破解百万美元数学难题后神秘消失的男人：英语精读讲义

In 2000,

2000年，

the world's leading mathematicians gathered in Paris

全球顶尖的数学家齐聚巴黎，

to identify seven of the most important unsolved problems in their

旨在评选出他们领域内七个最重要的未解

field. The nonprofit Clay Mathematics Institute organized the meeting

难题。非营利组织克雷数学研究所组织了这场会议，

and pledged a million dollars to the first person to solve any of the seven Millennium problems. 短語搭配

并承诺向首位解决七个千禧年大奖难题中任意一个的人颁发一百万美元的奖金。

So far, only one has been solved.

到目前为止，只有一个难题被解决了。

In 1904, French mathematician Henri Poincaré posed this problem about the nature of space.

1904年，法国数学家亨利·庞加莱提出了这个关于空间性质的问题。

He suggested that if you have a three-dimensional space with no holes,

他提出，如果你有一个没有洞的三维空间，

it can be made into a sphere without ripping or cutting it.

无需撕裂或切割，就可以把它变成一个球体。

For example,

例如，

a blob could be formed into a sphere.

一团水滴可以被塑造成一个球体。

But it gets more interesting than that.

但事情比这更有趣。

To a topologist, a ball and a pillow are the same

在拓扑学家看来，球和枕头是一样的，

because they can be reshaped into one another.

因为它们可以被互相改变成对方的形状。

Similarly, a bagel and a mug are the same because they both have one hole,

同样，贝果（百吉饼）和马克杯也是一样的，因为它们都有一个洞，

making them topologically equivalent even though they're not spheres.

即使它们不是球体，在拓扑学上它们也是等价的。

Poincaré suggested that anything without holes is equivalent to a sphere,

庞加莱认为，任何没有洞的物体只要足够小，就等同于一个球体，

so long as the object is small enough. 語法

只要这个物体足够小。

It can't extend infinitely in any direction.

它不能在任何方向上无限延伸。

He believed his conjecture to be true, 語法

他相信自己的猜想是正确的，

but couldn't prove it.

但无法证明它。

His conjecture was generalized to any number of dimensions,

他的猜想后来被推广到了任意维数，

including four dimensions,

包括四维，

which was particularly challenging to solve.

这尤为难以证明。

That left the three-dimensional case,

这就剩下了三维的情况，

Poincaré's original conjecture,

即庞加莱最初的猜想，

which frustrated mathematicians for a century,

它让数学家们沮丧了整整一个世纪，

until 2002,

直到2002年，

when a mysterious paper floated on the internet. 習語

当一篇神秘的论文出现在互联网上。

Within this paper was a solution to the Poincaré conjecture.

这篇论文中包含了庞加莱猜想的解答。

The author was Russian mathematician Grigori Perelman,

作者是俄罗斯数学家格里戈里·佩雷尔曼，

known as Grisha.

大家叫他格里沙。

Grisha grew up in the Soviet Union

格里沙在苏联长大，

and attended an elite high school in St. Petersburg specializing in math.

并在圣彼得堡一所专攻数学的精英高中就读。

Unlike the other exceptional kids in class,

与班上其他天赋异禀的孩子不同，

he was never distracted.

他从不分心。

He just sat and listened.

他只是坐在那里听讲。

He even refused to eat his lunch,

他甚至拒绝吃午餐，

as his teacher Valery Ryzhik told author Masha Gessen in her book on Grisha,

正如他的老师瓦列里·雷日克在玛莎·格森关于格里沙的书中提到的，

"Maybe his entire nervous system was so tuned to the learning process 語法

“也许他的整个神经系统都高度适应于学习过程，

that he could not stray from it."

以至于他根本无法分心。”

At 16,

16岁时，

he won a gold medal at the International Mathematical Olympiad with a perfect score.

他以满分赢得了国际数学奥林匹克竞赛的金牌。

Being part of the Soviet Olympiad team

作为苏联奥林匹克代表队的一员，

meant he could be admitted to Leningrad State University without having to take the entrance exams. 語法

这意味着他无需参加入学考试即可被列宁格勒国立大学录取。

The university was notoriously discriminatory,

这所大学因歧视而臭名昭著，

admitting only two Jewish students a year.

每年只招收两名犹太学生。

but Grisha's place on the team allowed him to bypass this quota. 用詞

但格里沙在代表队的地位让他得以避开这个名额限制。

After completing his studies,

完成学业后，

he did graduate work at the renowned Steklov Mathematical Institute St. Petersburg branch,

他在著名的斯捷克洛夫数学研究所圣彼得堡分所攻读研究生，

unheard of for a Jew. 習語

这对犹太人来说是前所未闻的。

Grisha was accepted because influential figures like mathematician Alexander Alexandrov campaigned on his behalf 短語搭配

格里沙之所以被录取，是因为像数学家亚历山大·亚历山德罗夫这样有影响力的人物为他奔走，

and offered to supervise him.

并提出愿意担任他的导师。

When Grisha began his grad work in 1987,

当格里沙在1987年开始读研时，

the Iron Curtain was starting to lift, 文化背景

铁幕开始拉开，

allowing Soviet citizens to travel abroad for the first time in decades.

几十年来第一次允许苏联公民出国旅行。

The renowned mathematician Mikhail Gromov arranged for Grisha to give talks in the US on geometry,

著名数学家米哈伊尔·格罗莫夫安排格里沙在美国举办几何学方面的讲座，

his area of expertise.

这也是他的专长领域。

Gromov mentioned Grisha to the right people,

格罗莫夫向对口的人士推荐了格里沙，

ensuring he was invited to do postdoctoral work at NYU's Courant Institute of Mathematical Sciences

确保他受邀前往纽约大学库朗数学科学研究所进行博士后研究，

and Stony Brook University.

以及石溪大学。

Besides math,

除了数学，

his other passion was walking from Manhattan all the way to South Brooklyn

他的另一大爱好是从曼哈顿一直走到南布鲁克林，

to get his special black bread from a Russian shop.

去一家俄罗斯商店买他特别喜欢的黑面包。

He later moved to the West Coast to take up a prestigious fellowship at UC Berkeley. 短語動詞

后来他搬到了西海岸，接受了加州大学伯克利分校享有盛誉的研究员职位。

Once his fellowship came to an end,

一旦他的研究员任期结束，

top American universities tried to poach him. 用詞

美国顶尖大学纷纷试图挖走他。

Princeton's top brass were so impressed by his guest lecture, 習語

普林斯顿大学的高层对他的客座讲座印象极深，

they approached him about becoming an assistant professor

他们与他接洽，希望他成为助理教授，

and asked for his CV.

并向他索要简历。

Grisha reportedly responded,

据报道，格里沙回答说：

"Why would you need any more information?"

“你们还需要什么更多信息呢？”

Masha Gessen's book describes how Grisha didn't want to settle for anything less than a tenured position, 短語動詞

玛莎·格森的书描述了格里沙如何不愿屈就于任何低于终身教职的职位，

whereas the university wanted the 29-year-old to earn his way there. 習語

而大学方面却希望这位29岁的年轻人靠自己努力去争取。

When Tel Aviv University,

当特拉维夫大学，

where Grisha's sister was studying mathematics,

也就是格里沙的妹妹学习数学的地方，

offered him a full professorship,

向他提供正教授职位时，

he rejected that too.

他也拒绝了。

He explained he could work better back in his homeland

他解释说，回到祖国他能工作得更好，

and returned to Russia to the Steklov Institute.

于是他回到了俄罗斯的斯捷克洛夫研究所。

What he was working on, 語法

他当时在研究什么，

nobody knew.

无人知晓。

Grisha was quietly tackling one of the toughest problems in math.

格里沙正在默默攻克数学界最难的难题之一。

How did he prove Poincaré's conjecture?

他是如何证明庞加莱猜想的呢？

Well,

嗯，

he managed to prove another conjecture,

他设法证明了另一个猜想，

which indirectly proved Poincaré's.

从而间接证明了庞加莱猜想。

In the late 70s,

在70年代末，

American mathematician William Thurston suggested that any 3D shape can be decomposed into eight different geometric structures,

美国数学家威廉·瑟斯顿提出任何三维形状都可以分解为八种不同的几何结构，

and one of these eight shapes is the three-dimensional sphere,

这八种形状之一就是三维球体，

which is central to Poincaré's conjecture.

这正是庞加莱猜想的核心。

Thurston never managed to prove his own theory,

瑟斯顿一直未能证明自己的理论，

but American mathematician Richard Hamilton gave it a go, 習語

但美国数学家理查德·汉密尔顿进行了尝试，

trying to tackle both Poincaré's and Thurston's conjectures.

试图同时攻克庞加莱和瑟斯顿的猜想。

He couldn't prove them,

他未能证明它们，

but he did develop the blueprint that helped Grisha finally crack the century-old mystery. 習語

但他确实制定了蓝图，帮助格里沙最终解开了这个世纪之谜。

Grisha relied on Hamilton's powerful mathematical tool called Ricci flow to study shapes.

格里沙依靠汉密尔顿称为“里奇流”的强大数学工具来研究形状。

Think of Ricci flow like heat spreading through an object, 表達脈絡

可以把里奇流想象成热量在物体中扩散，

smoothing out bumps and irregularities over time. 短語動詞

随着时间的推移，使凹凸和不规则的地方变得平滑。

As Ricci flow progresses,

随着里奇流的推进，

certain regions can become very thin,

某些区域会变得非常薄，

forming necks.

形成“颈部”。

Grisha used a process called surgery to cut off these necks to study the pieces separately.

格里沙使用了一种叫做“手术”的过程来切断这些颈部，以便单独研究各个部分。

He realized that these pieces ultimately represented the simple shapes

他意识到这些部分最终代表了简单的形状，

that correspond to the structures predicted by Thurston's conjecture.

这与瑟斯顿猜想预测的结构相对应。

So,

因此，

by solving Thurston's conjecture,

通过证明瑟斯顿猜想，

he in turn proved Poincaré's. 表達脈絡

他也顺带证明了庞加莱猜想。

Grisha published three papers totaling 992 pages.

格里沙发表了三篇论文，总计992页。

When he uploaded the first to arxiv.org,

当他将第一篇上传至 arxiv.org，

a public forum operated by Cornell University,

一个由康奈尔大学运营的公共论坛时，

he emailed about a dozen American mathematicians to give them the heads up. 習語

他给十多位美国数学家发了电子邮件，提前通知了他们。

This was totally out of the blue. 習語

这完全出乎意料。

He hadn't spoken to his colleagues for years

他已经多年没有和同事们说过话了，

and barely responded to their emails.

也几乎不回复他们的邮件。

Mathematicians spent over three years scrutinizing his proof to see if he had really solved the problem.

数学家们花了三年多时间仔细审查他的证明，以确定他是否真的解决了这个问题。

But Richard Hamilton was not one of them.

但理查德·汉密尔顿并不在其中。

Grisha was apparently hurt that Hamilton,

显然，格里沙感到很受伤，因为汉密尔顿，

whose foundational work he relied on for his proof,

这位他证明过程中所依赖的奠基性工作的主人，

showed little interest in his achievement.

对他的成就似乎兴趣不大。

Grisha told the New Yorker,

格里沙告诉《纽约客》：

"I had the impression he had read only the first part of my paper."

“我的印象是他只读了我论文的第一部分。”

Why was Hamilton so apparently disinterested?

为什么汉密尔顿显得如此漠不关心？

As author Masha Gessen put it, 表達脈絡

正如作家玛莎·格森所说：

"It took Perelman less than half of his first paper to get past the point at which Hamilton had been stuck for two decades.

“佩雷尔曼只用了第一篇论文不到一半的篇幅，就突破了汉密尔顿停滞二十年的瓶颈。

No wonder Hamilton was silent.

难怪汉密尔顿保持沉默。

One can only imagine what it must have felt like to see one's life's ambition hijacked 語法

人们只能想象，眼看自己一生的抱负被人半路截胡，

and then fulfilled by some upstart with unkempt hair and long fingernails."

接着由一个头发凌乱、指甲很长的新秀去实现，那会是什么感受。”

Mathematicians who showed more enthusiasm finally had the chance to speak with Grisha in person

表现出更多热情的数学家们终于有机会亲自与格里沙交谈，

when he was invited to lecture at several American universities.

当他受邀到美国几所大学讲学时。

By 2006,

到了2006年，

it became clear that he had indeed solved Poincaré's conjecture.

很明显他确实证明了庞加莱猜想。

In a confusing twist, 表達脈絡

在一次令人困惑的波折中，

two Chinese mathematicians Cao Huai-Dong and Zhu Xi-Ping

两位中国数学家曹怀东和朱熹平

claimed they had proved the Poincaré conjecture,

声称他们证明了庞加莱猜想，

calling it a crowning achievement. 表達脈絡

并称其为一项无上的成就。

But the crown belonged only to Grisha.

但那顶王冠只属于格里沙。

Yet,

然而，

he declined the $1 million prize.

他拒绝了这一百万美元的奖金。

Money never motivated him.

金钱从未成为他的动力。

He told a Russian newspaper,

他告诉一家俄罗斯报纸：

"I know how to control the universe,

“我知道如何控制宇宙，

so tell me,

所以告诉我，

why should I run for a million?" 語氣意圖

我为什么要为了一百万而去奔波？”

A Fields Medal is awarded to Grigori Perelman from St. Petersburg. 文化背景

菲尔兹奖被授予来自圣彼得堡的格里戈里·佩雷尔曼。

Grisha was also awarded the highest honor in math,

格里沙还被授予了数学界的最高荣誉，

the equivalent of the Nobel Prize,

相当于诺贝尔奖，

but he didn't show up to the award ceremony in Madrid. 短語動詞

但他没有出席在马德里举行的颁奖典礼。

I regret that Dr. Perelman has declined to accept the medal.

“我很遗憾佩雷尔曼博士拒绝接受这枚奖章。”

Grisha explained to the Telegraph that he wasn't interested in the attention.

格里沙向《每日电讯报》解释说，他对这种关注不感兴趣。

I do not think anything that I say can be of the slightest public interest. 用詞

我不认为我说的任何话能引起哪怕一丝公众利益。

I know that self-promotion happens a lot,

我知道自我推销这种事很常见，

and if people want to do that,

如果人们想那么做，

good luck to them. 語氣意圖

祝他们好运。

But I do not regard it as a positive thing.

但我不认为这是件好事。

Newspapers should be more discerning over who they write about.

报纸在选择报道对象时应该更有眼光。

They should have more taste.

他们应该更有品味。

This was one of the rare interviews he did.

这是他做过的罕见的采访之一。

He wasn't a fan of journalists prodding,

他不喜欢记者的穷追猛打，

and once when a reporter managed to reach him on his phone,

有一次，当一位记者设法打通了他的电话时，

he responded,

他回答说：

"You are disturbing me.

“你在打扰我。

I am picking mushrooms."

我在采蘑菇。”

Despite offers to teach at MIT, Princeton, and Columbia,

尽管麻省理工学院、普林斯顿大学和哥伦比亚大学都提出了任教邀请，

he turned them all down. 短語動詞

他还是把它们全拒绝了。

The mathematician and investor Jim Simons,

数学家兼投资者吉姆·西蒙斯，

who had elevated Stony Brook's math department to top-tier status,

曾将石溪大学的数学系提升到顶尖水平，

reportedly offered Grisha any salary and any terms he desired.

据报道曾向格里沙提供他想要的任何薪水和条件。

But Grisha refused and returned to Russia in the spring of 2004.

但格里沙拒绝了，并在2004年春回到了俄罗斯。

He resumed working for the Steklov Institute and was promoted to lead researcher,

他恢复了在斯捷克洛夫研究所的工作，并被提升为首席研究员，

receiving a salary of around $400 a month.

月薪大约只有400美元。

Once,

有一次，

when he got paid nearly double his monthly salary

当他拿到几乎是月薪两倍的工资时，

because his lab had leftover grant money after completing a project,

因为他的实验室在一个项目完成后还有剩余的经费，

he insisted the extra money be returned to the institute's accounting office. 語法

他坚持把多出的钱退回给研究所的财务处。

Grisha lived his life by his own set of principles. 短語搭配

格里沙按照自己的一套原则生活。

And then,

然后，

in December 2005,

在2005年12月，

he left the Steklov Institute.

他离开了斯捷克洛夫研究所。

As recounted by author Gessen,

据作家格森转述，

Grisha reportedly told the institute's director,

据传格里沙对研究所的主任说：

"I have nothing against the people here, 語氣意圖

“我对这里的人没有任何意见，

but I have no friends.

但我没有朋友。

And anyway,

而且不管怎样，

I have been disappointed in mathematics,

我对数学感到失望，

and I want to try something else.

我想尝试一些别的事情。

I quit."

我辞职。”

Not only did he withdraw from the mathematical world, 語法

他不仅退出了数学界，

but from society as a whole.

而且退出了整个社会。

Very little is known about what he got up to afterward, 短語動詞

关于他后来的生活，人们知之甚少，

except that he lived with his mom.

只知道他和他的母亲住在一起。

A picture of what appears to be Grisha looking disheveled and far removed from the accolades he chose not to receive, 習語

一张疑似格里沙的照片最近在网上流传，他看起来衣衫不整，

circulated online recently.

与他拒领的荣誉毫无关联。

As for what happened to the $1 million he refused to accept, 表達脈絡

至于他拒绝接受的那一百万美元怎么处理了，

the Clay Institute used Grisha's prize money to fund the Poincaré Chair, 文化背景

克雷研究所用格里沙的奖金资助了“庞加莱教席”，

a temporary position for young promising mathematicians at the Henri Poincaré Institute in Paris.

这是巴黎亨利·庞加莱研究所为有前途的年轻数学家设立的一个临时职位。

Grisha's story is both inspiring and thought-provoking,

格里沙的故事既令人鼓舞又发人深省，

highlighting the incredible heights of human intellect

彰显了人类智慧的惊人高度

and the personal choices that define our lives.

以及决定我们个人生活的那些选择。

If you've been inspired by his achievements and want to improve your own skills in math,

如果你被他的成就所启发，并希望提高自己的数学技能，

you'll love learning with Brilliant.

你会喜欢在 Brilliant 上学习。

Geometry was fundamental to Grisha's work,

几何学是格里沙工作的基础，

and you can get hands-on with these concepts in Brilliant's measurement course.

你可以在 Brilliant 的测量课程中亲自实践这些概念。

You'll learn to recognize relationships between shapes,

你将学会识别形状之间的关系，

to find angle measures,

在无需计算的情况下找出角度，

side lengths,

边长，

and areas without calculations.

和面积。

I personally use Brilliant for 10 minutes a day to explore the How LLMs Work course.

我个人每天都会花10分钟使用 Brilliant 探索“大型语言模型是如何运作的”课程。

It's one of my favorites

这是我最喜欢的课程之一，

because it offers a great way to get hands-on with how real language models generate text that sounds human.

因为它提供了一个很好的方式让你亲身体验真正的语言模型是如何生成听起来像人类的文本的。

There's something for everyone,

适合每个人的内容都有，

no matter your skill level, 語法

无论你的技能水平如何，

whether you're a beginner wanting to learn how to program 語法

无论你是想要学习编程的初学者，

or you'd like to brush up on what you already know, 短語動詞

还是你想复习已经掌握的知识，

Brilliant has something for you,

Brilliant 都有适合你的内容，

and you can start learning for free by signing up at brilliant.org/newsthink.

你可以通过在 brilliant.org/newsthink 注册，免费开始学习。

You'll get to try Brilliant for free for 30 days.

你将获得免费试用 Brilliant 30天的机会。

That's brilliant.org/newsthink,

网址是 brilliant.org/newsthink，

link in the description,

链接在描述中，

or scan my custom QR code on your screen.

或者扫描屏幕上的专属二维码。

If you sign up with my link or code,

如果你使用我的链接或代码注册，

you'll also get 20% off Brilliant's annual premium subscription,

你还将获得 Brilliant 年度高级订阅的八折优惠，

giving you access to thousands of lessons.

让你能访问成千上万的课程。

Thanks for watching.

感谢收看。

For NewsThink,

这里是 NewsThink，

I'm Cindy Pom.

我是 Cindy Pom。