What is it that French people do better than all the others?

法國(guó)人在什么方面做得比別人好呢？

If you would take polls,

如果你去做個(gè)投票調(diào)查，

the top three answers might be: love,

排名前三的或許是：愛(ài)情，

wine and whining.

紅酒，和發(fā)牢騷。

Maybe.

可能吧。

But let me suggest a fourth style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>但我還想提出第四個(gè)答案：數(shù)學(xué)。

Did you know that Paris has more mathematicians than any other city in the world?

你們知道巴黎的數(shù)學(xué)家比世界上其它任何一個(gè)城市 都要多嗎？

And more streets with mathematicians' names, too.

而且以數(shù)學(xué)家的名字命名的街道數(shù)量也更多。

And if you look at the statistics of the Fields Medal,

如果你查查菲爾茲獎(jiǎng)的統(tǒng)計(jì)，

often called the Nobel Prize for mathematics,

它也經(jīng)常被稱作“諾貝爾數(shù)學(xué)獎(jiǎng)”，

and always awarded to mathematicians below the age of 40,

只授予40歲以下的數(shù)學(xué)家，

you will find that France has more Fields medalists per inhabitant than any other country.

你會(huì)發(fā)現(xiàn)，就人均獲獎(jiǎng)數(shù)量來(lái)說(shuō)， 法國(guó)是世界第一。

What is it that we find so sexy in math?

我們?cè)跀?shù)學(xué)中到底發(fā)現(xiàn)了什么讓人著迷的東西？

After all, it seems to be dull and abstract,

畢竟它看上去那么無(wú)聊、抽象，

just numbers and computations and rules to apply.

只是數(shù)字、計(jì)算、定理而已。

Mathematics may be abstract,

數(shù)學(xué)可能很抽象，

but it's not dull and it's not about computing.

但是它并不無(wú)聊， 而且它并不都是計(jì)算。

It is about reasoning and proving our core activity.

它是有關(guān)邏輯的推理， 讓我們的所作所為都有理有據(jù)。

It is about imagination,

它有關(guān)豐富的想象，

the talent which we most praise.

我們最常歌頌的人類天賦。

It is about finding the truth.

它還有關(guān)真理的追尋。

There's nothing like the feeling which invades you when after months of hard thinking,

當(dāng)你苦思冥想數(shù)月之后， 終于找到問(wèn)題的正確解法那一刻，

you finally understand the right reasoning to solve your problem.

那種感受真的無(wú)與倫比。

The great mathematician André Weil likened this -- no kidding -- to sexual pleasure.

偉大的數(shù)學(xué)家安德雷·韋依 把這種感受比作（不開(kāi)玩笑的說(shuō)） 比作性快感。

But noted that this feeling can last for hours,

但是他還說(shuō)這種感受可以持續(xù)數(shù)小時(shí)

or even days.

甚至數(shù)天。

The reward may be big.

這種回報(bào)可能難以估量。

Hidden mathematical truths permeate our whole physical world.

隱藏的數(shù)學(xué)規(guī)律滲透在我們整個(gè)物質(zhì)世界中。

They are inaccessible to our senses but can be seen through mathematical lenses.

我們的感官無(wú)法接觸到它們，但可以通過(guò)數(shù)學(xué)鏡片看到它們。

Close your eyes for moment and think of what is occurring right now around you.

閉上眼睛一小會(huì)兒， 想一想你周圍此時(shí)此刻正在發(fā)生的事。

Invisible particles from the air around are bumping style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>周圍空氣中的看不見(jiàn)的粒子每秒鐘都在撞擊你，每秒鐘數(shù)十億次，

all in complete chaos.

完全是混亂無(wú)序的狀態(tài)。

And still, their statistics can be accurately predicted by mathematical physics.

然而， 它們的行為可以用數(shù)學(xué)物理學(xué)精準(zhǔn)地預(yù)測(cè)。

And open your eyes now to the statistics of the velocities of these particles.

現(xiàn)在打開(kāi)你的眼睛看看這些分子的速率分布統(tǒng)計(jì)。

The famous bell-shaped Gauss Curve,

這是著名的鐘形高斯曲線，

or the Law of Errors -- of deviations with respect to the mean behavior.

也可以叫做誤差律—— 關(guān)于分子平均行為的一些偏差。

This curve tells about the statistics of velocities of particles in the same way as a demographic curve would tell about the statistics of ages of individuals.

這條曲線告訴我們粒子的速率分布情況， 正如一條人口統(tǒng)計(jì)曲線，能夠告訴我們?nèi)丝诘哪挲g分布情況。

It's style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>這是有史以來(lái)最重要的曲線之一。

It keeps style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>它的規(guī)律不斷地重復(fù)，

from many theories and many experiments,

在諸多理論與實(shí)驗(yàn)中呈現(xiàn)，

as a great example of the universality which is so dear to us mathematicians.

它是數(shù)學(xué)的普適性的體現(xiàn)， 而這種性質(zhì)對(duì)我們數(shù)學(xué)家至關(guān)重要。

Of this curve,

關(guān)于這個(gè)曲線，

the famous scientist Francis Galton said,

著名科學(xué)家弗朗西斯·高爾頓說(shuō)：

'It would have been deified by the Greeks if they had known it.

“如果古希臘人知道這個(gè)規(guī)律， 他們一定會(huì)把它神化的。

It is the supreme law of unreason.'

這是無(wú)理性的最高法則?！?/strong>

And there's no better way to materialize that supreme goddess than Galton's Board.

高爾頓板就是 把這個(gè)“神靈”實(shí)體化的最佳體現(xiàn)。

Inside this board are narrow tunnels through which tiny balls will fall down randomly,

在這個(gè)板子里有一些狹道， 一些掉落的小球會(huì)隨機(jī)通過(guò)這里，

going right or left, or left, etc.

有些往右，有些往左。

All in complete randomness and chaos.

完全是隨機(jī)的、混亂的。

Let's see what happens when we look at all these random trajectories together.

讓我們看看這些隨機(jī)路線會(huì)呈現(xiàn)怎樣的規(guī)律。

This is a bit of a sport,

這其實(shí)算是鍛煉身體，

because we need to resolve some traffic jams in there.

因?yàn)槲覀兊檬柰ㄒ恍矶碌臓顩r。

Aha.

啊哈。

We think that randomness is going to play me a trick style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>看來(lái)隨機(jī)性要在這個(gè)舞臺(tái)上跟我開(kāi)個(gè)小玩笑了。

There it is.

好了！

Our supreme goddess of unreason.

這個(gè)無(wú)理性的至高無(wú)上的神，

the Gauss Curve,

高斯曲線，

trapped here inside this transparent box as Dream in 'The Sandman'

被困在這個(gè)透明的盒子里，就像《睡魔》漫畫里的夢(mèng)魘

comics.

一樣。

For you I have shown it,

我向各位展示了這個(gè)規(guī)律，

but to my students I explain why it could not be any other curve.

但向我的學(xué)生，我要解釋為什么它不可能是任何其它的曲線。

And this is touching the mystery of that goddess,

這就近乎揭開(kāi)了這個(gè)神靈的面紗，

replacing a beautiful coincidence by a beautiful explanation.

把一個(gè)美麗的巧合變成一個(gè)賞心悅目的數(shù)學(xué)解釋。

All of science is like this.

一切的科學(xué)都是這樣的。

And beautiful mathematical explanations are not style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>美麗的數(shù)學(xué)解法并不只是為了我們自己開(kāi)心。

They also change our vision of the world.

它們也改變了我們對(duì)世界的看法。

For instance, Einstein, Perrin, Smoluchowski,

舉個(gè)例子， 愛(ài)因斯坦、 佩蘭、 斯莫魯霍夫斯基，

they used the mathematical analysis of random trajectories and the Gauss Curve to explain and prove that our world is made of atoms.

他們對(duì)粒子的隨機(jī)軌跡進(jìn)行了數(shù)學(xué)分析，再加上高斯曲線， 他們解釋并證明了我們的世界由原子組成。

It was not the first time that mathematics was revolutionizing our view of the world.

這并不是第一次， 數(shù)學(xué)已經(jīng)多次顛覆了我們的世界觀。

More than 2,000 years ago,

兩千多年前，

at the time of the ancient Greeks,

在古希臘的時(shí)代，

it already occurred.

就已經(jīng)顛覆了。

In those days,

在那個(gè)時(shí)代，

only a small fraction of the world had been explored,

人們只探索了世界的很小一部分，

and the Earth might have seemed infinite.

而地球看上去無(wú)邊無(wú)際。

But clever Eratosthenes, using mathematics,

但聰明的埃拉托斯提尼，運(yùn)用數(shù)學(xué)，

was able to measure the Earth with an amazing accuracy of two percent.

成功的測(cè)量了地球的大小，誤差只有驚人的2%。

Here's another example.

還有另一個(gè)例子。

In 1673, Jean Richer noticed that a pendulum swings slightly slower in Cayenne than in Paris.

1673年，讓·里奇注意到卡宴的鐘擺擺動(dòng)速度比巴黎略慢。

From this observation alone,

只用這一個(gè)現(xiàn)象，

and clever mathematics,

以及一些巧妙的數(shù)學(xué)推導(dǎo)，

Newton rightly deduced that the Earth is a wee bit flattened at the poles,

牛頓正確地推斷出地球在兩極地區(qū)稍稍扁一些，

like 0.3 percent -- so tiny that you wouldn't even notice it style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>大概只有0.3%， 這種細(xì)微的差別在 觀察地球全貌時(shí)根本無(wú)法發(fā)現(xiàn)。

These stories show that mathematics is able to make us go out of our intuition measure the Earth which seems infinite,

這些故事說(shuō)明了， 數(shù)學(xué)能夠讓我們超越自己的直覺(jué)， 測(cè)量看似不可測(cè)的地球尺寸，

see atoms which are invisible or detect an imperceptible variation of shape.

觀察看不見(jiàn)的原子， 或是檢測(cè)肉眼不可識(shí)別的微小形變。

And if there is just style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>如果你們只能從我的演講中了解到一樣?xùn)|西，

it is this: mathematics allows us to go beyond the intuition and explore territories which do not fit within our grasp.

那應(yīng)該就是：數(shù)學(xué)讓我們超越人類直覺(jué)， 并且探索我們所無(wú)法觸及的領(lǐng)域。

Here's a modern example you will all relate to: searching the Internet.

這有個(gè)例子各位都非常熟悉：上網(wǎng)。

The World Wide Web,

萬(wàn)維網(wǎng)，

more than style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>有著超過(guò)十億個(gè)網(wǎng)頁(yè)， 難道你想全部搜索一遍嗎？

Computing power helps,

計(jì)算機(jī)可能有幫助，

but it would be useless without the mathematical modeling to find the information hidden in the data.

但是如果沒(méi)有了數(shù)學(xué)模型， 它就是一堆廢鐵， 無(wú)法搜尋數(shù)據(jù)中隱藏的信息。

Let's work out a baby problem.

讓我們做一道很簡(jiǎn)單的題。

Imagine that you're a detective working style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>想象你是一個(gè)偵探， 正在調(diào)查一個(gè)犯罪案件，

and there are many people who have their version of the facts.

很多人參與其中，并且各執(zhí)一詞。

Who do you want to interview first?

你想先詢問(wèn)誰(shuí)呢？

Sensible answer: prime witnesses.

合理的答案是：主要的目擊者。

You see, suppose that there is person number seven,

想想看， 假設(shè)有一位7號(hào)證人，

tells you a story,

告訴了你一件事情，

but when you ask where he got if from,

但當(dāng)你問(wèn)他從哪里聽(tīng)說(shuō)的，

he points to person number three as a source.

他說(shuō)3號(hào)證人是消息來(lái)源。

And maybe person number three, in turn,

有可能3號(hào)證人

points at person number style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>也相應(yīng)地指向1號(hào)證人作為主要消息來(lái)源。

Now number style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>現(xiàn)在1號(hào)證人是主要目擊者了，

so I definitely want to interview him -- priority.

所以我一定想要先去采訪他。

And from the graph we also see that person number four is a prime witness.

從這幅圖中，我們同樣看到4號(hào)證人，是一位主要目擊者。

And maybe I even want to interview him first,

我可能更想先去采訪他，

because there are more people who refer to him.

因?yàn)樗惶峒暗拇螖?shù)比1號(hào)還要多。

OK, that was easy,

好吧，這還算簡(jiǎn)單的，

but now what about if you have a big bunch of people who will testify?

但是如果你有一大群人要作證呢？

And this graph,

這張圖

I may think of it as all people who testify in a complicated crime case,

我可以把它當(dāng)作 一件復(fù)雜案件的所有證人，

but it may just as well be web pages pointing to each other,

但也可以把它看作是互相鏈接的網(wǎng)頁(yè)，

referring to each other for contents.

互相引用其中的內(nèi)容。

Which style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>哪些網(wǎng)頁(yè)最有權(quán)威性呢？

Not so clear.

還不太清楚。

Enter PageRank, style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>于是PageRank問(wèn)世了， 它是谷歌最早的基石之一。

This algorithm uses the laws of mathematical randomness to determine automatically the most relevant web pages,

這種算法運(yùn)用了數(shù)學(xué)隨機(jī)性的定律， 來(lái)自動(dòng)判斷哪些網(wǎng)頁(yè)關(guān)聯(lián)最多，

in the same way as we used randomness in the Galton Board experiment.

與我們?cè)诟郀栴D板實(shí)驗(yàn)中運(yùn)用隨機(jī)性的方法一樣。

So let's send into this graph a bunch of tiny,

那就把一堆小小的數(shù)碼玻璃珠放到這個(gè)圖表中，

digital marbles and let them go randomly through the graph.

讓它們隨機(jī)的在圖中穿行。

Each time they arrive at some site,

每當(dāng)它們到達(dá)某個(gè)網(wǎng)頁(yè)，

they will go out through some link chosen at random to the next style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>它們就會(huì)隨機(jī)選擇一個(gè)鏈接，

And again, and again, and again.

然后跳轉(zhuǎn)到另一頁(yè)，一遍又一遍重復(fù)。

And with small, growing piles,

用這些小小的光點(diǎn)，

we'll keep the record of how many times each site has been visited by these digital marbles.

我們記錄下每個(gè)網(wǎng)頁(yè)被訪問(wèn)的次數(shù)， 就用這些數(shù)碼珠子。

Here we go.

開(kāi)始吧。

Randomness, randomness.

一切隨機(jī)。

And from time to time,

有時(shí)候呢，

also let's make jumps completely randomly to increase the fun.

我們就完全隨機(jī)跳躍，以增加樂(lè)趣。

And look at this: from the chaos will emerge the solution.

看看這個(gè)：在一片混亂中產(chǎn)生了一個(gè)答案。

The highest piles correspond to those sites which somehow are better connected than the others,

這里最高的幾堆對(duì)應(yīng)著那些相對(duì)來(lái)說(shuō)鏈接更多的網(wǎng)頁(yè)，

more pointed at than the others.

被引用更多次的網(wǎng)頁(yè)。

And here we see clearly which are the web pages we want to first try.

在這里我們清晰地看到， 哪一些是我們最想先看的網(wǎng)頁(yè)。

Once again, the solution emerges from the randomness.

再一次， 問(wèn)題的解答來(lái)源于隨機(jī)性。

Of course, since that time,

當(dāng)然，從那以后，

Google has come up with much more sophisticated algorithms,

谷歌已經(jīng)發(fā)明出 數(shù)不勝數(shù)的復(fù)雜算法，

but already this was beautiful.

但是這個(gè)算法已經(jīng)很好了。

And still, just style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>然而， 這只是滄海一粟。

With the advent of digital area,

隨著數(shù)字領(lǐng)域的飛速發(fā)展，

more and more problems lend themselves to mathematical analysis,

越來(lái)越多的問(wèn)題需要用數(shù)學(xué)分析來(lái)解決，

making the job of mathematician a more and more useful style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>讓數(shù)學(xué)家這個(gè)工作變得越來(lái)越實(shí)用，

to the extent that a few years ago,

以至于大約幾年前，

it was ranked number style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>它在數(shù)百個(gè)職業(yè)中排名第一， 這份排名是有關(guān)最好和最差的職業(yè)， 由華爾街日?qǐng)?bào)在2009年發(fā)表。

Mathematician -- best job in the world.

數(shù)學(xué)家是世界上最好的工作。

That's because of the applications: communication theory, information theory, game theory, compressed sensing, machine learning, graph analysis, harmonic analysis.

這是因?yàn)樗鼞?yīng)用廣泛：通訊理論、 信息理論、 博弈論、 壓縮傳感、 機(jī)器學(xué)習(xí)、 圖表分析、 諧波分析。

And why not stochastic processes, linear programming,

為什么不是隨機(jī)過(guò)程，線性規(guī)劃，

or fluid simulation?

或者流體模擬。

Each of these fields have monster industrial applications.

以上每一個(gè)領(lǐng)域都有規(guī)模巨大的工業(yè)應(yīng)用。

And through them,

透過(guò)它們可以看出，

there is big money in mathematics.

數(shù)學(xué)的商機(jī)是無(wú)限的。

And let me concede that when it comes to making money from the math,

我必須承認(rèn)， 談到用數(shù)學(xué)賺錢，

the Americans are by a long shot the world champions, with clever,

美國(guó)人可是遙遙領(lǐng)先全世界，

emblematic billionaires and amazing, giant companies, all resting, ultimately,

有一群標(biāo)志性絕頂聰明的領(lǐng)導(dǎo)者， 還有讓人大開(kāi)眼界的商業(yè)巨頭，

on good algorithm.

歸根結(jié)底都不約而同地依賴好的算法。

Now with all this beauty,

數(shù)學(xué)兼具著美、

usefulness and wealth,

實(shí)用性， 以及無(wú)限商機(jī)，

mathematics does look more sexy.

它似乎的確更有魅力了。

But don't you think that the life a mathematical researcher is an easy style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>但是你千萬(wàn)別以為數(shù)學(xué)家的生活很輕松。

It is filled with perplexity, frustration,

它充滿了困惑，沮喪，

a desperate fight for understanding.

是追求真知的絕望之戰(zhàn)。

Let me evoke for you style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>我給大家說(shuō)一說(shuō)我的數(shù)學(xué)生涯中最特別的一天。

Or should I say,

或者我該說(shuō)，

one of the most striking nights.

最特別的一晚。

At that time,

那個(gè)時(shí)候，

I was staying at the Institute for Advanced Studies in Princeton -- for many years,

我待在普林斯頓大學(xué)的高等研究所里，

the home of Albert Einstein and arguably the most holy place for mathematical research in the world.

這里曾是愛(ài)因斯坦多年的家， 也很可能是世界上數(shù)學(xué)研究的神圣之顛。

And that night I was working and working style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>那天晚上我苦思冥想， 尋找一個(gè)非常隱晦的證明，

which was incomplete.

非常不完整。

It was all about understanding the paradoxical stability property of plasmas,

它是有關(guān)于等離子體的矛盾穩(wěn)定特性的了解，

which are a crowd of electrons.

這里指的是一團(tuán)電子云。

In the perfect world of plasma,

在等離子體的理想世界，

there are no collisions and no friction to provide the stability like we are used to.

是沒(méi)有任何碰撞的， 而且沒(méi)有任何摩擦力， 使其像我們習(xí)慣的那么穩(wěn)定。

But still, if you slightly perturb a plasma equilibrium,

然而， 如果你輕微打破等離子體平衡，

you will find that the resulting electric field spontaneously vanishes,

你會(huì)發(fā)現(xiàn)相應(yīng)產(chǎn)生的電場(chǎng)會(huì)自發(fā)的消失，

or damps out,

或者是減弱，

as if by some mysterious friction force.

好像受到了某種神秘摩擦力的影響。

This paradoxical effect,

這種矛盾的特性，

called the Landau damping,

叫做朗道阻尼，

is style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>是等離子物理中最重要的現(xiàn)象之一，

and it was discovered through mathematical ideas.

而且它是由數(shù)學(xué)思想推導(dǎo)出來(lái)的。

But still, a full mathematical understanding of this phenomenon was missing.

然而， 對(duì)此現(xiàn)象的完整數(shù)學(xué)理解還不完善。

And together with my former student and main collaborator Clément Mouhot,

和我以前的學(xué)生和主要合作者克萊門特·穆特一起，

in Paris at the time,

我們那時(shí)在巴黎，

we had been working for months and months style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>我們?yōu)榱藢ふ疫@個(gè)證法已經(jīng)花了好幾個(gè)月。

Actually, I had already announced by mistake that we could solve it.

實(shí)際上， 我還以為我們可以解決這個(gè)問(wèn)題。

But the truth is,

然而事實(shí)上，

the proof was just not working.

那種證法完全無(wú)效。

In spite of more than 100 pages of complicated, mathematical arguments,

即使是一百多頁(yè)的復(fù)雜數(shù)學(xué)推導(dǎo)，

and a bunch discoveries,

還有一大堆的新發(fā)現(xiàn)，

and huge calculation,

巨大的計(jì)算量，

it was not working.

依然得不出什么結(jié)論。

And that night in Princeton,

在普林斯頓的那個(gè)晚上，

a certain gap in the chain of arguments was driving me crazy.

證明中的一個(gè)小缺口讓我近乎瘋狂。

I was putting in there all my energy and experience and tricks,

我對(duì)它使出渾身解數(shù)，

and still nothing was working.

但是依舊沒(méi)有進(jìn)展。

1 a.m., 2 a.m., 3 a.m., not working.

凌晨一點(diǎn)、兩點(diǎn)、三點(diǎn)， 毫無(wú)進(jìn)展。

Around 4 a.m.,

大概凌晨四點(diǎn)的時(shí)候，

I go to bed in low spirits.

我無(wú)精打采的上床。

Then a few hours later,

幾個(gè)小時(shí)后，

waking up and go, 'Ah,

我從床上爬起來(lái)， “啊，

it's time to get the kids to school --'

該送孩子們上學(xué)了?！?/strong>

What is this?

這是什么？

There was this voice in my head, I swear.

我確定，我的腦袋里有個(gè)聲音。

'Take the second term to the other side,

“把第二個(gè)任期帶到另一邊，

Fourier transform and invert in L2.'

傅里葉展開(kāi)然后在L2域反變換?！?/strong>

Damn it, that was the start of the solution!

可惡！這才要開(kāi)始解了??！

You see, I thought I had taken some rest,

我以為我自己在休息，

but really my brain had continued to work style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>但實(shí)際上，我的大腦一直在思考這個(gè)問(wèn)題。

In those moments,

在那些時(shí)刻，

you don't think of your career or your colleagues,

你不會(huì)想到你的職業(yè)生涯或是你的同事，

it's just a complete battle between the problem and you.

這只是你自己與問(wèn)題之間的斗爭(zhēng)。

That being said,

但說(shuō)到這里，

it does not harm when you do get a promotion in reward for your hard work.

如果你因努力工作而得到升職，當(dāng)然是很好的事情。

And after we completed our huge analysis of the Landau damping,

在我們完成了朗道阻尼方面的重大研究后，

I was lucky enough to get the most coveted Fields Medal from the hands of the President of India,

我很幸運(yùn)地獲得了我夢(mèng)寐以求的菲爾茲獎(jiǎng)，我從印度總統(tǒng)手中接過(guò)此獎(jiǎng)，

in Hyderabad style='margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-family: Arial, Helvetica, sans-serif; font-size: 14px;       text-align: left;       background-color: rgb(244, 250, 244);  '>那是在2010年8月19日， 在海德拉巴城。

2010 -- an honor that mathematicians never dare to dream,

2010年-這是數(shù)學(xué)家們從來(lái)不敢夢(mèng)想的榮譽(yù)，

a day that I will remember until I live.

我也會(huì)將這天永遠(yuǎn)銘記在心。

What do you think,

對(duì)于這樣的情況，

on such an occasion?

你們覺(jué)得怎樣呢？

Pride, yes?

很自豪，對(duì)吧？

And gratitude to the many collaborators who made this possible.

還有對(duì)主要合作者的感激之情。

And because it was a collective adventure,

而且因?yàn)檫@是一個(gè)集體研究，

you need to share it,

你需要把成果公開(kāi)，

not just with your collaborators.

而非只是與合作者共享。

I believe that everybody can appreciate the thrill of mathematical research,

我相信每個(gè)人都可以欣賞數(shù)學(xué)研究的刺激感，

and share the passionate stories of humans and ideas behind it.

并且分享精彩研究過(guò)程中的人和事。

And I've been working with my staff at Institut Henri Poincaré,

我在昂利·龐加萊研究所與我的團(tuán)隊(duì)工作，

together with partners and artists of mathematical communication worldwide,

還有一些其他的合伙人、世界各地的數(shù)學(xué)交流藝術(shù)家，

so that we can found our own,

于是我們就可以創(chuàng)立我們自己的，

very special museum of mathematics there.

非常特別的數(shù)學(xué)博物館。

So in a few years,

再過(guò)幾年，

when you come to Paris,

當(dāng)你來(lái)到巴黎，

after tasting the great,

在你們品嘗過(guò)美味酥脆的

crispy baguette and macaroon,

法國(guó)長(zhǎng)面包和馬卡龍（蛋白杏仁餅甜點(diǎn)）之后，

please come and visit us at Institut Henri Poincaré,

請(qǐng)各位也來(lái)我們的 昂利·龐加萊研究所轉(zhuǎn)一轉(zhuǎn)，

and share the mathematical dream with us.

與我們共享一個(gè)數(shù)學(xué)的夢(mèng)。

Thank you.

謝謝。