当代最伟大的数学家：英语精读讲义

You don't usually see crowds gathering for a math professor,

通常你不会看到人群为一位数学教授而聚集，

but Terence Tao is anything but ordinary. 習語

但 Terence Tao（陶哲轩）绝不普通。

By the age of two,

在两岁时，

he taught himself to read and count.

他就自学了阅读和数数。

By nine,

到了九岁，

he was studying university-level math.

他已经在学习大学水平的数学了。

And by 20,

而到二十岁，

he graduated with a PhD from Princeton.

他就获得了 Princeton 的博士学位。

Most math geniuses are considered a little strange.

多数数学天才都被认为有些奇怪。

Isaac Newton was intense and obsessive.

Isaac Newton 情绪暴躁且偏执。

John Nash was paranoid with delusions.

John Nash 患有妄想症。

Grigori Perelman withdrew almost completely from public life.

Grigori Perelman 几乎完全退出了公众视线。

My videos on them are linked in the description.

关于他们的视频链接都在描述栏里。

On the other hand, 表達脈絡

另一方面，

Tao is super normal.

Tao 却非常正常。

That's a credit to his parents. 短語搭配

这要归功于他的父母。

His mom,

他的妈妈，

a high school math teacher from Hong Kong,

一位来自香港的高中数学老师，

and his father,

还有他的爸爸，

a pediatrician,

一位儿科医生，

raised him and his two younger brothers in Adelaide, Australia.

在澳大利亚的阿德莱德抚养他和他的两个弟弟。

They didn't push him relentlessly,

他们没有冷酷地逼迫他，

ensuring he would develop emotionally and socially,

而是确保他在情感和社交上得到发展，

even though they knew he was special.

即便他们知道他很特别。

When he was two,

两岁时，

he taught children twice his age how to count using wooden blocks. 語法

他就用木块教比他大一倍的孩子如何数数。

As a child,

在孩童时期，

he was assessed to have an IQ over 160,

他被评估为智商超过160，

and he scored 760 on the math portion of the SAT 文化背景

他在 SAT 的数学部分考了760分，

when he was just eight years old.

而那时他才仅仅八岁。

He was hooked on math 習語

他迷上了数学，

when he realized it could help explain the world,

当他意识到数学可以帮助解释这个世界，

like how satellites can guide millions of drivers

比如卫星是如何引导数百万驾驶员，

to within a few meters 短語搭配

精确到几米之内，

using precise geometry and orbits.

所用的就是精密的几何学和轨道知识。

What sets Tao apart is how he thinks. 講解

让 Tao 脱颖而出的是他的思考方式。

When he struggled with a problem involving rotating waves,

当他在解一道关于旋转波的难题时，

this is how he came up with the solution. 短語動詞

他是这样想出解决办法的。

You know, I tried to visualize

你知道，我试图想象

being the wave that the equation was

自己就是那个方程式

uh was modeling.

呃，正在模拟的波。

And I remember having my eyes closed on the floor.

我记得我闭着眼睛躺在地板上。

I was rolling around

我在地上滚来滚去，

trying to imagine how different parts of the wave evolved.

试图想象波的不同部分是如何演变的。

Um and uh in fact,

嗯，呃，事实上，

I was staying at my aunt's place at the time

当时我正住在我姑姑家，

and she saw me rolling on the floor,

她看到我在地板上打滚，

and I couldn't explain what I was doing.

而我也无法解释我在做什么。

But I did actually understand 語法

但我确实明白了，

um I found a way to transform the solution

嗯，我找到了一种转换解法的方法，

to make it easier to solve. 語法

让它变得更容易解决。

And it actually helped quite a lot to...

这真的有很大的帮助……

so physically physically do that.

像那样进行身体上的动作。

For the longest time,

在很长一段时间里，

he didn't think being a mathematician was a real career

他并不认为当数学家是一份真正的职业，

and figured he'd end up as a shopkeeper balancing the books. 講解

并以为自己最终会成为一名算账的店主。

But when his undergraduate advisor stepped in, 短語動詞

但是当他的本科导师介入后，

everything changed.

一切都改变了。

His advisor encouraged him to focus on mathematical research

他的导师鼓励他专注于数学研究，

and to study abroad.

并出国留学。

When Tao applied to Princeton,

当 Tao 申请 Princeton 时，

his application included a letter of recommendation

他的申请材料中包含了一封推荐信，

from the great Hungarian mathematician Paul Erdős.

来自伟大的匈牙利数学家 Paul Erdős。

I am sure he will develop into a first-rate mathematician

“我确信他将成长为一名一流的数学家，

and perhaps into a really great one.

甚至可能成为一位真正伟大的数学家。

I recommend him in the highest possible terms. 短語搭配

我以最高评价向您推荐他。”

Tao would become famous for tackling problems involving prime numbers.

Tao 后来因为攻克涉及质数的难题而声名鹊起。

One of the reasons he won the Fields Medal, 文化背景

这也是他赢得 Fields Medal 的原因之一，

the Nobel Prize of math, in 2006.

该奖项在2006年被誉为数学界的诺贝尔奖。

Prime numbers are divisible only by one and themselves. 用詞

质数只能被一和它本身整除。

And as numbers grow larger,

随着数字越来越大，

primes become rarer

质数变得越来越稀少，

with ever-increasing gaps between them.

它们之间的间隔也不断增加。

For centuries,

几个世纪以来，

mathematicians wondered,

数学家们都在想，

do primes behave randomly,

质数的分布是随机的吗，

or is there hidden order beneath the surface? 習語

还是表面之下隐藏着秩序？

In 2004,

在2004年，

Tao and British mathematician Ben Green proved

Tao 和英国数学家 Ben Green 证明了，

that no matter how sparse prime numbers become, 語法

无论质数变得多么稀疏，

you can always find long sequences of evenly spaced primes, 用詞

你总能找到由等距质数组成的长序列，

called arithmetic progressions,

也就是等差数列，

if you look far enough.

只要你找得足够远。

3, 5, and 7

3、5和7

are prime numbers spaced evenly by two.

是间距均匀为2的质数。

That's an arithmetic progression of length three.

那是一个长度为3的等差数列。

There are longer ones.

还有更长的。

7, 37, 67, and 97

7、37、67和97

are all prime,

都是质数，

each separated by 30,

每个间隔为30，

with an arithmetic progression of length four.

组成了一个长度为4的等差数列。

However far out you go, 語法

无论你探索得多远，

sequences like this exist for whatever length you desire.

无论你想要多长的序列，这样的序列都存在。

They didn't prove it by hunting for patterns one by one. 習語

他们并不是通过逐一寻找规律来证明的。

They used powerful tools from different branches of math

他们使用了来自不同数学分支的强大工具，

to show that the structure of the primes

来证明质数的结构

forces these progressions to exist. 語法

必然会导致这些数列的存在。

Tao compared the idea to counting grains of sand in a box. 短語搭配

Tao 将这个想法比作数盒子里的沙粒。

You don't count each grain one by one.

你不会一粒一粒地去数。

You weigh the box,

你会称一下盒子的重量，

subtract the container,

减去容器的重量，

and divide by the average weight of a single grain

然后除以单粒沙子的平均重量，

to get an accurate count of how many are likely to be inside.

从而得出里面可能有多少沙粒的准确数字。

Unlike many mathematicians who spend a lifetime specializing in one area,

与许多一生只专注于一个领域的数学家不同，

Tao moves freely across math fields,

Tao 在数学各个领域中游刃有余，

often working collaboratively.

并经常与人合作。

One day in 2004,

2004年的一天，

Stanford mathematician Emmanuel Candès

Stanford 的数学家 Emmanuel Candès

brought Tao a problem he'd run into 短語動詞

把他在与放射科医生合作时

while working with radiologists.

遇到的一个问题带给了 Tao。

They were trying to make MRI scans faster,

他们试图让 MRI 扫描更快，

but the math just wasn't working.

但数学计算却总是行不通。

That conversation led them to launch an entirely new field,

那次对话促使他们开创了一个全新的领域，

compressed sensing. 用詞

压缩感知。

To understand compressed sensing,

要理解压缩感知，

think about an image.

想象一张图片。

If you delete pixels,

如果你删除像素，

the information is gone and the image is ruined.

信息就会丢失，图片也就毁了。

But compressed sensing doesn't see pixels, 表達脈絡

但压缩感知看到的不是像素，

it sees patterns.

它看到的是模式。

If an image has sufficient underlying structure,

如果一张图片有足够的底层结构，

you don't need to record every pixel to recover it.

你就不需要记录每一个像素来还原它。

Even if some of the information is discarded, 語法

即使丢弃了一些信息，

you can still reconstruct the original image.

你仍然可以重建原始图像。

Here's a simple analogy.

这里有一个简单的类比。

You can probably read this without much trouble.

你大概可以毫不费力地读出这句话。

Even if lots of letters are missing,

即使丢失了很多字母，

you can still read it because English has structure.

你仍然能读懂，因为英语有其结构。

Their work led to faster MRI scans

他们的工作不仅让 MRI 扫描变得更快，

and also attracted the military,

还吸引了军方的注意，

where the goal is often to see an area using many simple sensors

军方的目标通常是使用许多简单的传感器来观察一个区域，

rather than relying on extremely expensive ones. 語法

而不是依赖极其昂贵的传感器。

Work like this made him quickly stand out. 短語動詞

像这样的工作让他迅速脱颖而出。

He became a tenured professor at UCLA when he was 24, 文化背景

他在24岁时成为 UCLA 的终身教授，

teaching students who were almost the same age.

教授的学生几乎和他同龄。

He later married Laura,

后来他与 Laura 结婚，

a former student of his,

她曾是他的学生，

who went on to become an engineer at NASA's Jet Propulsion Laboratory. 短語動詞

后来成为 NASA Jet Propulsion Laboratory 的工程师。

Together,

在一起后，

they have two children,

他们有两个孩子，

and he's passed his spark of curiosity on to them. 短語動詞

他也把自己的好奇心传递给了他们。

When his son was four,

当他的儿子四岁时，

Tao would ask questions like, 語法

Tao 会问一些这样的问题，

"If there are 10 cookies and five people in the living room,

“如果客厅里有10块饼干和5个人，

how many does each person get?"

每个人能分到多少块？”

His son also showed a strong inclination toward languages,

他的儿子也表现出了强烈的语言倾向，

unlike Tao,

这与 Tao 不同，

who struggled with English and Latin in school.

Tao 在学校时英语和拉丁语成绩并不好。

He preferred mathematics,

他更喜欢数学，

where answers were concrete,

因为数学的答案是具体的，

true or false,

非真即假，

right or wrong.

非对即错。

At one point,

有一次，

a hedge fund approached him,

一家对冲基金联系了他，

eager to put his extraordinary mathematical mind to work in finance, 習語

渴望将他非凡的数学头脑用于金融领域，

a job that would have been extremely lucrative, 語法

那份工作绝对利润丰厚，

but he turned it down for the pure joy of staying in academia. 短語動詞

但他拒绝了，只因为享受留在学术界的那份纯粹的快乐。

And while he's certainly not hurting for money, 習語

虽然他确实不缺钱，

his UCLA professorship pays handsomely,

他在 UCLA 的教授职位薪水丰厚，

with public records showing he earned 784,000 in 2024.

公开记录显示他在2024年的收入为78.4万美元。

He's been more interested in the questions that fascinate him 語法

但他一直对自己感兴趣的问题更为痴迷，

than in the dollars they might generate.

而不是它们可能带来的金钱。

One of those fascinating questions is whether AI can solve

其中一个引人入胜的问题是，AI 是否能解决

long-standing open problems in pure mathematics. 用詞

纯数学领域长期悬而未决的公开问题。

Tao has been tracking how AI tools

Tao 一直在跟踪 AI 工具

like advanced versions of ChatGPT

比如高级版本的 ChatGPT

tackle unsolved puzzles by Paul Erdős,

如何处理 Paul Erdős 留下的未解难题，

even maintaining a public database of these attempts.

甚至还维护了一个公开的尝试数据库。

Recently,

最近，

ChatGPT solved Erdős's problem number 281,

ChatGPT 解决了 Erdős 的第281号问题，

generating a proof that has held up under expert review. 短語動詞

并生成了一个经得起专家审查的证明。

Tao called it perhaps the most unambiguous

Tao 称这或许是最明确无误的

instance of AI independently solving an open problem.

AI 独立解决公开问题的案例。

Today,

如今，

Terence Tao is one of the most recognizable mathematicians in the world.

Terence Tao 是世界上最著名的数学家之一。

He is so sought after that his website includes a simple notice, 語法

他非常受欢迎，以至于他的网站上包含了一条简单的通知，

"I am declining almost all interviews at this time." 語氣意圖

“目前我拒绝几乎所有的采访。”

I reached out as well, 短語動詞

我也试着联系了他，

knowing full well the answer might be no. 短語搭配

虽然我很清楚答案可能是“不”。

If I do hear back, 短語動詞

如果我确实收到了回复，

I'll leave an update in a pinned comment.

我会在置顶评论里更新。

Despite the attention,

尽管备受瞩目，

the Mozart of math has remained remarkably humble. 習語

这位数学界的 Mozart 却保持着非凡的谦逊。

That attitude reflects the Chinese philosophy he grew up with,

这种态度反映了他从小接触的中国哲学，

which emphasizes humility.

强调谦虚。

As his father put it,

正如他父亲所说，

"Even if you are very successful,

“即使你非常成功，

you tend to say,

你也会倾向于说，

"No, I'm just pretty average."

‘不，我只是挺普通的。’”

In Terence Tao's case,

但在 Terence Tao 身上，

that couldn't be further from the truth. 習語

事实并非如此。

Tao wants to teach more non-mathematicians how to think mathematically,

Tao 想要教导更多非数学家如何用数学方式思考，

saying, "I believe you can teach this to almost anybody."

他说：“我相信你可以把这门学问教给几乎任何人。”

And he's right,

而且他是对的，

if you're taught the right way.

前提是你使用了正确的教学方法。

That's one of the reasons I love using Brilliant.

这就是我喜欢使用 Brilliant 的原因之一。

It's a completely different way of learning.

这是一种完全不同的学习方式。

Instead of passively sitting through lectures, 講解

不是被动地坐在那里听课，

you're actively solving problems step by step,

而是主动地一步一步去解决问题，

learning intuitively.

进行直观地学习。

I've been playing around with Brilliant's exponential functions. 短語動詞

我一直在把玩 Brilliant 的指数函数课程。

What's great is how interactive it is.

最棒的是它的互动性。

It just clicks way more naturally. 習語

它让你理解起来更加自然流畅。

Brilliant has a range of courses in algebra and calculus

Brilliant 提供了一系列代数和微积分课程，

that meet you at your skill level 習語

能匹配你的技能水平，

while letting you challenge yourself and grow.

同时也能让你挑战自我、不断成长。

They also have a whole host of courses in coding, 短語搭配

他们还有大量编程课程，

science,

科学，

and AI,

以及 AI 领域的课程，

all built around learning by doing. 講解

全都是围绕“边做边学”的理念构建的。

You can start learning for free at brilliant.org/newsthink

你可以在 brilliant.org/newsthink 免费开始学习，

or scan the QR code on your screen.

或者扫描屏幕上的二维码。

Brilliant's also giving you 20% off their annual premium subscription

Brilliant 还提供年度高级订阅的20%折扣，

if you use my custom link in the description,

只要你使用描述栏里我的专属链接，

giving you unlimited access to thousands of lessons.

你就能无限次访问数千节课程。

Thanks for watching.

感谢收看。

For Newsthink,

我是 Newsthink 的

I'm Cindy Pom.

Cindy Pom。