破解百萬美元數學難題後神秘消失的男人：英語精讀講義

In 2000,

2000年，

the world's leading mathematicians gathered in Paris

全球頂尖的數學家齊聚巴黎，

to identify seven of the most important unsolved problems in their

旨在評選出他們領域內七個最重要的未解

field. The nonprofit Clay Mathematics Institute organized the meeting

難題。非營利組織克雷數學研究所組織了這場會議，

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

並承諾向首位解決七個千禧年大獎難題中任意一個的人頒發一百萬美元的獎金。

So far, only one has been solved.

到目前為止，只有一個難題被解決了。

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

1904年，法國數學家亨利·龐加萊提出了這個關於空間性質的問題。

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

他提出，如果你有一個沒有洞的三維空間，

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

無需撕裂或切割，就可以把它變成一個球體。

For example,

例如，

a blob could be formed into a sphere.

一團水滴可以被塑造成一個球體。

But it gets more interesting than that.

但事情比這更有趣。

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

在拓撲學家看來，球和枕頭是一樣的，

because they can be reshaped into one another.

因為它們可以被互相改變成對方的形狀。

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

同樣，貝果與馬克杯也是一樣的，因為它們都有一個洞，

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

即使它們不是球體，在拓撲學上它們也是等價的。

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

龐加萊認為，任何沒有洞的物體都等同於一個球體，

so long as the object is small enough. 文法

只要這個物體足夠小。

It can't extend infinitely in any direction.

它不能在任何方向上無限延伸。

He believed his conjecture to be true, 文法

他相信自己的猜想是正確的，

but couldn't prove it.

但無法證明它。

His conjecture was generalized to any number of dimensions,

他的猜想後來被推廣到了任意維數，

including four dimensions,

包括四維，

which was particularly challenging to solve.

這尤為難以證明。

That left the three-dimensional case,

這就剩下了三維的情況，

Poincaré's original conjecture,

即龐加萊最初的猜想，

which frustrated mathematicians for a century,

它讓數學家們沮喪了整整一個世紀，

until 2002,

直到2002年，

when a mysterious paper floated on the internet. 慣用語

當一篇神秘的論文出現在網際網路上。

Within this paper was a solution to the Poincaré conjecture.

這篇論文中包含了龐加萊猜想的解答。

The author was Russian mathematician Grigori Perelman,

作者是俄羅斯數學家格里戈里·佩雷爾曼，

known as Grisha.

大家叫他格里沙。

Grisha grew up in the Soviet Union

格里沙在蘇聯長大，

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

並在聖彼得堡一所專攻數學的菁英高中就讀。

Unlike the other exceptional kids in class,

與班上其他天賦異稟的孩子不同，

he was never distracted.

他從不分心。

He just sat and listened.

他只是坐在那裡聽講。

He even refused to eat his lunch,

他甚至拒絕吃午餐，

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

正如他的老師瓦列里·雷日克在瑪莎·格森關於格里沙的書中提到的，

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

「也許他的整個神經系統都高度適應於學習過程，

that he could not stray from it."

以至於他根本無法分心。」

At 16,

16歲時，

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

他以滿分贏得了國際數學奧林匹亞競賽的金牌。

Being part of the Soviet Olympiad team

作為蘇聯奧林匹亞代表隊的一員，

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

這意味著他無需參加入學考試即可被列寧格勒國立大學錄取。

The university was notoriously discriminatory,

這所大學因歧視而臭名昭著，

admitting only two Jewish students a year.

每年只招收兩名猶太學生。

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

但格里沙在代表隊的地位讓他得以避開這個名額限制。

After completing his studies,

完成學業後，

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

他在著名的斯捷克洛夫數學研究所聖彼得堡分所攻讀研究所，

unheard of for a Jew. 慣用語

這對猶太人來說是前所未聞的。

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

格里沙之所以被錄取，是因為像數學家亞歷山大·亞歷山德羅夫這樣有影響力的人物為他奔走，

and offered to supervise him.

並提出願意擔任他的指導教授。

When Grisha began his grad work in 1987,

當格里沙在1987年開始讀研究所時，

the Iron Curtain was starting to lift, 文化背景

鐵幕開始拉開，

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

幾十年來第一次允許蘇聯公民出國旅行。

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

著名數學家米哈伊爾·格羅莫夫安排格里沙在美國舉辦幾何學方面的講座，

his area of expertise.

這也是他的專長領域。

Gromov mentioned Grisha to the right people,

格羅莫夫向對口的人士推薦了格里沙，

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

確保他受邀前往紐約大學庫朗數學科學研究所進行博士後研究，

and Stony Brook University.

以及石溪大學。

Besides math,

除了數學，

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

他的另一大愛好是從曼哈頓一直走到南布魯克林，

to get his special black bread from a Russian shop.

去一家俄羅斯商店買他特別喜歡的黑麵包。

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

後來他搬到了西海岸，接受了加州大學柏克萊分校享有盛譽的研究員職位。

Once his fellowship came to an end,

一旦他的研究員任期結束，

top American universities tried to poach him. 用詞

美國頂尖大學紛紛試圖挖走他。

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

普林斯頓大學的高層對他的客座講座印象極深，

they approached him about becoming an assistant professor

他們與他接洽，希望他成為助理教授，

and asked for his CV.

並向他索要履歷。

Grisha reportedly responded,

據報導，格里沙回答說：

"Why would you need any more information?"

「你們還需要什麼更多資訊呢？」

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

瑪莎·格森的書描述了格里沙如何不願屈就於任何低於終身教職的職位，

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

而大學方面卻希望這位29歲的年輕人靠自己努力去爭取。

When Tel Aviv University,

當特拉維夫大學，

where Grisha's sister was studying mathematics,

也就是格里沙的妹妹學習數學的地方，

offered him a full professorship,

向他提供正教授職位時，

he rejected that too.

他也拒絕了。

He explained he could work better back in his homeland

他解釋說，回到祖國他能工作得更好，

and returned to Russia to the Steklov Institute.

於是他回到了俄羅斯的斯捷克洛夫研究所。

What he was working on, 文法

他當時在研究什麼，

nobody knew.

無人知曉。

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

格里沙正在默默攻克數學界最難的難題之一。

How did he prove Poincaré's conjecture?

他是如何證明龐加萊猜想的呢？

Well,

嗯，

he managed to prove another conjecture,

他設法證明了另一個猜想，

which indirectly proved Poincaré's.

從而間接證明了龐加萊猜想。

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,

美國數學家威廉·瑟斯頓提出任何三維形狀都可以分解為八種不同的幾何結構，

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

這八種形狀之一就是三維球體，

which is central to Poincaré's conjecture.

這正是龐加萊猜想的核心。

Thurston never managed to prove his own theory,

瑟斯頓一直未能證明自己的理論，

but American mathematician Richard Hamilton gave it a go, 慣用語

但美國數學家理查·漢彌爾頓進行了嘗試，

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

試圖同時攻克龐加萊和瑟斯頓的猜想。

He couldn't prove them,

他未能證明它們，

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

但他確實制定了藍圖，幫助格里沙最終解開了這個世紀之謎。

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

格里沙依靠漢彌爾頓稱為「里奇流」的強大數學工具來研究形狀。

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

可以把里奇流想像成熱量在物體中擴散，

smoothing out bumps and irregularities over time. 片語動詞

隨著時間的推移，使凹凸和不規則的地方變得平滑。

As Ricci flow progresses,

隨著里奇流的推進，

certain regions can become very thin,

某些區域會變得非常薄，

forming necks.

形成「頸部」。

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

格里沙使用了一種叫做「手術」的過程來切斷這些頸部，以便單獨研究各個部分。

He realized that these pieces ultimately represented the simple shapes

他意識到這些部分最終代表了簡單的形狀，

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

這與瑟斯頓猜想預測的結構相對應。

So,

因此，

by solving Thurston's conjecture,

透過證明瑟斯頓猜想，

he in turn proved Poincaré's. 表達脈絡

他也順帶證明了龐加萊猜想。

Grisha published three papers totaling 992 pages.

格里沙發表了三篇論文，總計992頁。

When he uploaded the first to arxiv.org,

當他將第一篇上傳至 arxiv.org，

a public forum operated by Cornell University,

一個由康乃爾大學營運的公共論壇時，

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

他給十多位美國數學家發了電子郵件，提前通知了他們。

This was totally out of the blue. 慣用語

這完全出乎意料。

He hadn't spoken to his colleagues for years

他已經多年沒有和同事們說過話了，

and barely responded to their emails.

也幾乎不回覆他們的郵件。

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

數學家們花了三年多時間仔細審查他的證明，以確定他是否真的解決了這個問題。

But Richard Hamilton was not one of them.

但理查·漢彌爾頓並不在其中。

Grisha was apparently hurt that Hamilton,

顯然，格里沙感到很受傷，因為漢彌爾頓，

whose foundational work he relied on for his proof,

這位他證明過程中所依賴的奠基性工作的主人，

showed little interest in his achievement.

對他的成就似乎興趣不大。

Grisha told the New Yorker,

格里沙告訴《紐約客》：

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

「我的印象是他只讀了我論文的第一部分。」

Why was Hamilton so apparently disinterested?

為什麼漢彌爾頓顯得如此漠不關心？

As author Masha Gessen put it, 表達脈絡

正如作家瑪莎·格森所說：

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

「佩雷爾曼只用了第一篇論文不到一半的篇幅，就突破了漢彌爾頓停滯二十年的瓶頸。

No wonder Hamilton was silent.

難怪漢彌爾頓保持沉默。

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

人們只能想像，眼看自己一生的抱負被人半路截胡，

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

接著由一個頭髮凌亂、指甲很長的新秀去實現，那會是什麼感受。」

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

表現出更多熱情的數學家們終於有機會親自與格里沙交談，

when he was invited to lecture at several American universities.

當他受邀到美國幾所大學講學時。

By 2006,

到了2006年，

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

很明顯他確實證明了龐加萊猜想。

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

兩位中國數學家曹懷東和朱熹平

claimed they had proved the Poincaré conjecture,

聲稱他們證明了龐加萊猜想，

calling it a crowning achievement. 表達脈絡

並稱其為一項無上的成就。

But the crown belonged only to Grisha.

但那頂王冠只屬於格里沙。

Yet,

然而，

he declined the $1 million prize.

他拒絕了這一百萬美元的獎金。

Money never motivated him.

金錢從未成為他的動力。

He told a Russian newspaper,

他告訴一家俄羅斯報紙：

"I know how to control the universe,

「我知道如何控制宇宙，

so tell me,

所以告訴我，

why should I run for a million?" 語氣意圖

我為什麼要為了一百萬而去奔波？」

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

菲爾茲獎被授予來自聖彼得堡的格里戈里·佩雷爾曼。

Grisha was also awarded the highest honor in math,

格里沙還被授予了數學界的最高榮譽，

the equivalent of the Nobel Prize,

相當於諾貝爾獎，

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

但他沒有出席在馬德里舉行的頒獎典禮。

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

「我很遺憾佩雷爾曼博士拒絕接受這枚獎章。」

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

格里沙向《每日電訊報》解釋說，他對這種關注不感興趣。

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

我不認為我說的任何話能引起哪怕一絲大眾利益。

I know that self-promotion happens a lot,

我知道自我推銷這種事很常見，

and if people want to do that,

如果人們想那麼做，

good luck to them. 語氣意圖

祝他們好運。

But I do not regard it as a positive thing.

但我不認為這是件好事。

Newspapers should be more discerning over who they write about.

報紙在選擇報導對象時應該更有眼光。

They should have more taste.

他們應該更有品味。

This was one of the rare interviews he did.

這是他做過的罕見的採訪之一。

He wasn't a fan of journalists prodding,

他不喜歡記者的窮追猛打，

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

有一次，當一位記者設法打通了他的電話時，

he responded,

他回答說：

"You are disturbing me.

「你在打擾我。

I am picking mushrooms."

我在採蘑菇。」

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

儘管麻省理工學院、普林斯頓大學和哥倫比亞大學都提出了任教邀請，

he turned them all down. 片語動詞

他還是把它們全拒絕了。

The mathematician and investor Jim Simons,

數學家兼投資者吉姆·西蒙斯，

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

曾將石溪大學的數學系提升到頂尖水準，

reportedly offered Grisha any salary and any terms he desired.

據報導曾向格里沙提供他想要的任何薪水和條件。

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

但格里沙拒絕了，並在2004年春回到了俄羅斯。

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

他恢復了在斯捷克洛夫研究所的工作，並被提升為首席研究員，

receiving a salary of around $400 a month.

月薪大約只有400美元。

Once,

有一次，

when he got paid nearly double his monthly salary

當他拿到幾乎是月薪兩倍的薪水時，

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

因為他的實驗室在一個專案完成後還有剩餘的經費，

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

他堅持把多出的錢退回給研究所的會計室。

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

格里沙按照自己的一套原則生活。

And then,

然後，

in December 2005,

在2005年12月，

he left the Steklov Institute.

他離開了斯捷克洛夫研究所。

As recounted by author Gessen,

據作家格森轉述，

Grisha reportedly told the institute's director,

據傳格里沙對研究所的主任說：

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

「我對這裡的人沒有任何意見，

but I have no friends.

但我沒有朋友。

And anyway,

而且不管怎樣，

I have been disappointed in mathematics,

我對數學感到失望，

and I want to try something else.

我想嘗試一些別的事情。

I quit."

我辭職。」

Not only did he withdraw from the mathematical world, 文法

他不僅退出了數學界，

but from society as a whole.

而且退出了整個社會。

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

關於他後來的生活，人們知之甚少，

except that he lived with his mom.

只知道他和他的母親住在一起。

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

一張疑似格里沙的照片最近在網路上流傳，他看起來衣衫不整，

circulated online recently.

與他拒領的榮譽毫無關聯。

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

至於他拒絕接受的那一百萬美元怎麼處理了，

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獎金資助了「龐加萊教席」，

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

這是巴黎亨利·龐加萊研究所為有前途的年輕數學家設立的一個臨時職位。

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

格里沙的故事既令人鼓舞又發人深省，

highlighting the incredible heights of human intellect

彰顯了人類智慧的驚人高度

and the personal choices that define our lives.

以及決定我們個人生活的那些選擇。

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啟發，並希望提高自己的數學技能，

you'll love learning with Brilliant.

你會喜歡在 Brilliant 上學習。

Geometry was fundamental to Grisha's work,

幾何學是格里沙工作的基礎，

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

你可以在 Brilliant 的測量課程中親自實踐這些概念。

You'll learn to recognize relationships between shapes,

你將學會識別形狀之間的關係，

to find angle measures,

在無需計算的情況下找出角度，

side lengths,

邊長，

and areas without calculations.

和面積。

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

我個人每天都會花10分鐘使用 Brilliant 探索「大型語言模型是如何運作的」課程。

It's one of my favorites

這是我最喜歡的課程之一，

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

因為它提供了一個很好的方式讓你親身體驗真正的語言模型是如何生成聽起來像人類的文本的。

There's something for everyone,

適合每個人的內容都有，

no matter your skill level, 文法

無論你的技能水平如何，

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

無論你是想要學習寫程式的初學者，

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

還是你想複習已經掌握的知識，

Brilliant has something for you,

Brilliant 都有適合你的內容，

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

你可以透過在 brilliant.org/newsthink 註冊，免費開始學習。

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

你將獲得免費試用 Brilliant 30天的機會。

That's brilliant.org/newsthink,

網址是 brilliant.org/newsthink，

link in the description,

連結在描述中，

or scan my custom QR code on your screen.

或者掃描螢幕上的專屬 QR Code。

If you sign up with my link or code,

如果你使用我的連結或代碼註冊，

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

你還將獲得 Brilliant 年度高級訂閱的八折優惠，

giving you access to thousands of lessons.

讓你能存取成千上萬的課程。

Thanks for watching.

感謝收看。

For NewsThink,

這裡是 NewsThink，

I'm Cindy Pom.

我是 Cindy Pom。