，你知道吗？

And so math to me, the content is beautiful.

所以对我来说，数学的内容很美。

It’s not just the calisthenics that I wanna make myself stronger for solving a problem for a finance company, ’cause that’s what really matters.

我想让自己变得更强大，为一家金融公司解决问题，这不仅仅是健身操，因为这才是真正重要的。

I wanna do it for human flourishing, like Francis Su would say.

我想为人类的繁荣而努力，就像弗朗西斯·苏（Francis Su）所说的那样。

Like what I think you’ve been pushing, Ravi.

就像我认为你一直在推动的那样，拉维。

Not just for my own bulking up because the content is inherently rich and makes me a happier person before I’m dead.

不仅仅是为了我自己的成长，因为内容本身就很丰富，让我在死之前成为一个更快乐的人。

What’s the meaning of life?

生命的意义是什么？

I wanna do math while I’m alive.

我想趁我还活着的时候做数学。

Is AI useful to me in what my goals are?

人工智能对我实现目标有用吗？

To the extent that it’s helping, I’m gonna use it, and to the extent that it’s not, I’m gonna stop and go for a walk and play ball with my kids.

如果它有帮助，我就会使用它，如果没有帮助，我就会停下来散步，和我的孩子们一起打球。

If you seed an interactive theorem prover with no library of what mathematics is.

如果您在没有数学库的情况下播种交互式定理证明器。

Audience Question: So far, AI is controlled by private companies, and access to the best models is increasingly being gated by financial resources.

观众提问：到目前为止，人工智能由私营公司控制，获得最佳模型的机会越来越受到财政资源的限制。

And I’m concerned about this divide between researchers who are going to have access and those who don’t.

我对将获得访问权限的研究人员和无法获得访问权限的研究人员之间的这种分歧感到担忧。

Historically, our field has been known for all you need is pen and paper.

从历史上看，我们的领域一直以笔和纸而闻名。

To what extent will that no longer be true, and how can we make sure math is still accessible to everyone?

这种情况在多大程度上将不再如此？我们如何确保每个人仍然可以接触数学？

Audience Question: My question is, I think there are some missing pieces.

观众提问：我的问题是，我认为有一些缺失的部分。

Now, as AI begins churning out proofs, I think we are realizing that this is not the- what mathematicians want, just like the number of proofs.

现在，随着人工智能开始大量生产证明，我认为我们正在意识到这不是数学家想要的，就像证明的数量一样。

I think the missing piece I feel is aesthetics.

我认为我觉得缺失的部分是美学。

And we haven’t really defined that.

我们还没有真正定义这一点。

Like, why is a problem interesting or why is a proof interesting?

比如，为什么一个问题很有趣，或者为什么一个证明很有趣？

Where is the beauty?

美在哪里？

Where is depth?

深度在哪里？

Where is interconnectedness?

互联互通在哪里？

I think because these haven’t been defined, when you’re faced with hundreds of proof generated by AI, you have no idea what to look at.

我认为因为这些还没有被定义，当你面对人工智能生成的数百个证据时，你不知道该看什么。

So, is somebody working on, like, measuring these?

那么，有人正在研究测量这些吗？

We already have a good human sense as what’s aesthetically pleasing.

我们已经具备了良好的人类审美意识。

We know what’s interesting.

我们知道什么是有趣的。

We know most of the proofs that are produced by AIs are not interesting.

我们知道人工智能产生的大多数证明并不有趣。

We know some of them are fantastically interesting and beautiful.

我们知道其中一些非常有趣且美丽。

So I don’t think it’s mechanizable, and that pleases me a little bit that, it’s a human subject, that it’s a human understanding that matters.

所以我不认为它是机械化的，这让我有点高兴，因为它是一个人类主题，重要的是人类的理解。

I realize that’s not a very happy, it’s not like a very conclusive answer, so maybe I should pass it to someone else.

我意识到这不是一个令人高兴的问题，也不是一个非常结论性的答案，所以也许我应该将其传递给其他人。

It’s much more fun to know something without knowing how you know it.

知道某件事而不知道你是如何知道的会更有趣。

I’m really happy that our field is not looking at metrics and there are Fields Medalists with an H-index of four or something.

我真的很高兴我们的领域没有关注指标，而且有些菲尔兹奖得主的 H 指数为 4 左右。

These, these things are completely meaningless.

这些这些东西完全没有意义。

Uh, it’s a problem when we have to go to the dean and say, “No, no, this person really is very good.

呃，当我们必须去找院长说，“不，不，这个人真的非常好。

Please look at their papers,” which the dean will not understand.

请看他们的论文。”院长听不懂。

It is hard to…

很难……

I don’t think I would want…

我想我不会想要……

I don’t think it’s possible to quantify, but it’s something that you meet someone at the ICM from another country, brought up in a completely different school system, and you meet and you hear about a new theorem, and you both nod your head and you think, “That was amazing.”

我认为这是不可能量化的，但这是你在 ICM 遇到来自另一个国家的人，在完全不同的学校系统中长大的事情，你们见面并听到一个新定理，你们都点头，然后想，“这太棒了。”

Audience Question: Um, thanks for the great conversation.

观众提问：嗯，谢谢你们的精彩对话。

think unfortunately, historically, the mathematical community has not appreciated exposition and teaching in the same way that it has solving really hard problems.

不幸的是，从历史上看，数学界并没有像解决真正困难的问题那样重视解释和教学。

I mean, this goes back to, like, Bertrand Russell describing people that describe math as being less than the people that solve math problems.

我的意思是，这可以追溯到伯特兰·罗素（Bertrand Russell）描述那些认为数学不如解决数学问题的人。

Do you think this will shift in the age of AI towards an appreciation of pedagogy and of exposition?

您认为人工智能时代这会转向对教学法和阐述的欣赏吗？

Audience Question: Thank you for this conversation.

观众提问：谢谢您接受这次谈话。

I had a question for the entire panel.

我有一个问题要问整个小组。

So the panelists laid out a vision of what AI use in education ideally looks like, right?

因此，小组成员提出了人工智能在教育中的理想应用的愿景，对吗？

You ask students not to use AI to train their minds.

你要求学生不要用人工智能来训练他们的思维。

But this vision is sort of incompatible with the current infrastructure for like grad school applications or postdoc applications or tenure track applications or what have you, where, you know, it seems like the only thing that matters is how much you publish, how hard the problems you’re solving are, and so on, so on.

但这种愿景与当前的基础设施有点不兼容，例如研究生院申请、博士后申请、终身教职申请或你拥有的、在哪里，你知道，似乎唯一重要的是你发表了多少文章，你要解决的问题有多难，等等。

The best person with a calculator is the best person without a calculator.

拥有计算器的最好的人也是没有计算器的最好的人。

How do you see this infrastructure changing?

您如何看待这种基础设施的变化？

And what is your advice to a current graduate student worried about the fact that not wanting to use AI, say, in order to train their minds, would leave them behind, especially given how slow the timelines of infrastructure changes tend to be?

对于现在的研究生来说，您有什么建议，他们担心不想使用人工智能（例如，为了训练他们的思维）会让他们落后，特别是考虑到基础设施变革的时间表往往很慢？

And I do think the best mathematics, some people will do very well augmented by AI, other people will not.

我确实认为最好的数学，有些人在人工智能的增强下会做得很好，而其他人则不会。

I will say to graduate students, if they wonder, “Do I need to use AI?” I would say, “No, currently.” But I would also say don’t be afraid of it if it helps.

如果研究生想知道“我需要使用人工智能吗？”，我会问他们。我会说：“目前还没有。”但我也想说，如果它有帮助的话，不要害怕。

If you need to look for references, use it in the way you feel comfortable with.

如果您需要寻找参考，请以您觉得舒服的方式使用它。

But the evidence currently out, don’t go to Twitter, don’t follow what other people are saying.

但目前的证据已经出来了，不要上推特，不要关注其他人在说什么。

Don’t be afraid.

不要害怕。

Uh, what really is happening on the ground is that the people who are using it effectively are using it in a very specific way, and I think the people who are best at it, who will give you the best advice are fellow graduate students who are similarly struggling with it at the same level, where they will say use it to perhaps…

呃，实际情况是，有效使用它的人正在以一种非常具体的方式使用它，我认为最擅长这方面的人，会给你最好建议的人是研究生同学，他们在同一水平上同样在努力解决这个问题，他们会说用它来也许……

track down the thing to do.

追踪要做的事情。

How do I think about this?

我怎么看待这个问题？

But then you go away, and learn who among your peers is learning the fastest, and maybe they’re using an AI to guide them on what to think, or maybe not.

但随后你离开，了解你的同龄人中谁学得最快，也许他们正在使用人工智能来指导他们思考什么，也可能不是。

And so I don’t think you need to use AI.

所以我认为你不需要使用人工智能。

I don’t think you should be afraid of it either.

我认为你也不应该害怕它。

I think the broader question of how systems have to change is, is important.

我认为系统如何改变这个更广泛的问题很重要。

And I don’t know, but I, I think the community is seriously thinking about it.

我不知道，但我认为社区正在认真考虑这个问题。

Audience Question: Um, So one thing that we’ve heard a lot about is how AI is changing the way that we’re attacking these problems, the way we’re thinking really.

观众提问：嗯，我们经常听到的一件事是人工智能如何改变我们解决这些问题的方式，改变我们真正的思考方式。

And I get a little pessimistic and wonder, you know, is it gonna change the way we think in a bad way?

我有点悲观，想知道，它会以一种不好的方式改变我们的思维方式吗？

I don’t think students necessarily start using AI as a tool thinking, “Okay, I’m going to hurt my knowledge and the way I go about these problems,” but slowly over time it does, and I worry that the same thing might happen to mathematicians.

我不认为学生们一定会开始使用人工智能作为工具，思考“好吧，我会损害我的知识和我解决这些问题的方式”，但随着时间的推移，它会慢慢地发生，我担心同样的事情可能会发生在数学家身上。

So my question is, are we really just like frogs boiling in a pot of water?

那么我的问题是，我们真的就像锅里煮青蛙一样吗？

Are we gonna know when we’re supposed to jump out?

我们知道什么时候应该跳出去吗？

So I, I think that’s a fair question, and it’s tough when you’re the person.

所以我认为这是一个公平的问题，但当你是那个人时，这很难。

It’s easy to see it from the outside.

从外面很容易看到它。

It’s tougher when you’re the person deciding.

当你是做决定的人时，事情就更困难了。

What is the purpose of this operation?

这个操作的目的是什么？

Is it that I want the solution to the problem, or is it that you’re supposed to sit there being frustrated and get the stamina for frustration that it takes to do any kind of difficult thing that human beings want to do?

是我想要问题的解决方案，还是你应该坐在那里感到沮丧，并获得做人类想做的任何困难事情所需的挫折耐力？

I feel it a little bit when I learn a new subject with AI that sometimes I get the link to the paper and I get, then maybe I’ll get the summary.

当我用人工智能学习一门新学科时，我有一点感觉，有时我会得到论文的链接，然后我可能会得到摘要。

But in the old days, I would’ve read the paper and I would’ve fought with it for a few days.

但在过去，我会阅读报纸并与之斗争几天。

So, there’s a trade-off, and as I s-said earlier, we need to fight with things for a long period of time and be stuck.

所以，这是一个权衡，正如我之前所说的，我们需要与事物进行长期斗争并陷入困境。

And I don’t have much time right now, and so I sometimes make this trade-off.

而且我现在没有太多时间，所以有时我会做出这样的权衡。

But I’m making potentially the same mistake the undergraduate is the day before the homework is due.

但我可能会在本科生交作业的前一天犯同样的错误。

Audience Question: Um, As a grad student, I feel, uh, low-hanging fruit is very important for, uh, grad students for, like, getting started, getting confidence in math.

观众提问：嗯，作为一名研究生，我觉得，呃，容易实现的目标对于研究生来说非常重要，比如开始，对数学建立信心。

And my concern is that AI will swoop, and take all the low-hanging fruit, and then maybe, uh, it’ll be hard for a lot of people to get started.

我担心人工智能会突然出现，夺走所有唾手可得的果实，然后也许，呃，很多人会很难开始。

And I’m concerned about like, the Average Joe mathematician who doesn’t work on things that are, like, safe from AI.

我担心那些普通的数学家，他们不从事不受人工智能影响的事情。

But, yeah.

但是，是的。

I was wondering what your thoughts are on that.

我想知道你对此有何想法。

Like, there may be tractable graduate student beginning level questions that you could get by talking to your friend who’s a psychologist.

例如，您可以通过与心理学家朋友交谈来解决一些易于处理的研究生初级问题。

I am gonna go applied on you for a minute.

我要去给你申请一分钟。

We want you in applied math.

我们想要你学应用数学。

There’s a lot to do, and science may be more resistant than math.

有很多事情要做，科学可能比数学更有抵抗力。

So, the good thing is advisors are concretely thinking about how next to think about the right way, the right sources of problems.

因此，好处是顾问们正在具体思考下一步如何以正确的方式、正确的问题根源进行思考。

I don’t feel like graduate students are the ones that are gonna invent new fields.

我不认为研究生会发明新领域。

Unless, except for maybe three or four.

除非，除了也许三四个。

But, I do worry.

但是，我确实担心。

That’s the, one of the few things that I think are real concerns.

这是我认为真正令人担忧的少数事情之一。

Uh, but at least I share the concern, and we’re thinking hard about it.

呃，但至少我也有同样的担忧，而且我们正在认真考虑这个问题。

So don’t give up, uh, because it’s important to get the graduate students through this stage and continue to train because they’re the ones who are going to drive the field forward four years later.

所以不要放弃，呃，因为让研究生度过这个阶段并继续训练很重要，因为他们将在四年后推动该领域向前发展。

The goal is for you to learn actually what theorem X is, learn the innards of how it works, because when you shake it just a little bit, you, you learn some more about, oh, actually the reason this is happening is because of this and not that and you thought it would work, but it actually doesn’t work and here’s where I’m stuck and so on.

我们的目标是让你真正了解定理 X 是什么，了解它的工作原理，因为当你稍微摇动它时，你会了解更多，哦，实际上发生这种情况的原因是因为这个而不是那个，你认为它会起作用，但实际上不起作用，这就是我被困住的地方等等。

There’s still so much, even with the AI assisting you in that path, there’s still so much for you to learn.

还有很多东西，即使有人工智能在这条路上帮助你，你仍然有很多东西需要学习。

The goal isn’t necessarily just to arrive at X prime.

我们的目标不一定只是达到 X prime。

Now, if you’re saying, “Okay, but AI already knows X prime,” who’s pressing the button on the AI to get X prime, right?

现在，如果你说，“好吧，但是 AI 已经知道 X prime”，那么谁按下 AI 上的按钮来获得 X prime，对吧？

At the end of the day, someone has to ask the AI the question, and of course it can ask its own questions, but even then someone’s prompting it to say, “Go ask questions.”

归根结底，必须有人向人工智能提出问题，当然它也可以问自己的问题，但即便如此，还是有人会提示它说：“去问问题。”

So, it’s like it’s not turtles all the way down.

所以，就好像它不是一路下来的海龟。

Someone is paying the electric bill of what’s being asked and, uh, that person’s doing it for a reason.

有人正在支付所要求的电费，呃，那个人这样做是有原因的。

At the end of the day, what is being done has to be valued by human beings, otherwise it’s not going to get done.

归根结底，所做的事情必须得到人类的重视，否则就无法完成。

The danger is that now we have to really trust students to work on their own, and the purpose of it is not to get the answer.

危险在于，现在我们必须真正信任学生自己做事，而这样做的目的不是为了得到答案。

It was never to get the answer on a test.

从来不是为了在考试中得到答案。

It was to train your mind.

这是为了训练你的头脑。

Audience QA: So like many people in this room, I of course agree that math does amazing things to sharpen minds and to enrich lives.

观众问答：就像在座的许多人一样，我当然同意数学在磨砺思维和丰富生活方面发挥着惊人的作用。

But at the same time, there’s a lot of other disciplines that can lay similar claims, and much has been said even today about, you know, humanities and that maybe math is going to start looking a little more like those.

但与此同时，还有很多其他学科可以提出类似的主张，即使在今天，关于人文学科也已经有很多说法，也许数学将开始看起来更像这些学科。

So my question is do you think that as a profession, we need to be thinking about some sort of a value-added statement that would actually work to, in real life, nurture an ecosystem of people who would be engaged in this brave new math that’s being shaped up?

所以我的问题是，你是否认为作为一种职业，我们需要考虑某种增值声明，这种声明实际上可以在现实生活中培养一个由人们组成的生态系统，让他们参与到正在形成的这一勇敢的新数学中？

Or do you think that such a value-added statement will just kind of happen by itself?

或者您认为这样的增值声明会自动发生吗？

At many schools, math is one of the biggest majors.

在许多学校，数学是最大的专业之一。

At our school, math is one of the biggest majors.

在我们学校，数学是最大的专业之一。

Why?

为什么？

Not because people are going to become PhD mathematicians.

不是因为人们将成为数学博士。

It’s because this, these habits of mind, this, way of thinking are empirically, more and more today, even more than ever, are incredibly useful.

因为这个、这些思维习惯、这个、思维方式是经验性的，在今天越来越多，甚至比以往任何时候都非常有用。

Our students, if you want a job where you know what you’re gonna be doing in 50 years, you should not be a math major.

我们的学生们，如果你想要一份知道 50 年后你会做什么的工作，你不应该是数学专业的。

If you want to be a job in a career that doesn’t even exist yet, that where you’re gonna make the future, our students rule the world.

如果你想在一个尚不存在的职业中找到一份工作，在你将创造未来的地方，我们的学生统治世界。

In fact, I was just given from the Italian Mathematical Society, they did a study on the value added of mathematics to the economy.

事实上，我刚刚收到意大利数学会的邀请，他们做了一项关于数学对经济增值的研究。

This is, incredibly safe, and I think by hiding ourselves and pretending we’re not useful, that’s been really dangerous.

这是非常安全的，我认为隐藏自己并假装我们没有用，这真的很危险。

I think we need to have an informed public.

我认为我们需要有知情的公众。

They want to know math.

他们想了解数学。

They want to understand math.

他们想理解数学。

We can easily convince them how useful it is if we would just make the case for it.

如果我们能证明这一点，我们就可以轻松地让他们相信它有多么有用。

So thank you for that that very easy question.

谢谢你提出这个非常简单的问题。

The Joy of Why is produced by PRX Productions.

《为什么的喜悦》由 PRX Productions 制作。

The production team is Caitlin Faulds, Jade Abdul-Malik, Genevieve Sponsler, and Merritt Jacob.

制作团队包括 Caitlin Faulds、Jade Abdul-Malik、Genevieve Sponsler 和 Merritt Jacob。

The executive producer of PRX Productions is Jocelyn Gonzales.

PRX Productions 的执行制片人是乔斯林·冈萨雷斯 (Jocelyn Gonzales)。

Edwin Ochoa is our project manager.

埃德温·奥乔亚是我们的项目经理。

From Quanta Magazine , Simon Frantz and Samir Patel provided editorial guidance with support from Samuel Velasco, Kit Sudol, Simone Barr, and Michael Kanyongolo.

Quanta 杂志的 Simon Frantz 和 Samir Patel 在 Samuel Velasco、Kit Sudol、Simone Barr 和 Michael Kanyongolo 的支持下提供了编辑指导。

Samir Patel is Quanta’s editor-in-chief.

萨米尔·帕特尔 (Samir Patel) 是广达的主编。

The episode art is by Chanelle Nibbelink, and our logo is by Jacky King and Kristina Armitage.

剧集艺术由 Chanelle Nibbelink 创作，我们的徽标由 Jacky King 和 Kristina Armitage 创作。

Note: Alex Kontorovich is a member of Quanta Magazine’s advisory board .

注：Alex Kontorovich 是 Quanta 杂志顾问委员会成员。

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获取发送到您的电子邮件收件箱的最重要新闻的摘要

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《Quanta》杂志对评论进行审核，以促进知情、实质性、文明的对话。

Abusive, profane, self-promotional, misleading, incoherent or off-topic comments will be rejected.

辱骂、亵渎、自我推销、误导、语无伦次或偏离主题的评论将被拒绝。

Moderators are staffed during regular business hours (New York time) and can only accept comments written in English.

版主在正常工作时间（纽约时间）有工作人员，并且只能接受英文评论。