欢迎来到数学领域的AI危机

对着麦克风说话，我挺有自信的。

I'm pretty confident talking into a mic.

嘿。

Hey.

我现在就在这么做。

I'm doing it right now.

但家里那些活儿，我什么都拿不准。

But home projects, I second guess everything.

那个噪音正常吗？

Is that noise normal?

那是水渍吗？

Is that water damage?

而且我到底该找谁呢？

And who should I even call?

这时候就该用Thumbtack了。

That's where Thumbtack comes in.

上传一张照片或语音留言，他们的人工智能搜索就能帮你诊断问题，并为你匹配当地评分最高的专业师傅。

Upload a photo or voice notes, and their AI powered search helps diagnose the issue and match you with the right top rated local pro.

不用再自己瞎猜或花几个小时到处找，你能得到明确的答案，放心地雇到合适的专业人士。

Instead of second guessing or searching for hours, you get clarity and can hire the right pro with confidence.

下一个家装项目，试试Thumbtack吧。

For your next home project, try Thumbtack.

他们懂房子。

They know homes.

今天就雇对的人。

Hire the right pro today.

我收到一条短信。

I've got a text.

夏天可能快结束了，但一位新的重磅人物已经进入了别墅。

The summer might be almost over, but a new bombshell has entered the villa.

来认识一下Deepgram Flux TTS的声音。

Meet the voices of Deepgram Flux TTS.

我是德鲁。

I'm Drew.

低调随性。

Low key casual.

我是亚历克西斯，一个充满活力的早起型人。

I'm Alexis, an upbeat morning person.

我是海莉，总是很开心。

I'm Hailey, always cheerful.

Flux TTS 有一些真实有个性的声音，随时准备开口说话。

Flux TTS has some real personalities that are ready to speak.

你可以打断、暂停，然后继续说话，不会丢失思路。

You can interrupt, pause, and keep talking without losing the plot.

想聊聊天吗？

Fancy a chat?

快来试试所有声音，9月12日前免费，访问 deepgram.com/keep talking。

Come try all the voices free through September 12 at deepgram.com/ keep talking.

适用条款。

Terms apply.

我们通过保护全球AI领军企业来保障全球AI的未来。

We secure the world's AI future by securing the world's AI leaders.

AI的采用速度远超企业的安全防护能力。

AI is being adopted faster than companies can secure it.

敏感数据正在AI模型中流转，攻击者也在利用AI以前所未有的速度和精准度发起攻击。

Sensitive data is moving across AI models, and attackers are using AI to strike with unprecedented speed and precision.

因此，CrowdStrike打造了面向AI时代的AgenTix网络安全平台，既保护AI，又阻止入侵。

That's why CrowdStrike built the AgenTix cybersecurity platform for the AI era, to secure AI and to stop breaches.

让你放心拥抱AI，而不是妥协。

So you can embrace AI with confidence, not compromise.

CrowdStrike。

CrowdStrike.

我们守护AI。

We secure AI.

我们阻止漏洞。

We stop breaches.

大家好，

Hello, and

欢迎收听《解码器》。

welcome to Decoder.

我是《The Verge》的主编尼尔·帕特尔，《解码器》是我的节目，聊的是大创意和其他问题。

I'm Neil I Patel, editor in chief of The Verge, and Decoder is my show about big ideas and other problems.

今天，我要和《The Verge》驻伦敦的AI记者罗伯特·哈特聊聊，AI正在对数学领域做什么，以及许多顶尖数学家因此面临的生存危机。

Today, I'm talking to Robert Hart, The Verge's London based AI reporter, about what AI is doing to the field of mathematics and the existential crisis that many leading mathematicians are having about it.

这里的新闻是，OpenAI刚刚发布了一组解决长期数学难题的方案，在数学界引起了轰动。

The news here is that OpenAI just published a set of solutions to long standing problems in math that went off like a bombshell in the field.

这在数学界引发了巨大争议，罗布采访了我们这个时代一些最有成就的数学家，聊了这件事。

It's caused a huge debate in the math community and Rob talked to some of the most accomplished mathematicians of our time about it.

有趣的是，AI系统在小学算术上仍然很糟糕，但在高端抽象数学上却越来越擅长。

It's funny that AI systems are still pretty bad at elementary school arithmetic, but they're getting increasingly good at very high end abstract math.

这一切都给高等数学领域带来了几个大问题。

All of this raises some big questions for the field of advanced mathematics.

如果人工智能能做这种水平的数学，那是不是意味着AI实验室可以把这些技能应用到其他领域呢？

If AI can do math of this caliber, does that mean AI labs can transfer those skills to other domains?

如果前沿模型直接解决了所有悬而未决的问题，那那些旨在培养新一代人类数学家、让他们在解决现有问题的同时发现新问题的学术资助和大学项目还有什么意义呢？

What good are the academic grants and university programs designed to train new generations of human mathematicians to identify new problems as they try to solve existing ones if the frontier models simply solve all of the outstanding questions.

也许最重要的是，如果所有这些对数学的关注只是前沿AI实验室的又一次营销活动，他们似乎根本不在乎这个最古老、最基础的学术学科之一会变成什么样。

And perhaps most importantly, what if all this attention to math is just another marketing exercise for the frontier AI labs who don't seem to care less about what happens to one of the oldest and most fundamental academic disciplines there is.

这里面的内容很多，Rob和很多人聊过，他们对这些事情各有各的看法。

There's a lot here and Rob talked to a lot of people with a lot of views on all of it.

好的。

Okay.

Verge的AI记者Robert Hart，聊聊AI对数学的影响。

Verge AI reporter Robert Hart on what AI is doing to math.

我们开始吧。

Here we go.

罗伯特·哈特，你是我们在伦敦的AI记者，在The Verge工作。

Robert Hart, you are our London based AI reporter here at The Verge.

欢迎来到Decoder。

Welcome to Decoder.

谢谢你的邀请。

Thank you for having me.

我很高兴能和你聊聊。

I am very excited to talk to you.

最近你深入研究了AI和数学，有很多事情发生。

There's a lot going on in particular with AI and math that you recently dove into.

你和很多顶尖数学家聊过，关于AI给数学带来的危机。

You spoke to a lot of leading mathematicians about the crisis in mathematics due to AI.

感觉事情很多，而且关于这两者之间的互动，还有很多未知和待发现的地方。

It feels like a lot and also like there's a lot yet to know and discover about the interaction of these two things.

一个完整的生存危机，这完全是Decoder喜欢的话题。

A full existential crisis, which is pure decoder bait.

大体跟我们说说发生了什么吧。

Broadly tell us what's going on.

我觉得“很多”这个词概括得挺到位的。

I think a lot sums it up quite well.

我的意思是，基本上，这有点像一场存在主义危机，关于数学到底是什么、数学家们在做什么、以及未来数学家的角色是什么。

I mean, basically, a bit of an existential crisis within what is mathematics, what are mathematicians doing, what is the role of mathematicians going forward.

而其中很大一部分是由AI能力的某种转变所引发的，这种转变在最近六个月到一年里可以说是爆发式的。

And a lot of that has been spurred by a phrase transition in what AI is capable that has kind of exploded would be a reasonable way of saying in the last six months to a year.

它从非常糟糕，一下子变得在专业层面上看起来真的很不错，时间非常短。

And it's gone from being very terrible to seemingly genuinely quite good at a professional level in a very short space of time.

所以我觉得，这就像其他领域过去五年一直在努力应对的问题，被压缩到了很短的时间里。

So I think it's a lot of what these other fields have been struggling to deal with for the last five years in a very compressed period of time.

我会把它和软件工程放在一起看。

I I would put that next to software engineering.

我们已经在软件工程领域经历了一段时间的AI危机。

We've been living through the AI crisis in software engineering for some amount of time.

但就在2024年，甚至去年，大家的普遍看法还是AI模型在数学方面特别差。

But as recently as 2024, even last year, the conventional wisdom was that AI models were particularly bad at math.

最著名的例子就是它们数不清单词strawberry里有多少个r。

The famous example is they could not count the number of r's in the word strawberry.

就连简单的数数都难住它们了。

Even just counting sort of eluded them.

那是什么让它们在数学上变好了呢？

What has happened to make them better at math?

它们是不是还是不太擅长基础算术，但擅长高等数学，还是说介于两者之间？

Are they still bad at, like, general arithmetic and they're good at advanced math, or is it something in between?

对。

Yeah.

我的意思是，它们在数学的某些领域确实还是特别特别差。

I mean, they are still truly, truly terrible at some areas of math.

比如，我真的去查过。

Like, I I did check.

现在他们能数草莓里的r了。

They can do strawberries now.

我觉得有人调整过。

I think someone's tweaked

我觉得草莓是硬编码进去的。

I think strawberry is hard coded.

我想说清楚一点。

I wanna be very clear.

我的阴谋论是，草莓那个问题是硬编码在那些模型里的。

My conspiracy theory is that the strawberry thing is hard coded in solid models.

我也这么觉得。

I think so.

我有两个。

I have two.

这个阴谋论我信。

That is a conspiracy I'll buy into.

不过，是的。

And, but yeah.

我的意思是，它在这些方面还是很差劲。

I mean, it's it's still terrible at those kind of things.

我是说，它就是数学。

I mean, it's math.

就是算术。

It's arithmetic.

我是说，连星期几都搞不清楚。

It's I mean, even the days of the week.

我男朋友前几天说，它老以为今天是星期三。

My boyfriend was saying the other day, he's it keeps thinking it's Wednesday.

其实不是星期三。

It's not Wednesday.

或者时间，我是说，几个月前，Alyssa Welly 好像写过，ChatGPT 不会看时间。

Or time, I mean, Alyssa Welly for for us a few months ago, think, wrote the chat GPT, can't tell time.

还是不行。

Still can't.

那并不是数学的全部。

That's not all of maths.

所以这里有一种脱节。

Like so there's this sort of disconnect.

我们总是认为，擅长数学就得擅长数数、加法或乘法。

Think we always equate, or to be good at math, you've got to be good at counting or adding or multiplying.

但很多其实是推理。

And a lot of it is reasoning.

如果你看学术数学论文，很多时候你不会看到数字，这正好说明了这一点。

If you look at academic math papers, a lot of the time you won't see numbers, which sums that one up, I think.

所以它们在这些方面还是很差，但现在在另一方面却非常擅长。

So they're still terrible, but they're now also very good at this other part.

至于为什么，我觉得在某个点上，这些系统能达到一个临界点。

And as to why, I mean, I think at some point you reach critical mass of what these systems can do.

就像我们之前说的，写作和编程方面我们已经看到了，它们很擅长在不同领域之间建立联系，或者用新方法应用旧知识，诸如此类的事情。

We've seen it as we said with writing, we've seen it with programming, and they're very good at kind of forging connections between different areas or applying old methods in new ways or or those kind of things.

而且看起来，他们训练的新模型似乎已经达到了那个临界点，突然就开窍了，现在能做数学了。

And it appears that the newer models they're training have apparently reached that level where it clicks, and now it can do math.

不过，也得说清楚，我们谈论它的时候，尤其是从外部来看，好像它是一个统一的学科。

I mean, it's important to say as well, like, it's we speak of it and especially from the outside as a sort of unitary discipline.

但想象一下，比如生物学，从直接观察动物、描述行为，一直到细胞机制和生物化学，范围很广。

But, mean, imagine, say, biology, you've got something that would range from, like, literally watching animals and describing behavior all the way through to, like, cellular mechanisms and biochemistry.

数学也不是一个统一的学科。

Like, math is not a unitary discipline either.

有些方面它真的很擅长。

Some bits it's really good at.

有些方面，比如数数，还是很差。

Some bits like counting, still really bad.

即使在更抽象的层面上，一些专家告诉我，拓扑学似乎是它仍然不太擅长的领域之一。

And even on the more kind of abstract levels of that, I mean, some experts told me that they floated topology as one area that it's apparently still quite bad at.

说实话，这个我没法验证。

I can't verify that, to be honest.

这超出了我的专业范围，但确实是这样。

It's beyond my own expertise, but it's still yeah.

情况有点复杂。

It's a bit of a mixed bag.

所以你把数学描述成一个巨大的领域，显然有很多很多学术方向，而且有些部分模型已经做得相当好了。

So you described mathematics as a huge field, obviously, many, many academic areas of interest and there are some parts where the models have gotten quite good.

有些部分，可能是人们认为数学最基本的部分，比如简单的计数，它们仍然很吃力，中间还有很大的范围。

Some parts, maybe the basic parts of the people think of as math, which is simply counting where they're they're still struggling and there's a wide range in the middle.

中间那个很大的范围是不是就是存在危机所在？

Is it the wide range in the middle where the existential crisis is?

人们不知道会发生什么，还是说危机在那些模型表现很好的部分？

People don't know what's gonna happen, or is it at the parts where it's really good?

两者都有。

Bit of both,

我觉得这会是贯穿整个讨论的一个主题。

which I feel is gonna be a running theme through this.

我的意思是，没人真的担心它只是个平庸的数学家，但显然，这个领域所做的事情影响巨大。

I mean, no one's really afraid of it being a mediocre mathematician, but obviously, there's a huge element of of what what this field does.

而且，从研究的角度来看，比如前沿领域，就像我们看到很多引起轰动的成果那样，它能做什么呢？

And, like, in terms of the research elements, like, cutting edge kind of as we see with a lot of the results that generate hype, like, what can it do?

现在有些领域它似乎能产出和优秀数学家相当的工作，但另一些领域，它连数都数不清。

There are areas now where it seems to be producing work that is on par with good mathematicians alongside other parts where, yeah, it can't count.

所以我觉得，所有这些都牵扯到它是否会重塑就业结构和资金结构。

So I think it's and and all caught up in that is whether it's going to kind of rewrite employment structures, funding structures.

而且，你还提出了一个模糊的问题：什么是数学知识？

I mean, you also raised the murky question of, what is mathematical knowledge?

还有这些工作者将要承担的角色。

Like and and the roles that these workers will be doing as well.

所以，所有这些问题都交织在一起。

So it's kind of all of that wrapped into one.

我觉得这跟AI在各个领域的崛起差不多，只要你能给问题增加算力或者计算能力，而且有一定的可验证性，模型似乎就会不断变好。

I think that tracks broadly with sort of the rise of AI in every field, where you can just add horsepower or compute to a problem and there's some kind of verifiability, it seems like the models continue to get better.

但在中间那些需要一些世界知识或者模型需要对世界本身有真正理解的部分，它们似乎就吃力了。

Everything in the middle where you might need some world knowledge or the models might need some actual intelligence about the world itself, they seem to struggle.

数学中那些部分，至少你文章里报道的和实验室在讨论的，看起来几乎都是完全自包含的理论问题，模型可以生成一个证明或者解决一个没人能解决的问题，然后尝试验证它确实存在，而且可以一遍又一遍地运行。

The parts of math, at least reported out in your piece and what the labs are talking about, they seem to be almost entirely self contained theoretical problems where the models can generate a proof or solve a problem that no one's been able to solve and then try to verify that that has existed and they can just run it again and again and again.

这就把我们带到了今年五月，一个我们其实没见过的OpenAI内部模型，推翻了一个80年历史的单位距离猜想。

That brings us I think to May of this year where an internal OpenAI model, which we have not really seen, disproved the unit distance conjecture, which is an 80 old problem.

然后就在最近，我们听说了OpenAI的Astra。

And then just recently, we heard about Astra from OpenAI.

Astra就是那个看起来像是开关被拨动，大家都觉得这是存在主义危机的那个。

Astra is the one where it seemed like the switch flipped and everyone decided it was an existential crisis.

Astra到底做了什么，为什么它这么重要？

What did Astra achieve and why is it a big deal?

我也很确定Astra可能也参与了之前那个问题。

I'm also pretty sure that Astra was probably behind the earlier one as well.

OpenAI只是把它列为一个未命名的内部模型。

OpenAI just listed it as a unnamed internal model.

那很可能就是Astra。

It's probably Astra.

我问他们的时候他们没回答，但就这样吧。

They didn't answer me when I asked, but there we go.

几周前，OpenAI发了一篇博客，还附了一大堆文件，我记得有几百页，用来证明这些成果。

OpenAI, a few weeks ago, dropped a blog along with a lot of paperwork, proving it, I think several 100 pages that they described.

他们称之为数学和理论计算机科学领域的十项进展。

They called it 10 advances in mathematics and theoretical computer science.

基本上就是一系列学科，他们声称最新的模型Astra在某种程度上解决了这些问题，我记得其中一个是量子博弈论，这个我完全不知道怎么解释。

It was basically an array of disciplines that they claimed the newest model Astra had solved in some capacity that ranged from I think one was in quantum game theory, which I don't know how to begin to explain.

更不知道怎么解释的是高维空间中的球体堆积问题，也就是超过三维的情况，还有其他很多不同的学科。

And even less how to explain is kind of there was seer packing in higher dimensions, so more than three dimensions, and there was sort of a lot of other different disciplines as well.

这确实在社区里引起了很大的轰动。

And it was I mean, yeah, it it caused a lot of stir in the community.

我觉得这有点像个重磅炸弹。

It was, I think, a bit of a bombshell.

我是说，就像我们之前说的，之前有过一些零星的突破，但一下子抛出十个，而且都是挺大的突破。

I mean, as we'd said, there'd been these individual breakthroughs that happened, but to drop 10 in one go, and they were quite big ones.

研究人员告诉我，是的，如果这些是人类解决的，我们会觉得很了不起。

I mean, researchers had sort of told me that, yeah, these were if if a human had solved these, we would be impressed.

如果一个人解决了全部十个，我们可能根本不会相信。

If a human had solved all 10, we probably wouldn't believe it.

我觉得重要的是，这些确实是他们真正关心的问题。

They're problems they actually care about as well, I think, is an important one.

之前很多突破都被指责为数学家不太在意的领域，而这些问题，优秀的数学家们花了很多时间试图解决，却没能解决。

A lot of kind of previous ones have been accused of areas that mathematicians didn't really bother with, and these are ones that mathematicians, good mathematicians have spent a lot of time trying to solve and had them.

我们得在这里暂停一下，插播一段广告。

We need to pause here for a quick break.

我们马上回来。

We'll be right back.

嘿，大家好，最近怎么样？

Hey, what's up guys?

我是Babish，In The Booth with Babish的主持人。

It's Babish, host of In The Booth with Babish.

在本周的节目中，我邀请了多米尼克·塞萨，他在A24的新电影《托尼》中饰演安东尼·波登。

On this week's episode, I sit down with Dominic Sessa, who plays Anthony Bourdain in the new A24 film, Tony.

我们聊了聊如何进入角色，扮演美食界最伟大的偶像之一，当然，还有他会在剧组里选谁上床、结婚或杀掉。

We talk about getting into character as one of food's greatest icons, and of course, which castmates he'd fuck, marry, or kill.

完整剧集请到YouTube观看，或者在你收听播客的任何平台收听。

Watch the full episode on YouTube or listen wherever you get your podcasts.

时间是你最重要的资产，而人工智能正在改变商业的速度。

Time is your most important asset, and AI is transforming the speed of business.

你的创新以及如何保护它，取决于你选择信任的技术。

Your innovation and how you protect it depends on the technology you choose to trust.

财富100强中有70%的企业信任CrowdStrike领先的AI原生网络安全平台，该平台旨在保护他们的业务以及推动其创新的AI。

70% of the Fortune one hundred trust CrowdStrike's leading AI native cybersecurity platform built to secure their business and the AI fueling their innovation.

人工智能正在改变世界。

AI is changing the world.

我们在守护它。

We're securing it.

CrowdStrike。

CrowdStrike.

我们阻止入侵。

We stop breaches.

本期节目由Rippling赞助播出。

Support for the show comes from Rippling.

想象一下，你刚发现销售团队可能完不成销售指标。

Imagine you just found out your sales team is at risk of missing quota.

别慌，直接问Rippling AI就行。

No need to panic, just ask Rippling AI.

因为它基于你的实时人事和业务数据，Rippling AI可以把Rippling和Salesforce的数据整合到一个会议用的仪表盘上，显示各区域的配额完成情况、人员编制趋势和月度收入与配额的对比。

Since it's built on your real time people and business data, Rippling AI can pull metrics from Rippling and Salesforce into a meeting ready dashboard showing quota attainment, headcount trajectory, and monthly revenue to quota by region.

几秒钟内，你就能清楚看到配额风险背后的原因，并在错过之前解决它。

In seconds, you can see exactly what's behind your quota risk and fix it before it's missed.

问题得到解答，行动已经采取，危机化解了。

Question answered, action taken, crisis averted.

所以，当你有关键的业务问题需要答案时，不要只是提交工单，然后等上几周才拿到过时的报告。

So when you have critical business questions that need answers, don't just file a ticket and wait weeks for an outdated report.

描述你的需求，让 Rippling AI 根据你的实时人员和业务数据立即构建，无论是带有详细图表的仪表板，还是带有正确触发器、条件和审批的自动化工作流。

Describe what you need and have Rippling AI build it instantly from your live people and business data, whether it's a dashboard with detailed charts or automated workflows with the right triggers, conditions, and approvals.

准备好推动你的业务了吗？

Ready to roll your business?

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Head to rippling.ai/decoder to get the only AI built to give you full visibility and take complex actions across your entire organization.

网址是 rippling.ai/decoder。

That's rippling.ai/decoder.

今天就注册，获取独家访问权限。

Sign up for exclusive access today.

我们回来了，和The Verge的Robert Hart聊聊AI的数学能力，以及这个月初发布的全新AI模型Astra。

We're back with The Verge's Robert Hart talking about AI's math capabilities and what happened earlier this month with an all new AI model called Astra.

我们来聊聊这十个。

Let's talk about these 10.

这些是你报道出来的。

They're you reported them out.

OpenAI确实提供了一些文档，但这些成果并不是凭空冒出来的。

OpenAI did produce some documentation, but they're not all entirely horse powered out of nothing.

对吧？

Right?

它们是基于之前的工作。

They're based on previous work.

这里存在一些归属问题。

There's some question of attribution.

他们的回应是什么？

What was the response?

是模型自己做到的，还是我们经常在AI领域看到的那种反应，基本上就是说，你偷了别人的东西，还不注明出处，你站在巨人的肩膀上，却提都不提。

Is it, oh, the models did this or was it the response we see to so much AI work which basically boils down to, well, you stole this and didn't attribute anyone and you've you've built on the shoulders of giants without mentioning it.

那大家的反应怎么样？

How did the response land?

总的来说，我采访到的人大多都挺 impressed 的。

By and large, it was generally one of being quite impressed from the people I spoke to.

就像我说的，这些都是数学家们关心的问题。

It was as I said, these are problems mathematicians cared about.

有一个问题特别引人注目，因为他们的致谢方式，还有他们在博客里宣布这些的方式。

There was one that drew particular attention for how they credited it and also how they just kind of announced all of this in their blog post.

OpenAI 一开始，我记得是说这10个问题。

OpenAI initially, I think it said that these are 10 problems.

过去十年都没有进展。

There have been no progress in the last ten years.

但如果你真的去读那些论文，其中一篇很清楚地写着，哦，我们是基于这两位研究者的进展。

And then if you actually read the papers, one of them, it quite clearly says, oh, we build on progress from these two researchers.

所以，我的意思是，后来这个说法也被悄悄地改了，但我接触的一些研究人员对此很不以为然，他们确实觉得这里面有这样一个问题：嗯，你确实没有给你在这里大量使用的东西署名，而且你自己也承认了这一点。

And so, I mean, that was later changed quite quietly as well, but a few of the researchers I spoke to were quite unimpressed and they they did feel it was an element of, well, yeah, you've not credited something that you've used heavily here and by your own acknowledgment.

话虽如此，我接触的一位被点名提到名字的研究人员，对整件事的态度也有点矛盾。

That said, one of the researchers I did speak to who was one of the ones named was a bit ambivalent on the whole thing as well.

真的是好坏参半。

It was a real mixed bag.

但我觉得，总的来说，除了这一点之外，可能有点夸大了之前已有的成果，不过后来他们纠正了这一点，这点还是值得肯定的。

But I mean, the general vibe I'd say other than this perhaps was oversold in terms of what came before, which was corrected to to their credit.

我觉得这算不上什么严重的问题，不过有一个人跟我描述的时候用了“草率”这个词。

I don't think it was anything other than I think the word sloppy was what was described to me by one person.

总体印象还是相当不错的。

The general impression was quite impressed.

真正让人在意的是那些实际的突破，而且确实推动了领域的发展。是的，就像我说的，如果这些成果是某位人类数学家做出来的，我觉得——实际上有好几位研究人员都说过，如果一位研究者解决了其中任何一个问题，他的学术生涯基本上就稳了。

Were actual breakthroughs that bothered people and it did move the field forward in a way that Yeah, as I said, if it was a human mathematician that had done these, I think I mean, several researchers actually said that, well, if a researcher had done any one of these problems, they'd probably be set for an academic career.

所以，是的，他们对成果本身印象深刻，但对其中一些成果的署名方式不太满意。

So, yeah, it was impressed with what it did if not the credit for some of them.

说起来挺有意思的，学术界的功劳归属就像整个游戏一样，而AI公司似乎能侥幸地马虎，而人类却不可能这样马虎。

Well, it's funny, you know, credit attribution in academia is like the whole game, and it seems like the AI companies get away with being sloppy in a way that no human would be able to get away with being sloppy.

发现的规模或工作本身是否弥补了这种马虎？

Did the scale of the discovery or the work overcome the sloppiness?

如果一个人完成了这些成就却同样马虎，反应会一样吗？

If a human had accomplished singles and had been as sloppy, would the reaction be the same?

我总觉得有点像是抄袭的成分。

I mean, part of me always wants to lean on the whole, like, oh, it looks like plagiarism kind of element.

但如果你真的去读他们写的论文，我是说，其中一位研究人员，大概全世界只有50个人会认真读这些内容。

But, like, if you actually read the papers they kind of produced, and I I mean, they're one of the researchers, I suppose, you said there's probably about 50 people in the world who are gonna bother reading through this in-depth.

其实很清楚。

It is very clear.

它并没有试图抄袭。

Like, it doesn't attempt to plagiarize.

我觉得说实话，只是新闻稿写得不好。

I think it was just a poor press release, to be honest.

虽然我有时候也挺想掺和一下的，但我觉得，毕竟我报道科学十多年了，新闻稿经常夸大实际发现的成果、重要性和新颖性。

And as as much as I love to to get in on it sometimes I mean, I find that having I suppose having covered science for a decade plus, the press releases are often overselling what discovery has actually been made and the import of it and the novelty of it.

我觉得这次的情况也不过是又一个例子罢了。

And I think that's just another case of what happened here.

这看起来是可重复的吗？

Does this seem repeatable?

他们提供了一些证据，证明他们解决了10个之前无法解决的问题。

There's some proof that they provided that they solved 10 problems that were unsolvable.

他们有没有提供任何证据，证明他们能再解决另外10个？

Do they provide any proof that they can solve another 10?

这就是问题所在。

That's the question.

而且，这也是个大未知数——天哪，我为此采访了将近十几个人，大家都想知道，他们为了得到这10个结果，到底尝试了多少次？

I mean, it's also so the big unknown from oh, god, the near dozen people I spoke to you for this was, well, how many did they try to get these 10?

谁知道呢？

Who knows?

他们知道，但他们不会说。

I mean, they know, but they won't say.

但这就是这里的大问题。

But that is the big question here.

就是说，不清楚他们到底尝试了多少次才得到这10个结果。

It's like, it's it's unclear how quite how many attempts it took to get these 10.

虽然这很厉害，但并不是说，我是说，如果这是他们第一次尝试就一下子拿出这10个令人印象深刻的结果，我会非常佩服。

Impressive as it is, it's not like that was I mean, I would be very impressed if it was the kind of first thing they sort of go and then out out come these 10 impressive results.

不清楚他们接下来会重点研究哪些领域，以及为什么。

It's unclear kind of what areas they would focus on next and why.

我想，他们选择公开哪些问题，可能是出于商业考虑，好让他们的模型能解决这些问题。

I mean, are, I imagine, business reasons as to putting together which problems they are choosing to publicize so their models can can do.

所以，是的。

So it's yeah.

而且所有AI实验室都在幕后招聘了一批资深数学家。

And they've all the AI labs have been hiring a sort of cohort of senior mathematicians behind the scenes.

所以我觉得，他们会不会再来一次，谁也说不准。

So it's anyone's guess, I think, as to whether they do it again.

但说到证明这个问题，我觉得数学在科学里算是个挺特别的学科，它的可重复性和实验科学不太一样。

But on the question of proof, I mean, maths is, I suppose, a bit it's an odd discipline in science and the repeatability is kind of not the same thing like with experimental sciences.

证明就是证明。

A proof is a proof.

如果它成立，那就是成立。

And if it works, it works.

问题在于，别人能不能看懂他们做了什么。

It's the problem here is, well, can people follow through what they've done?

每个领域都非常专业。

Each field is quite highly specialized.

所以会有那些领域的数学家去仔细检查。

So there'll be individual mathematicians who are in those fields that go through.

我采访过一些在这些领域工作的人，他们说看起来都很靠谱。

Those that I spoke to that worked in some of the fields that were covered here say it all looks very legit.

数学里还有一种叫Lean的编程语言，专门用来做计算验证。你可以把数学证明写成代码跑一遍，它基本上就能验证这个证明对不对。

There's also in maths there's a programming languagecomputational proving type thing called Lean where you can basically codify the mathematical proofs and run them through, and it kind of well, proves it.

我一直在说“证明”，其实它主要是检验整个推理过程的严谨性和假设是否成立，而且他们也已经把这个验证结果公开了。

I keep saying prove a lot here, but it it will test the rigor and the assumptions of everything going on there, and they've published that as well.

所以看起来确实是站得住脚的。

So it does appear to hold.

我接触过的人，虽然可能会说新闻稿里炒作成分比较多，但似乎没有人质疑他们声称的那些核心突破。

Like, no one I've spoken to, whilst they may say that the press release has a lot of hype or there's a lot of hype around it, no one seems to be doubting the kind of essential breakthroughs that they're claiming here.

我想在这个话题上再停留一下。

I wanna stay on this subject for one more second.

有数学证明。

There's the mathematical proof.

我们生成了一个证明，就像你说的，数学就是逻辑，所以它是可以重复验证的。

We've generated a proof and that is, as you say, just repeatable in a way that math is just logic.

你可以一步步检查，然后说这个证明是成立的。任何听过这个节目的人，如果高中时写过微积分证明，应该都记得那个过程。

You can just go through the steps and say this proof worked and anybody listening to this who had to suffer through writing a proof in calculus in high school probably remembers that process.

这里面有纯粹的逻辑部分。

There's something there that's pure logic.

然后还有一部分是软件代码，就像你提到的Lean，你可以把纯逻辑用代码表达出来，然后运行它看看是否有效。

Then there's a part of it that is software code as you're describing in lean, where you can take the pure logic, you can express it in code and you can run it to see if it works.

我理解AI在理论上擅长所有这些。

I understand how AI is theoretically good at all of that.

你只需要运行推理，推理会生成一些代码，然后运行代码，得到可验证的结果。

You're just you're just gonna run the reasoning and the reasoning is gonna generate some code, you're gonna run the code, get some verifiability.

我们在软件工程中已经看到这种情况，代码能运行或不能运行，可验证或不可验证，模型可以推理出来。

We've seen this play out in software engineering where the code runs or not, it's verifiable or not, and the models can just reason out about it.

然后，对我来说，你提到的那个大问题来了。

Then there's, to me, the the big question that you alluded to.

你需要运行多少次？

How many times do you have to run this?

我们能验证这些模型是自主完成的，而不是被实验室高薪聘请的人类数学家指导的吗？如果是那样的话，就说明这个领域要乱套了。

Can we verify that the models did this and they weren't directed by human mathematicians who've been hired at high rates by the labs in a way that suggests the field is going topsy-turvy?

你这里引用了詹姆斯·梅纳德的话，他获得了菲尔兹奖，这是数学界的最高荣誉，他说他一直在进行深刻的自我反思。

You have a quote here from James Maynard who has won the Fields Medal of the highest prize in in mathematics who said he's been soul searching.

我一直在看那句引用，你在文章里也引用了其他数学家的类似言论。

And I keep looking at a quote, you've got similar quotes from all these other mathematicians in the piece.

他们似乎都在反思一个他们自己都无法验证的事情，这有点讽刺，那就是模型是怎么做到这些的，以及这种能力是否具有可扩展性，从而对数学构成威胁。

And it seems like they're soul searching against a thing that kind of hilariously they cannot verify, which is how did the models do this, and is that thing scalable in a way that threatens mathematics?

关于模型是如何做到这些的，我们了解多少呢？

What do we know about how the models did this?

我觉得，关于这一点，我们知道的并不比平时多，甚至可以说，这里有几个问题。

I'd say as much as we normally do and do not know about this, it's I mean, are two I think there are a few issues kind of there.

一个是模型本身的特性。

One is the nature of the model as well.

这是一个未发布的模型，所以任何人想独立测试它，都只能祝你好运了。

This is an unreleased model, so good luck to anyone wanting to independently test it.

其实，任何专有模型都是这样。

I mean, the same if that goes with anything proprietary, really.

话虽这么说，我倒是倾向于相信他们，觉得他们在某种程度上没有撒谎，关于他们用的模型。

That said, I I'm inclined to kind of almost give the benefit of the doubt that they're not lying in some capacity about the models they're using.

至于另一方面，我觉得更值得关注的是我们怎么给模型提示，或者它是怎么被引导的，是不是由一个懂行的数学家来引导的。

As for the other part, I think it's perhaps more noteworthy on the kind of how do we prompt this or how is it being guided, and whether that's by a mathematician that knows what they're doing.

我觉得这可能是关键因素。我采访过的很多数学家，当他们尝试使用这些模型时——虽然通常是消费级模型，但这也反映了更广泛的现状。

I think that's probably a key factor here is a lot of mathematicians I spoke to when they've tried using these, and this is often the consumer models, but still it kind of speaks to a broader landscape.

他们说，如果你懂行，能指出问题，那模型就很好用。

And they say that if you know what you're doing and you can kind of point things out, it's good.

或者你可以把它当作一个工具，按你想要的方式使用，而如果你不知道怎么核实事实，你就做不到这一点。

Or or you can use it as a tool in a way that you kind of want and in a way that you wouldn't be able to if you didn't really know how to fact check it.

同时，我也遇到过这种情况，比如我用ChatGPT算个简单的加法，然后我说，这个数字不对。

I mean, same time as if I mean, I've had it where I've had chat GBT or saying doing a basic sum and I'm like, that number is not right.

它就说，非常抱歉。

It's like, we're so sorry.

你说得对。

You're right.

它还是错的。

It's this and it's still wrong.

但在这个层面上，这种能力还是需要的。

But, that's kind of still needed at this level as well.

我觉得这确实指向了一个更广泛的问题。

I think it does allude to a kind of broader problem.

就像你说的，这几乎是一种自我反思：如果我们能把它自动化，如果它发展到我们无法理解的地步，那会怎样？

You as you said, kind of this almost soul searching of, well, what if we can automate that away, and what if it gets to a point where we don't understand it?

这确实触及了一个更深层的问题，比如，数学到底是什么？

And that may really cuts to a deeper question of, like, well, what is mathematics?

我们为什么要研究数学？

Why do we do it?

为什么我们重视这个领域？

Why do we value it as a field?

我想每个人对此都有不同的答案。

I mean, everyone will have different answers to that, I think.

但我采访的很多人担心的是，这可能会超出人类兴趣的范围，那样的话，也许他们就不会去参与，或者它会成为感兴趣的人会去研究的东西，而其他人则照常继续。

But a fear of a lot of people I spoke to was that this might kind of move beyond the realm of human interest, and in which case, well, maybe they just won't engage with it, or it'll be something that interested people will go through and then the rest will kind of continue as normal.

你这里引用了一位苏黎世研究员约翰内斯·施密特的话，他说我们可能正走向一个局面，数学问题被AI“割草”般解决，但我们并没有真正推动领域前进，因为人类被排除在循环之外，他们要么不检查，要么不理解，要么不知道未来的突破可能在哪里。

You got a a quote here from a researcher in Zurich named Johannes Schmidt who says, we might be headed toward a situation where the math problems get, quote, mowed down by AI, but we don't actually push the field forward because humans are taken out of the loop and they're not either checking or they don't understand it or they don't know what the future breakthroughs might be.

这种情况发生的可能性有多大？

How likely does that feel?

这是个大问题吗？

Is that a big concern?

确实有这种成分，就是问题被“割草”般解决，尤其是那些被用作年轻数学家成长的训练场，让他们练手。

There is an element of that, of the of the mowing down of the problems and especially those are used as sort of a training field for younger mathematicians coming up and to kind of cut their teeth, so to speak.

但我也认为，这种把数学看作解决问题的观点，其实是局外人对数学事业的一种看法。

But I also think that kind of this problem solving idea in maths that that's that's what maths is is a very much outsider's perspective of the mathematical endeavor, I think.

所以我采访的很多数学家觉得，那种近乎打勾的部分，是领域中最无趣、最没价值的部分。

So a lot of the mathematicians I spoke to sort of found that almost tick box part the least interesting and valuable part of the field.

对他们来说，有价值的地方不是“你解决了什么”或“你证明了什么”。

Like, the the areas that are valuable for them aren't that, oh, you've solved something or you've proven something.

重要的是从那里发展出来的东西。

It's what happens from that.

我记得好像是詹姆斯·梅纳德说过，这个领域里最有趣的发现不是你解决了某个问题，而是从那个问题中衍生出来的东西。

And I I I think it was James Maynard that said that the most interesting kind of discoveries in this isn't that you've solved something, it's what evolves from that.

所以有时候，这些发现会开启全新的研究领域，是以前没人想到过的，或者是一种新工具，可以在各种有趣又令人兴奋的地方应用。

So is it like sometimes they open entire new fields of research that no one ever thought was possible or, oh, this is a new tool that you can apply everywhere, in fun and exciting ways.

我觉得我们也可以看看数学的普及化，比如我想到的是人们提出的那些定理。

I think if we look as well about what almost the kind of popularization of maths, like even kind of what I'm thinking of is kind of those theorems that people have posed.

真正持久的是问题本身，而不是解决方案。

It's the questions that endure, not the solutions.

就像人们总是记得费马大定理，而不是某个问题的具体解法。

Like, it's always kind of Fermat's last theorem, not like, well, here's the solution to whatever the last guy proposed.

我觉得这里的担忧是，AI会把这些所有的问题都一一解决掉。

I think the concern here is that, well, they're going to kind of tick off all of these questions.

通常在这个过程中，人们希望会衍生出新的令人兴奋的领域，或者提出新的问题，但AI不会这么做。

They're normally in the process of doing so, one would hope would branch out into all of these new exciting areas or pose new questions, but it won't do that.

这就是让人担心的地方。

That's the concern.

然后这会让这个领域变得很枯燥，所有问题都解决了，可能就没有什么可以继续探索的了。

And then that would kind of leave the field quite sterile, and it will have all of these things that have been done and maybe nothing left to pursue.

大家的普遍看法是，现在下结论还为时过早。

And the general consensus was, well, the jury's out.

现在说还太早。

It's too early to tell.

即使是人类数学家，也需要很长时间才能意识到这些事情的影响。

Like, even with human mathematicians, takes a lot of time to kind of realize the impact of these kind of things.

就像我说的，过去六个月到一年里，这个领域突然爆发了。我的意思是，数学本来就不是一个进展很快的学科，但现在真的还很难说这会不会成为一个问题，但它确实是个问题，而且是个大问题。

And it's as I said, it's kind of exploded in the last six months to a year, which I mean, math is not a fast moving discipline at the best of times, but it's it's too early to tell really whether whether that will then be a kind of concern, but it is a concern and a big one.

你这里还有一句梅纳德的话，他说，如果数学论文的发表标准是AI做不到的事情，而博士通常要读四年，那么挑战就在于，你要找的不是现在AI做不到的问题，而是四年后AI也做不到的问题。

You have another quote from Maynard here saying, if the standard for a publishable paper in math is something that an AI cannot do, particularly when a PhD is typically four years, the challenge is you're not trying to come up with a a problem that AI can't do now, it's an AI in four years time.

所以这其实和模型的进步速度有关，就像你说的，特别是在数学领域，进步似乎很快，但并不是在所有数学分支中都均匀地进步。

And so this is really related to the rate of improvement of the models, which as you say, particularly math, it seems to be increasing, but not at an even rate across all of the domains of mathematics.

这似乎就是引发大家深思的原因。

That appears to be what is causing the soul searching.

对吧？

Right?

如果你是个学生，今天刚开始，选了一个AI可能不太擅长的冷门领域，结果读到博士论文或研究做到一半，AI突然就把它解决了，那你就白干了。

If you're a student and you start today and you pick some obscure domain that maybe the AI isn't good at, sometime halfway through your PhD thesis or your PhD research, the AI will just solve it and you'll be done.

这对你来说真是个实实在在的问题。

And that is a real problem for you.

这个领域对此有反应了吗，还是大家还停留在震惊中，觉得老模型居然能开始做我们以为它们做不到的事情？

Is the field reacted to that yet or are they just in the shock of the old models can start to do things that we didn't think they were capable of?

是的。

Yeah.

我觉得真的就是震惊。

I think it's shock, really.

我每次做这些访谈都会带个小本子，专门记一些大致的感受，我在上面写了“创伤后应激”之类的词，因为感觉就是这样，而且虽然远不是普遍现象，但感觉事情发生得太快了，让很多人都措手不及。

I mean, I the little notebook I have whenever I do these interviews, I keep one to the side to to just do broad feelings, and I've written, like, shell shock in it because it just feels that it's and and it's it's far from universal, but it's it feels like it's happened so quickly that it has just taken a lot of people by surprise.

我的意思是，即使他们理论上知道，嗯，这迟早会来。

I mean, e even if it's they kind of knew in in theory that, well, this is coming.

他们看到各种AI数学初创公司纷纷涌现。

They've seen all these sort of start AI math startups kind of going.

他们看到同事们在不同实验室或工作领域之间流动。

They've seen colleagues being moving around to different, labs or kind of areas of work.

但，是的，这一切发生得太快了。

But, yeah, it's just happened very, very quick.

所以这让他们几乎没有时间去弄清楚，甚至不一定是在哪些领域它可能擅长。

And so it's given them very little time to kind of figure out what it's not necessarily even the fields that it might be good at.

更多的是，嗯，它能做什么？

It's more just like, well, like what can it do?

就像，事情发生得如此之快，以至于如果我想想六个月前，我想到的是英国的一个学年，从十月到十月，但我无法想象如果我在学习时遇到这种情况，在半年内它就能颠覆一切可能性。

Like, it's just that's how quickly it's happened is that like, if I think like what six months, I'm thinking of like an academic year in The UK from, well, it goes from like October through to well, October, but I can't imagine how when I was studying if something like this had come out and literally in the space of half a year, it just upended what was possible.

而且还是在夏天，所以学生们可能在假期后回到一个完全不同的学科。

And over the summer as well, so students are possibly coming back to a completely different discipline after a break.

我们得先休息一下。

We have to take on a short break.

我们马上回来。

We'll be back in just a minute.

今年夏天美国人对数据中心意见很大，但别忽略了人们对Flock的愤怒。

People are big mad about data centers in The United States this summer, but don't sleep on how mad people are about flock.

如果你没注意到Flock摄像头，别担心。

Flock cameras, if you haven't noticed them, don't worry.

它们已经注意到你了。

They've noticed you.

你可能在短视频或者Flock Talk上听说过它们。

You may have heard about them in your reels or on Flock Talk.

我这辈子从没像现在这样对政府这么生气，就因为有了Flock摄像头。

I have never in my life been as pissed at the government as I am now that flock cameras exist.

美国人正在跟Flock的AI监控摄像头开战，人们直接去把那些摄像头锯掉，彻底毁掉它们。

Americans are going to war against flock AI surveillance cameras, and people are going around and literally sawing them down, absolutely destroying them.

AI监控系统违背了我们国家自由和核心价值观的根本。

An AI surveillance apparatus goes against the very essence of freedom and the core values of our country.

这是不对的。

It's not right.

这不保守，也绝对算不上美国精神。

It's not conservative, and it sure as hell ain't American.

Flock监控摄像头已经遍布全国，除了阿拉斯加，每个州都有。

The flock surveillance cameras have popped up all over the nation, every state but Alaska.

但今年，全国几十个城市和县已经和Flock断绝了关系。

But this year, dozens of cities and counties across the country have cut ties with flock.

在今天的Vox《Explain》节目中，我们会告诉你原因。

And on today's Explain from Vox, we're gonna tell you why.

我们请回了The Verge的Robert Hart，来聊聊为什么数学家们对AI给这个学科带来的影响如此担忧。

We're back with The Verge's Robert Hart discussing why mathematicians are so concerned about what AI is doing to the discipline.

在这个领域里，确实存在一些怀疑的声音。

There's some skepticism here in the world.