解决世界上最著名数学难题的人：英语精读讲义

In 1994,

1994年，

Andrew Wiles solved a mystery that had stumped mathematicians for 357 years. 用詞

Andrew Wiles解开了一个困扰数学家357年的谜题。

The 17th century French mathematician Pierre de Fermat states that you can't find numbers

17世纪的法国数学家Pierre de Fermat提出，你无法找到这样的一些数字，

where x to the n + y to the n

使得x的n次方加y的n次方

is equal to z to the n

等于z的n次方，

when n is a whole number greater than two.

前提是n为大于2的整数。

For example,

例如，

3 to the power of 3 + 4 to the power of 3 equals 91, 文化背景

3的3次方加4的3次方等于91，

which is not the cube of any whole number.

这并不是任何整数的立方。

Fermat claims to have proved his theorem, 語法

Fermat声称自己已经证明了他的定理，

writing in his copy of Arithmetica,

他在自己那本《算术》（Arithmetica）

an ancient Greek text on number theory,

——一本古希腊数论文献的空白处写道：

"I have discovered a truly marvelous proof of this,

“我已经发现了一个真正绝妙的证明，

which this margin is too narrow to contain." 語法

但这里的空白太小，写不下。”

Unfortunately,

不幸的是，

he never wrote down his proof,

他从未将证明写下来，

not anywhere that anyone has ever found.

在任何地方都无人发现。

For over 300 years,

在三百多年的时间里，

mathematicians puzzled over this perplexing problem, 短語動詞

数学家们对这个令人费解的难题百思不得其解，

which is similar to the Pythagorean theorem,

它类似于勾股定理，

but applies to exponents greater than two.

但适用于大于2的指数。

Andrew Wiles was a young boy when he stumbled upon Fermat's Last Theorem 短語動詞

Andrew Wiles在1963年偶然发现了费马大定理时，

at a library in Cambridge,

还是个小男孩，

England in 1963.

当时他在英国剑桥的一家图书馆里。

As he recalled in an interview later featured in the book Fermat's Enigma

正如他后来在Simon Singh撰写的

by Simon Singh,

《费马最终定理》（Fermat's Enigma）一书

which I highly recommend,

（我强烈推荐这本书）的一篇采访中所回忆的那样：

"Here was a problem that I,

“这就是一个我，

a 10-year-old,

一个10岁的孩子，

could understand,

能够理解的难题，

and I knew from that moment

从那一刻起我就知道

that I would never let it go. 短語動詞

我绝对不会放弃它。

I had to solve it."

我必须解决它。”

His determination was extraordinary,

他的决心非同寻常，

considering the brightest minds in math

要知道数学界最顶尖的头脑

had failed to crack it for centuries. 用詞

几个世纪以来都没能攻克它。

The 18th century Swiss mathematician Leonhard Euler

18世纪的瑞士数学家Leonhard Euler

proved a specific case

证明了一个特定情况，

where there are no solutions

即当n等于3时

for n equals 3,

没有解，

but his work didn't extend to other exponents.

但他的研究未能扩展到其他指数。

Euler even asked a friend to search Fermat's house

Euler甚至请朋友去搜查Fermat的家，

just in case he had scribbled down his proof somewhere, 短語搭配

以防他把证明潦草地写在了某个地方，

with no luck.

但一无所获。

The wealthy German industrialist Paul Wolfskehl

富有的德国工业家Paul Wolfskehl

was so miserable because the woman he loved 語法

曾因为深爱的女人

didn't love him back

不爱他而痛苦不堪，

that he planned to end his life,

以至于计划结束自己的生命，

only to be reinvigorated by Fermat's puzzle. 語法

却因Fermat的这个难题而重新振作。

He never solved it himself,

他自己从未能解开它，

but he offered a reward of 100,000 German marks

但他悬赏了十万德国马克，

to anyone who could,

奖励给任何能解开它的人，

motivating the next generation of mathematicians.

从而激励了下一代的数学家们。

When Andrew Wiles was a grad student at the University of Cambridge

当Andrew Wiles在剑桥大学读研究生时，

in the 1970s,

那是在20世纪70年代，

his supervisor John Coates

他的导师John Coates

suggested he study elliptic curves,

建议他研究椭圆曲线，

which proved crucial for solving Fermat's Last Theorem. 短語搭配

这被证明对解决费马大定理至关重要。

In the 1950s,

在20世纪50年代，

Japanese mathematicians Yutaka Taniyama and Goro Shimura

日本数学家谷山丰（Yutaka Taniyama）和志村五郎（Goro Shimura）

suggested that for every elliptic curve,

提出，对于每一条椭圆曲线，

there was a corresponding modular form.

都对应着一个模形式。

The Taniyama-Shimura conjecture connected two distinct areas of mathematics.

“谷山-志村猜想”将数学中两个不同的领域联系了起来。

Later,

后来，

Ken Ribet,

加州大学伯克利分校的教授

a professor at UC Berkeley,

Ken Ribet，

linked their conjecture to Fermat's Last Theorem.

将他们的猜想与费马大定理联系在了一起。

How?

怎么做到的？

He showed that if Fermat's Last Theorem were false, 語法

他证明了如果费马大定理是错误的，

certain elliptical curves would have to exist.

那么必然存在某些特定的椭圆曲线。

However,

然而，

the Taniyama-Shimura conjecture implied that those curves could not exist.

谷山-志村猜想意味着这些曲线不可能存在。

Therefore,

因此，

if the Taniyama-Shimura conjecture were true,

如果谷山-志村猜想是真的，

Fermat's Last Theorem would also be true.

费马大定理也必为真。

Proving the conjecture would prove Fermat's Last Theorem.

证明了这个猜想也就证明了费马大定理。

The problem was Taniyama and Shimura

问题在于谷山和志村

never proved their own conjecture.

从未证明过他们自己的猜想。

Tragically,

悲剧的是，

Taniyama committed suicide in 1958,

谷山在1958年自杀身亡，

leaving a note that read,

留下了一张字条，上面写着：

"I am in the frame of mind that I lost confidence in my future."

“我处于对未来失去信心的心境中。”

His fiancee took her own life shortly after,

不久之后，他的未婚妻也结束了自己的生命，

writing,

她写道：

"We promised each other that no matter where we went, 語法

“我们曾互相承诺，无论去哪里，

we would never be separated.

我们永远都不会分开。

Now that he is gone,

既然他已经走了，

I must go too in order to join him."

我也必须去陪伴他。”

In 1986,

1986年，

Andrew Wiles was sipping iced tea at a friend's house

Andrew Wiles正在朋友家喝着冰茶，

when his friend mentioned Ken Ribet

朋友提到Ken Ribet

had proved the link between Taniyama-Shimura and Fermat's Last Theorem.

已经证明了谷山-志村猜想和费马大定理之间的联系。

Andrew recalled,

Andrew回忆说：

"I was electrified. 習語

“我被电到了。

I knew that moment that the course of my life was changing,

那一刻我就知道我人生的轨迹改变了，

because this meant that to prove Fermat's Last Theorem,

因为这意味着要想证明费马大定理，

all I had to do was prove the Taniyama-Shimura conjecture. 語法

我只需证明谷山-志村猜想。

It meant that my childhood dream was now a respectable thing to work on.

这意味着我的童年梦想现在成了一项值得去做的正经工作。

I just knew that I could never let that go."

我只知道我绝不能放手。”

By this time,

到这个时候，

Andrew had moved to the US

Andrew已经搬到了美国，

where he was a mathematics professor at Princeton University.

在普林斯顿大学担任数学教授。

When he wasn't lecturing,

当他不讲课的时候，

he was in his attic office

他就在阁楼的办公室里，

trying to prove that every single elliptic equation

试图证明每一个椭圆方程

could be correlated with a modular form.

都能与一个模形式相关联。

Only his wife knew what he was up to. 習語

只有他的妻子知道他在干什么。

He kept his work a secret,

他对自己的工作保密，

not wanting to be distracted.

不想被打扰。

Though,

不过，

there may have been another reason for his secrecy.

他的保密可能还有另一个原因。

He may have feared that if his progress leaked,

他可能担心，如果自己的进展泄露出去，

a rival mathematician might beat him to the punch and claim the glory. 習語

竞争对手可能会捷足先登抢走荣誉。

He cleverly threw his colleagues off track 習語

他巧妙地转移了同事们的注意力，

by publishing his ongoing research on elliptic equations every six months,

每半年发表一次自己关于椭圆方程的阶段性研究，

making it seem like he was keeping busy 表達脈絡

让人觉得他一直很忙，

while actually devoting his time to the age-old enigma.

而实际上他把时间都倾注在了那个古老的谜题上。

He began by proving the connection for a specific class of elliptic curves,

他首先证明了一类特定椭圆曲线的关联，

like knocking down the first domino in a long line. 表達脈絡

就像推倒了长长一排多米诺骨牌中的第一张。

The challenge was to ensure that if one domino fell,

挑战在于要确保如果一张骨牌倒下，

it would topple the next.

它能推倒下一张。

Andrew had to show that if one element of the elliptic curve series

Andrew必须证明，如果椭圆曲线序列中的一个元素

matched the corresponding element in the modular form series,

与模形式序列中的对应元素相匹配，

then the next elements would also match.

那么随后的元素也会匹配。

Yet,

然而，

he struggled to topple the rest of the dominoes.

他在试图推倒剩余骨牌时陷入了困境。

Five years after working in secret,

在秘密研究了五年之后，

he decided to emerge from his hermit-like state

他决定从隐居状态中走出来，

in hopes of finding new ideas.

希望能找到新的灵感。

In 1991,

1991年，

he attended a major math conference in Boston

他在波士顿参加了一个大型数学会议，

where his PhD supervisor John Coates mentioned that a student of his,

他的博士生导师John Coates提到，他的一个学生，

Matthias Flach,

Matthias Flach，

was working on a powerful way of analyzing elliptic equations,

正在研究一种分析椭圆方程的强力方法，

building on the work of Russian mathematician Viktor Kolyvagin. 短語動詞

该方法基于俄罗斯数学家Viktor Kolyvagin的研究。

Andrew realized this Kolyvagin-Flach method

Andrew意识到这个Kolyvagin-Flach方法

could help him topple the rest of the dominoes,

能帮他推倒剩下的多米诺骨牌，

ultimately proving every elliptic equation

最终证明每个椭圆方程

could be matched to a modular form.

都能与一个模形式相匹配。

But this involved incredibly hard mathematics

但这涉及极其艰深的数学，

and took several more years.

并又花了好几年的时间。

After seven years of working all by himself,

在独自一人研究了七年之后，

he finally decided he needed some help.

他终于决定自己需要一些帮助。

In 1993,

1993年，

he confided in his colleague at Princeton, 短語搭配

他向他在普林斯顿的同事、

mathematician Nick Katz.

数学家Nick Katz吐露了秘密。

They arranged a secret weekly meeting disguised as a graduate course

他们安排了每周一次的秘密会议，伪装成研究生课程，

where Nick meticulously checked and verified Andrew's calculations

Nick在那里细致地检查和验证Andrew的计算，

and assessed that the Kolyvagin-Flach method worked perfectly.

并评估Kolyvagin-Flach方法是否完美奏效。

There was still one missing piece of the puzzle.

但拼图中仍然缺失一块。

Andrew used a key insight gleaned from a paper by American mathematician Barry Mazur

Andrew运用从美国数学家Barry Mazur的一篇论文中获得的关键启示，

to complete the puzzle in May 1993.

在1993年5月完成了这块拼图。

It was time to tell the world he had solved the world's hardest math problem.

是时候向世界宣告他已解开了世界上最难的数学题了。

He chose to do so at a conference at the Isaac Newton Institute

他选择在牛顿研究所的一场会议上宣布，

in June 1993

时间是1993年6月，

in his hometown of Cambridge.

地点在他的家乡剑桥。

An air of excitement filled the room

房间里弥漫着兴奋的气氛，

as rumors spread of his breakthrough

因为关于他在

on the more than 300-year-old mystery.

这个有着300多年历史的谜题上取得突破的谣言已经传开。

Andrew recalled,

Andrew回忆说：

"There was a typical dignified silence

“在我念出证明过程时，

while I read out the proof,

现场有一种典型的庄严寂静，

and then I just wrote up the statement of Fermat's Last Theorem.

然后我刚好写下了费马大定理的陈述。

I said,

我说：

"I think I'll stop here."

‘我想我就停在这里吧。’

And then there was sustained applause."

接着便响起了经久不息的掌声。”

Mathematicians usually don't make headlines,

数学家通常不会上头条，

but this was an exception.

但这次是个例外。

The excitement was palpable,

兴奋之情溢于言表，

yet the proof still needed to be verified.

但证明依然需要得到验证。

He submitted his draft to the journal Inventiones Mathematicae,

他把手稿提交给了《数学发明》期刊，

where the editor Barry Mazur

编辑Barry Mazur

selected six referees to pore over Andrew's 200-page work. 短語動詞

挑选了六位审稿人来研读Andrew长达200页的论文。

This was subject matter that perhaps only a half dozen people in the world could fully grasp,

正如屡获殊荣的纪录片《费马大定理》的导演John Lynch

as John Lynch, director of the award-winning documentary Fermat's Last Theorem, 表達脈絡

所言，

put it.

这是一门全世界大概只有六七个人能完全掌握的学科。

During this rigorous scrutiny,

在这种严格的审查中，

a flaw emerged.

出现了一个破绽。

One of the referees,

其中一位审稿人，

Andrew's Princeton colleague Nick Katz,

也就是Andrew在普林斯顿的同事Nick Katz，

discovered a gap in the part of the argument 用詞

在涉及Kolyvagin-Flach方法的论证部分

involving the Kolyvagin-Flach method.

发现了一个漏洞。

Nick and Andrew had missed this during their earlier secret meetings disguised as lectures.

Nick和Andrew在之前伪装成讲课的秘密会议上漏掉了这一点。

Was Andrew's proof about to collapse like a house of cards? 習語

Andrew的证明难道要像纸牌屋一样倒塌了吗？

Despite the setback,

尽管遇到了挫折，

he remained optimistic.

他依然保持乐观。

He was confident that Kolyvagin-Flach just needed a little tweaking.

他坚信Kolyvagin-Flach方法只需要一点点修正。

He retreated to his attic once again,

他再次退回到阁楼里，

but it was slow going. 習語

但进展缓慢。

His wife Nada had told him she wanted everything corrected by her birthday on October 6,

他的妻子Nada告诉他，希望他在10月6日她的生日之前把一切都改正过来，

two weeks away.

距离现在只有两周了。

But as time went on with no manuscript published,

但随着时间推移，论文迟迟未能发表，

rumors began circulating that there were issues with his proof.

开始有传言说他的证明出了问题。

Andrew had no choice but to address the speculation publicly in a forum at the end of 1993. 語法

Andrew别无选择，只能在1993年底的一个论坛上公开回应这些猜测。

"During the review process,

“在审查过程中，

a number of problems emerged,

出现了许多问题，

most of which have been resolved, 語法

其中大部分已经解决，

but one in particular I have not yet settled.

但有一个特定的问题我还没有处理好。

I believe that I will be able to finish this in the near future

我相信我会在不久的将来

using the ideas explained in my Cambridge lectures."

利用我在剑桥讲座中解释的思想来完成它。”

Winter passed and he was still nowhere close to completing the proof. 短語搭配

冬天过去了，他离完成证明还差得很远。

He decided to bounce ideas off of someone he trusted. 習語

他决定找个值得信赖的人交流想法。

His former student Richard Taylor,

他以前的学生Richard Taylor，

now a Cambridge lecturer and one of the referees who looked over his proof.

现在是剑桥讲师，也是审查他证明的审稿人之一。

They worked through the summer of 1994

他们整个1994年夏天都在工作，

without any progress.

但没有任何进展。

Andrew was at wit's end and thought of giving up. 習語

Andrew束手无策，甚至想过放弃。

But Richard persuaded him to keep working on until Richard returned to Cambridge in September.

但Richard说服他继续努力，直到Richard九月份返回剑桥。

That extra month made all the difference. 習語

那多出来的一个月带来了翻天覆地的改变。

The morning of Monday,

1994年9月19日，

September 19, 1994,

星期一的早晨，

Andrew was again intensely examining the Kolyvagin-Flach method,

Andrew再次专注地审视Kolyvagin-Flach方法，

trying desperately to understand why it didn't work.

拼命想弄明白它为什么不奏效。

Suddenly,

突然间，

he had an incredible revelation.

他获得了一个不可思议的启示。

Although the Kolyvagin-Flach method wasn't entirely successful,

虽然Kolyvagin-Flach方法并不完全成功，

it provided enough insight to revive his original approach

但它提供了足够的洞见来复活他最初的方案

using Iwasawa theory,

——运用岩泽理论（Iwasawa theory），

a theory of analyzing elliptic equations

这是他在剑桥当学生时学到的一种

that he had learned as a student at Cambridge.

分析椭圆方程的理论。

Combining the two methods,

将这两种方法结合起来，

which were inadequate on their own,

它们单独使用时都不够充分，

provided the eureka moment.

但结合在一起带来了顿悟的时刻。

"It was the most uh the most important moment of my working life.

“那是我，呃，我职业生涯中最重要的时刻。

Nothing I ever do again will

我以后做的任何事情都不会再……

I'm sorry."

抱歉。”

After eight years of dedicating himself to one task,

经过八年致力于这项单一的任务，

Andrew's 129-page proof was published in May 1995,

Andrew长达129页的证明在1995年5月发表，

putting to rest the greatest mystery in math. 習語

让数学界最大的未解之谜尘埃落定。

He reflected,

他反思道：

"Having solved this problem,

“解决了这个问题，

there's certainly a sense of loss. 短語搭配

当然有一种失落感。

But at the same time,

但与此同时，

there is this tremendous sense of freedom.

也有一种巨大的自由感。

That particular odyssey is now over. 習語

那段漫长的奥德赛之旅如今已经结束。

My mind is at rest."

我的心安定了。”

If you've been inspired by Andrew's remarkable achievement

如果你被Andrew的非凡成就所启发，

and want to improve your math skills,

并想提高自己的数学技能，

and who knows,

甚至，谁知道呢，

solve the next big mathematical mystery,

解决下一个重大的数学难题，

Brilliant is the perfect place to start.

Brilliant就是完美的起点。

If you've ever felt that math is hard,

如果你曾觉得数学很难，

Brilliant is a website and app

Brilliant就是能让

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数学变得简单直观的网站和应用。

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在他们的测量课程中，

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你将通过识别形状之间的关系，

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Brilliant has something for everyone.

Brilliant为每个人都提供了适合的内容。

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如果你对编程感兴趣，

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你可以熟悉Python，

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你可以通过视频描述里的专属链接注册，

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免费试用Brilliant 30天，

brilliant.org/newsthink

访问 brilliant.org/newsthink

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或扫描屏幕上的二维码。

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通过我的链接或二维码注册，

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让你能访问数以千计的课程。

Thanks for watching.

感谢观看。

For Newsthink, I'm Cindy Pom.

这里是Newsthink，我是Cindy Pom。