Imagine you're in a bar, or a club,

想像一下，你在酒吧或俱樂部，

and you start talking, and after a while, the question comes up,

你開始跟一位女士聊天，

"So, what do you do for work?"

過了一會，這個問題來了， 「那麼，你是做什麼工作的？」

And since you think your job is interesting,

因為你覺得你的工作很有趣，你說：

you say, "I'm a mathematician." (Laughter)

「我是一個數學家。」 （笑聲）

And inevitably, during that conversation

幾乎沒有例外，在那個談話中，

one of these two phrases come up:

下面兩句話之一會出現：

A) "I was terrible at math, but it wasn't my fault.

A) 「我的數學很差，但那不是我的錯。」

It's because the teacher was awful." (Laughter)

因為我的老師很爛。 （笑聲）

Or B) "But what is math really for?"

或者 B) 「數學到底有什麼用？」

(Laughter)

（笑聲）

I'll now address Case B.

我先來談案例 B)

(Laughter)

（笑聲）

When someone asks you what math is for, they're not asking you

當有人問你數學是什麼， 他們不是問你

about applications of mathematical science.

有關數學的科學應用。

They're asking you,

他們是問你，

why did I have to study that bullshit I never used in my life again? (Laughter)

為什麼我要學習一生 都不會用到的廢物科目？ (笑聲）

That's what they're actually asking.

這就是他們實際上問的。

So when mathematicians are asked what math is for,

所以，當數學家被問到數學是做什麼的，

they tend to fall into two groups:

它們傾向於分為兩類：

54.51 percent of mathematicians will assume an attacking position,

54.51%的數學家將採取進攻的姿態，

and 44.77 percent of mathematicians will take a defensive position.

而44.77％的數學家將採防禦的姿態。

There's a strange 0.8 percent, among which I include myself.

還有奇怪的0.8％，其中包括我自己。

Who are the ones that attack?

誰是那些採取攻擊姿態的人?

The attacking ones are mathematicians who would tell you

採取攻擊姿態的數學家會告訴你

this question makes no sense,

這個問題是沒有意義的，

because mathematics have a meaning all their own --

因為數學有其自身的意義 -

a beautiful edifice with its own logic --

像是一個美麗的大廈有它自己的邏輯 -

and that there's no point

而且不斷尋找

in constantly searching for all possible applications.

所有可能的應用是沒有意義的。

What's the use of poetry? What's the use of love?

詩歌有什麼用？愛有什麼用？

What's the use of life itself? What kind of question is that?

生活本身有什麼用？這是什麼樣的問題呢？

(Laughter)

(笑聲）

Hardy, for instance, was a model of this type of attack.

例如，哈迪，就是一個遭受這種攻擊的典型。

And those who stand in defense tell you,

那些採防禦姿的態會告訴你，

"Even if you don't realize it, friend, math is behind everything."

“即使你沒有意識到這一點， 朋友，數學是所有東西背後的一切。”

(Laughter)

(笑聲）

Those guys,

那些人，

they always bring up bridges and computers.

他們總是提到橋樑和電腦。

"If you don't know math, your bridge will collapse."

“如果你不知道數學，您的大橋將會倒塌。”

(Laughter)

(笑聲）

It's true, computers are all about math.

這是真的，電腦跟數學密切相關。

And now these guys have also started saying

而現在這些人也開始說，

that behind information security and credit cards are prime numbers.

在電腦資訊安全和信用卡背後就是質數。

These are the answers your math teacher would give you if you asked him.

這也就是你的數學老師會給你的答案。

He's one of the defensive ones.

他也是採防禦姿態的成員之一。

Okay, but who's right then?

好了，但到底誰是對的呢？

Those who say that math doesn't need to have a purpose,

是那些說數學並不需要有一個目的，

or those who say that math is behind everything we do?

還是那些說數學在我們所做的一切中？

Actually, both are right.

其實上，雙方都是是正確的。

But remember I told you

但請記住我告訴你的

I belong to that strange 0.8 percent claiming something else?

我屬於那奇怪自稱別的0.8％嗎？

So, go ahead, ask me what math is for.

因此，再問我一次數學是做什麼的。

Audience: What is math for?

觀眾：數學是做什麼的？

Eduardo Sáenz de Cabezón: Okay, 76.34 percent of you asked the question,

好吧，你們中76.34％的人問了這個問題，

23.41 percent didn't say anything,

23.41％的人什麼也沒有說，

and the 0.8 percent --

和剩下的0.8％ ，

I'm not sure what those guys are doing.

我不知道那些人在做什麼。

Well, to my dear 76.31 percent --

好吧，我那親愛的76.31％的觀眾，

it's true that math doesn't need to serve a purpose,

數學真的不需要有一個目的，

it's true that it's a beautiful structure, a logical one,

它真的是有一個美麗且有邏輯的結構，

probably one of the greatest collective efforts

而這也可能是人類在歷史上

ever achieved in human history.

集體努力實現的成就之一。

But it's also true that there,

但這也是真的：

where scientists and technicians are looking for mathematical theories

當科學家和技術人員在尋找

that allow them to advance,

使他們能進步的數學理論時，

they're within the structure of math, which permeates everything.

他們是在無處不在的數學結構中工作。

It's true that we have to go somewhat deeper,

這是真的，我們必須去深入了解，

to see what's behind science.

才能明白科學。

Science operates on intuition, creativity.

科學在直覺和創造力上運作。

Math controls intuition and tames creativity.

而數學控制直覺及馴服創造力。

Almost everyone who hasn't heard this before

幾乎每個沒有聽說過

is surprised when they hear that if you take

這個之前會覺得驚訝。當他們聽到如果你拿個

a 0.1 millimeter thick sheet of paper, the size we normally use,

我們通常使用的0.1毫米厚紙片，

and, if it were big enough, fold it 50 times,

而且，如果它夠大，把它折疊50次，

its thickness would extend almost the distance from the Earth to the sun.

它的厚度幾乎可以從地球延伸到太陽。

Your intuition tells you it's impossible.

你的直覺告訴你這是不可能的。

Do the math and you'll see it's right.

但數學告訴你它是正確的。

That's what math is for.

這就是數學的作用了。

It's true that science, all types of science, only makes sense

這是真的，科學，各類科學的意義在於

because it makes us better understand this beautiful world we live in.

因為它使我們更好地理解 我們生活的這個美麗的世界。

And in doing that,

而這樣做，

it helps us avoid the pitfalls of this painful world we live in.

它可以幫助我們在我們居住的 這個痛苦的世界裡避免重蹈覆轍。

There are sciences that help us in this way quite directly.

有些科學可以直接幫助我們。

Oncological science, for example.

例如，腫瘤學。

And there are others we look at from afar, with envy sometimes,

而且還有其他我們有時 帶著羨慕眼光從遠方觀看的科學，

but knowing that we are what supports them.

但我們知道，我們是支持它們的。

All the basic sciences support them,

所有的基礎科學都支持它們，

including math.

包括數學。

All that makes science, science is the rigor of math.

所有這一切創造科學，而數學是科學的嚴謹性。

And that rigor factors in because its results are eternal.

嚴謹是最重要的因素因為它的結果是永恆的。

You probably said or were told at some point

你可能在某些時候說過，或被告知，

that diamonds are forever, right?

鑽石是永恆的，對不對？

That depends on your definition of forever!

這取決於你對永恆的定義！

A theorem -- that really is forever.

一個數學定理真的是永恆的。

(Laughter)

（笑聲）

The Pythagorean theorem is still true

即使畢達哥拉斯死了，

even though Pythagoras is dead, I assure you it's true. (Laughter)

畢氏定理仍然是正確的，我保證。（笑聲）

Even if the world collapsed

即使世界坍塌

the Pythagorean theorem would still be true.

畢氏定理仍然是真的。

Wherever any two triangle sides and a good hypotenuse get together

只要任意兩個直角三角形邊 和合適的斜邊連在一起

(Laughter)

（笑聲）

the Pythagorean theorem goes all out. It works like crazy.

畢氏定理就能用。 它真是太有用了。

(Applause)

（掌聲）

Well, we mathematicians devote ourselves to come up with theorems.

好了，我們的數學家貢獻終身想出定理。

Eternal truths.

永恆的真理。

But it isn't always easy to know the difference between

但並不總是容易知道

an eternal truth, or theorem, and a mere conjecture.

它是一個永恆的真理， 或定理，或是單純的猜想。

You need proof.

你需要證明。

For example,

例如，

let's say I have a big, enormous, infinite field.

我有一個大的，巨大的，無限領域。

I want to cover it with equal pieces, without leaving any gaps.

我想以同樣的物件覆蓋它，不留空隙。

I could use squares, right?

我可以用正方形，對不對？

I could use triangles. Not circles, those leave little gaps.

我可以用三角形。但不能用圓形， 因為那會留下小缺口。

Which is the best shape to use?

用那個形狀是最好的？

One that covers the same surface, but has a smaller border.

一個覆蓋相同的表面，但具有較小邊的。

In the year 300, Pappus of Alexandria said the best is to use hexagons,

在公元300年，帕普斯說，最好是用六邊形，

just like bees do.

就像蜜蜂用的。

But he didn't prove it.

但他並沒有證明它。

The guy said, "Hexagons, great! Let's go with hexagons!"

這傢伙說，“六邊形，太棒了！讓我們用六邊形！“

He didn't prove it, it remained a conjecture.

他沒有提供證明，所以它仍然只是一個猜想。

"Hexagons!"

“六邊形”！

And the world, as you know, split into Pappists and anti-Pappists,

而這世界，你也知道， 分成帕普斯幫和反帕普斯幫，

until 1700 years later

直到1700年後

when in 1999, Thomas Hales proved

在公元1999年，托馬斯·黑爾斯證明了

that Pappus and the bees were right -- the best shape to use was the hexagon.

帕普斯和蜜蜂是正確的，最好的形狀是六邊形。

And that became a theorem, the honeycomb theorem,

而這也成為一個定理，蜂窩定理，

that will be true forever and ever,

而它將是真的，直到永遠，

for longer than any diamond you may have. (Laughter)

比任何你擁有的鑽石活的更久遠。 （笑聲）

But what happens if we go to three dimensions?

但是，當我們來到三度空間時要怎麼辦？

If I want to fill the space with equal pieces,

如果我想以相同的物件填補空間，

without leaving any gaps,

不留空隙，

I can use cubes, right?

我可以使用立方體，對不對？

Not spheres, those leave little gaps. (Laughter)

不能用球體，那會留下小缺口。（笑聲）

What is the best shape to use?

什麼形狀是最好的？

Lord Kelvin, of the famous Kelvin degrees and all,

以克氏溫標聞名的克爾文爵士，

said that the best was to use a truncated octahedron

說，最好使用截角八面體

which, as you all know --

因為，因為大家都知道

(Laughter) --

（笑聲）

is this thing here!

就是這個東西！

(Applause)

（掌聲）

Come on.

拜託。

Who doesn't have a truncated octahedron at home? (Laughter)

誰家沒有截角八面體？ （笑聲）

Even a plastic one.

即使是塑膠的。

"Honey, get the truncated octahedron, we're having guests."

“親愛的，去拿截角八面體，我們有客人來了。“

Everybody has one! (Laughter)

每個人都有！（笑聲）

But Kelvin didn't prove it.

但克爾文並沒有證明它。

It remained a conjecture -- Kelvin's conjecture.

它仍然是一個猜想 - 克爾文的猜想。

The world, as you know, then split into Kelvinists and anti-Kelvinists

而這世界，你也知道， 分成克爾文幫和反克爾文幫，

(Laughter)

（笑聲）

until a hundred or so years later,

直到一百年多年後，

someone found a better structure.

有人找到了更好的立方體。

Weaire and Phelan found this little thing over here --

Weaire和Phelan發現了這個小東西 -

(Laughter) --

（笑聲）

this structure to which they gave the very clever name

他們給這種立方結構取了個非常聰明的名字

"the Weaire-€“Phelan structure."

就是“Weaire - Phelan的結構”。

(Laughter)

（笑聲）

It looks like a strange object, but it isn't so strange,

它看起來像一個奇怪的物體， 但它不是那麼的陌生，

it also exists in nature.

因為它也存在於自然界。

It's very interesting that this structure,

這種結構是非常有趣的，

because of its geometric properties,

因為它的幾何特性，

was used to build the Aquatics Center for the Beijing Olympic Games.

被用來在北京奧運會設計游泳中心。

There, Michael Phelps won eight gold medals,

在那裡，菲爾普斯贏得了八面奧運金牌，

and became the best swimmer of all time.

並成為有史以來最好的游泳運動員。

Well, until someone better comes along, right?

好吧，直到有人發現更好的結構，對不對？

As may happen with the Weaire-€“Phelan structure.

就像是Weaire - Phelan結構。

It's the best until something better shows up.

直到更好的東西出現。

But be careful, because this one really stands a chance

但注意，因為這個是很有可能的

that in a hundred or so years, or even if it's in 1700 years,

在100年左右，或者是在1700年後，

that someone proves it's the best possible shape for the job.

有人會證明這是最好的結構。

It will then become a theorem, a truth, forever and ever.

然後，它會成為一個定理，一個真理，直到永遠。

For longer than any diamond.

比鑽石活得更久。

So, if you want to tell someone

所以，如果你想告訴別人

that you will love them forever

你會永遠愛他們，

you can give them a diamond.

你可以給他們鑽石。

But if you want to tell them that you'll love them forever and ever,

但是，如果你要告訴他們， 你一定會永永遠遠的喜歡他們，

give them a theorem!

給他們一個定理！

(Laughter)

（笑聲）

But hang on a minute!

等一下！

You'll have to prove it,

你必須要證明它，

so your love doesn't remain

讓你的愛不只是

a conjecture.

一個猜想。

(Applause)

（掌聲）