ABOUT THE SPEAKER
Eduardo Sáenz de Cabezón - Math educator
Eduardo Sáenz de Cabezón links science with humor and stories.

Why you should listen

Eduardo Sáenz de Cabezón links science with humor and stories. He studied theology and has a PhD in mathematics from the University of La Rioja. He speaks on these two topics in universities and secondary schools as a storyteller for children, youth and adults. Sáenz de Cabezón has also been a professor of Computer Information Systems, Discrete Mathematics and Algebra at the University of La Rioja since 2010.

He won the FameLab contest for scientific monologues in Spain in 2013.

More profile about the speaker
Eduardo Sáenz de Cabezón | Speaker | TED.com
TEDxRiodelaPlata

Eduardo Sáenz de Cabezón: Math is forever

Eduardo Sáenz de Cabezón: 數學恆久遠

Filmed:
1,878,468 views

數學是用來幹嘛的?這是那些一想到數學就昏昏欲睡的學生想破頭也想不明白的問題,數學家 Eduardo Sáenz de Cabezón 以幽默而優雅的方式進行了回答。作為任何科學的基礎,數學之美被 Eduardo 展現得淋漓盡致,而且,鑽石未必長久,數學定理才是真正的恆久遠。
- Math educator
Eduardo Sáenz de Cabezón links science with humor and stories. Full bio

Double-click the English transcript below to play the video.

00:13
Imagine想像 you're in a bar酒吧, or a club俱樂部,
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想像一下,你在酒吧或俱樂部,
你開始跟一位女士聊天,
00:19
and you start開始 talking, and after a while,
the question comes up,
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過了一會,這個問題來了,
「那麼,你是做什麼工作的?」
00:22
"So, what do you do for work?"
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00:24
And since以來 you think
your job工作 is interesting有趣,
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因為你覺得你的工作很有趣,你說:
「我是一個數學家。」
(笑聲)
00:26
you say, "I'm a mathematician數學家."
(Laughter笑聲)
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幾乎沒有例外,在那個談話中,
00:31
And inevitably必將, during that conversation會話
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下面兩句話之一會出現:
00:34
one of these two phrases短語 come up:
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A) 「我的數學很差,但那不是我的錯。」
00:37
A) "I was terrible可怕 at math數學,
but it wasn't my fault故障.
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00:41
It's because the teacher老師
was awful可怕." (Laughter笑聲)
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因為我的老師很爛。
(笑聲)
或者 B) 「數學到底有什麼用?」
00:44
Or B) "But what is math數學 really for?"
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(笑聲)
00:47
(Laughter笑聲)
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00:48
I'll now address地址 Case案件 B.
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我先來談案例 B)
(笑聲)
00:50
(Laughter笑聲)
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當有人問你數學是什麼,
他們不是問你
00:52
When someone有人 asks you what math數學 is for,
they're not asking you
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有關數學的科學應用。
00:57
about applications應用
of mathematical數學的 science科學.
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他們是問你,
01:00
They're asking you,
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01:01
why did I have to study研究 that bullshit廢話
I never used in my life again? (Laughter笑聲)
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為什麼我要學習一生
都不會用到的廢物科目? (笑聲)
這就是他們實際上問的。
01:05
That's what they're actually其實 asking.
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所以,當數學家被問到數學是做什麼的,
01:07
So when mathematicians數學家 are asked
what math數學 is for,
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它們傾向於分為兩類:
01:12
they tend趨向 to fall秋季 into two groups:
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54.51%的數學家將採取進攻的姿態,
01:14
54.51 percent百分 of mathematicians數學家
will assume承擔 an attacking進攻 position位置,
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而44.77%的數學家將採防禦的姿態。
01:20
and 44.77 percent百分 of mathematicians數學家
will take a defensive防禦性 position位置.
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還有奇怪的0.8%,其中包括我自己。
01:25
There's a strange奇怪 0.8 percent百分,
among其中 which哪一個 I include包括 myself.
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誰是那些採取攻擊姿態的人?
01:29
Who are the ones那些 that attack攻擊?
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採取攻擊姿態的數學家會告訴你
01:31
The attacking進攻 ones那些 are mathematicians數學家
who would tell you
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這個問題是沒有意義的,
01:33
this question makes品牌 no sense,
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因為數學有其自身的意義 -
01:35
because mathematics數學
have a meaning含義 all their own擁有 --
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像是一個美麗的大廈有它自己的邏輯 -
01:38
a beautiful美麗 edifice大廈 with its own擁有 logic邏輯 --
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而且不斷尋找
01:41
and that there's no point
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所有可能的應用是沒有意義的。
01:43
in constantly經常 searching搜索
for all possible可能 applications應用.
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詩歌有什麼用?愛有什麼用?
01:45
What's the use of poetry詩歌?
What's the use of love?
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生活本身有什麼用?這是什麼樣的問題呢?
01:47
What's the use of life itself本身?
What kind of question is that?
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(笑聲)
01:50
(Laughter笑聲)
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例如,哈迪,就是一個遭受這種攻擊的典型。
01:52
Hardy哈迪, for instance, was a model模型
of this type類型 of attack攻擊.
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那些採防禦姿的態會告訴你,
01:56
And those who stand in defense防禦 tell you,
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“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。”
01:58
"Even if you don't realize實現 it, friend朋友,
math數學 is behind背後 everything."
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(笑聲)
02:03
(Laughter笑聲)
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那些人,
02:04
Those guys,
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他們總是提到橋樑和電腦。
02:06
they always bring帶來 up
bridges橋樑 and computers電腦.
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“如果你不知道數學,您的大橋將會倒塌。”
02:10
"If you don't know math數學,
your bridge will collapse坍方."
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02:12
(Laughter笑聲)
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(笑聲)
這是真的,電腦跟數學密切相關。
02:14
It's true真正, computers電腦 are all about math數學.
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02:17
And now these guys
have also started開始 saying
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而現在這些人也開始說,
02:20
that behind背後 information信息 security安全
and credit信用 cards are prime主要 numbers數字.
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在電腦資訊安全和信用卡背後就是質數。
02:25
These are the answers答案 your math數學 teacher老師
would give you if you asked him.
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這也就是你的數學老師會給你的答案。
他也是採防禦姿態的成員之一。
02:29
He's one of the defensive防禦性 ones那些.
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02:31
Okay, but who's誰是 right then?
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好了,但到底誰是對的呢?
是那些說數學並不需要有一個目的,
02:33
Those who say that math數學
doesn't need to have a purpose目的,
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02:35
or those who say that math數學
is behind背後 everything we do?
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還是那些說數學在我們所做的一切中?
02:38
Actually其實, both are right.
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其實上,雙方都是是正確的。
02:40
But remember記得 I told you
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但請記住我告訴你的
02:42
I belong屬於 to that strange奇怪 0.8 percent百分
claiming自稱 something else其他?
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我屬於那奇怪自稱別的0.8%嗎?
02:45
So, go ahead, ask me what math數學 is for.
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因此,再問我一次數學是做什麼的。
02:48
Audience聽眾: What is math數學 for?
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觀眾:數學是做什麼的?
02:51
Eduardo愛德華多enz恩茨 de CabezCabezón: Okay,
76.34 percent百分 of you asked the question,
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好吧,你們中76.34%的人問了這個問題,
02:56
23.41 percent百分 didn't say anything,
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23.41%的人什麼也沒有說,
02:59
and the 0.8 percent百分 --
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和剩下的0.8% ,
03:00
I'm not sure what those guys are doing.
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我不知道那些人在做什麼。
03:03
Well, to my dear 76.31 percent百分 --
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好吧,我那親愛的76.31%的觀眾,
數學真的不需要有一個目的,
03:07
it's true真正 that math數學 doesn't need
to serve服務 a purpose目的,
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03:11
it's true真正 that it's
a beautiful美麗 structure結構體, a logical合乎邏輯 one,
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它真的是有一個美麗且有邏輯的結構,
03:14
probably大概 one
of the greatest最大 collective集體 efforts努力
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而這也可能是人類在歷史上
03:17
ever achieved實現 in human人的 history歷史.
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集體努力實現的成就之一。
03:19
But it's also true真正 that there,
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但這也是真的:
03:21
where scientists科學家們 and technicians技師
are looking for mathematical數學的 theories理論
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當科學家和技術人員在尋找
使他們能進步的數學理論時,
03:26
that allow允許 them to advance提前,
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03:28
they're within the structure結構體 of math數學,
which哪一個 permeates滲透 everything.
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他們是在無處不在的數學結構中工作。
這是真的,我們必須去深入了解,
03:32
It's true真正 that we have to go
somewhat有些 deeper更深,
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03:35
to see what's behind背後 science科學.
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才能明白科學。
03:37
Science科學 operates操作 on intuition直覺, creativity創造力.
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科學在直覺和創造力上運作。
而數學控制直覺及馴服創造力。
03:41
Math數學 controls控制 intuition直覺
and tames馴服 creativity創造力.
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03:45
Almost幾乎 everyone大家
who hasn't有沒有 heard聽說 this before
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幾乎每個沒有聽說過
這個之前會覺得驚訝。當他們聽到如果你拿個
03:47
is surprised詫異 when they hear
that if you take
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03:50
a 0.1 millimeter毫米 thick sheet of paper,
the size尺寸 we normally一般 use,
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我們通常使用的0.1毫米厚紙片,
而且,如果它夠大,把它折疊50次,
03:55
and, if it were big enough足夠,
fold it 50 times,
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03:58
its thickness厚度 would extend延伸 almost幾乎
the distance距離 from the Earth地球 to the sun太陽.
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它的厚度幾乎可以從地球延伸到太陽。
你的直覺告訴你這是不可能的。
04:04
Your intuition直覺 tells告訴 you it's impossible不可能.
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但數學告訴你它是正確的。
04:07
Do the math數學 and you'll你會 see it's right.
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04:09
That's what math數學 is for.
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這就是數學的作用了。
04:12
It's true真正 that science科學, all types類型
of science科學, only makes品牌 sense
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這是真的,科學,各類科學的意義在於
04:15
because it makes品牌 us better understand理解
this beautiful美麗 world世界 we live生活 in.
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因為它使我們更好地理解
我們生活的這個美麗的世界。
而這樣做,
04:19
And in doing that,
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04:20
it helps幫助 us avoid避免 the pitfalls陷阱
of this painful痛苦 world世界 we live生活 in.
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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。
有些科學可以直接幫助我們。
04:24
There are sciences科學 that help us
in this way quite相當 directly.
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04:27
Oncological腫瘤學 science科學, for example.
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例如,腫瘤學。
04:29
And there are others其他 we look at from afar,
with envy羨慕 sometimes有時,
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而且還有其他我們有時
帶著羨慕眼光從遠方觀看的科學,
04:32
but knowing會心 that we are
what supports支持 them.
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但我們知道,我們是支持它們的。
04:35
All the basic基本 sciences科學
support支持 them,
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所有的基礎科學都支持它們,
包括數學。
04:38
including包含 math數學.
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04:40
All that makes品牌 science科學, science科學
is the rigor嚴格 of math數學.
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所有這一切創造科學,而數學是科學的嚴謹性。
04:44
And that rigor嚴格 factors因素 in
because its results結果 are eternal永恆.
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嚴謹是最重要的因素因為它的結果是永恆的。
04:49
You probably大概 said or were told
at some point
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你可能在某些時候說過,或被告知,
04:51
that diamonds鑽石 are forever永遠, right?
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鑽石是永恆的,對不對?
04:56
That depends依靠 on
your definition定義 of forever永遠!
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這取決於你對永恆的定義!
04:58
A theorem定理 -- that really is forever永遠.
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一個數學定理真的是永恆的。
(笑聲)
05:00
(Laughter笑聲)
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05:02
The Pythagorean畢達哥拉斯 theorem定理 is still true真正
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即使畢達哥拉斯死了,
畢氏定理仍然是正確的,我保證。(笑聲)
05:05
even though雖然 Pythagoras畢達哥拉斯 is dead,
I assure保證 you it's true真正. (Laughter笑聲)
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05:08
Even if the world世界 collapsed倒塌
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即使世界坍塌
05:09
the Pythagorean畢達哥拉斯 theorem定理
would still be true真正.
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畢氏定理仍然是真的。
只要任意兩個直角三角形邊
和合適的斜邊連在一起
05:12
Wherever哪裡 any two triangle三角形 sides雙方
and a good hypotenuse斜邊 get together一起
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(笑聲)
05:16
(Laughter笑聲)
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05:17
the Pythagorean畢達哥拉斯 theorem定理 goes all out.
It works作品 like crazy.
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畢氏定理就能用。
它真是太有用了。
05:20
(Applause掌聲)
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(掌聲)
05:27
Well, we mathematicians數學家 devote奉獻 ourselves我們自己
to come up with theorems定理.
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好了,我們的數學家貢獻終身想出定理。
永恆的真理。
05:31
Eternal永恆 truths真理.
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05:33
But it isn't always easy簡單 to know
the difference區別 between之間
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但並不總是容易知道
05:35
an eternal永恆 truth真相, or theorem定理,
and a mere conjecture推測.
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它是一個永恆的真理,
或定理,或是單純的猜想。
05:38
You need proof證明.
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你需要證明。
05:41
For example,
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例如,
05:43
let's say I have a big,
enormous巨大, infinite無窮 field領域.
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我有一個大的,巨大的,無限領域。
05:48
I want to cover it with equal等於 pieces,
without leaving離開 any gaps空白.
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我想以同樣的物件覆蓋它,不留空隙。
我可以用正方形,對不對?
05:52
I could use squares廣場, right?
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05:54
I could use triangles三角形.
Not circles, those leave離開 little gaps空白.
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我可以用三角形。但不能用圓形,
因為那會留下小缺口。
05:58
Which哪一個 is the best最好 shape形狀 to use?
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用那個形狀是最好的?
06:01
One that covers蓋子 the same相同 surface表面,
but has a smaller border邊境.
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一個覆蓋相同的表面,但具有較小邊的。
06:05
In the year 300, Pappus冠毛 of Alexandria亞歷山大
said the best最好 is to use hexagons六邊形,
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在公元300年,帕普斯說,最好是用六邊形,
就像蜜蜂用的。
06:10
just like bees蜜蜂 do.
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06:12
But he didn't prove證明 it.
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但他並沒有證明它。
06:13
The guy said, "Hexagons六角形, great!
Let's go with hexagons六邊形!"
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這傢伙說,“六邊形,太棒了!讓我們用六邊形!“
06:16
He didn't prove證明 it,
it remained保持 a conjecture推測.
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他沒有提供證明,所以它仍然只是一個猜想。
06:19
"Hexagons六角形!"
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“六邊形”!
而這世界,你也知道,
分成帕普斯幫和反帕普斯幫,
06:21
And the world世界, as you know,
split分裂 into PappistsPappists and anti-Pappists抗Pappists,
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06:24
until直到 1700 years年份 later後來
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直到1700年後
06:30
when in 1999, Thomas托馬斯 Hales海爾斯 proved證實
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在公元1999年,托馬斯·黑爾斯證明了
06:35
that Pappus冠毛 and the bees蜜蜂 were right --
the best最好 shape形狀 to use was the hexagon六邊形.
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帕普斯和蜜蜂是正確的,最好的形狀是六邊形。
06:40
And that became成為 a theorem定理,
the honeycomb蜂窩 theorem定理,
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而這也成為一個定理,蜂窩定理,
而它將是真的,直到永遠,
06:43
that will be true真正 forever永遠 and ever,
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比任何你擁有的鑽石活的更久遠。 (笑聲)
06:45
for longer than any diamond鑽石
you may可能 have. (Laughter笑聲)
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06:48
But what happens發生 if we go
to three dimensions尺寸?
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但是,當我們來到三度空間時要怎麼辦?
06:51
If I want to fill the space空間
with equal等於 pieces,
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如果我想以相同的物件填補空間,
不留空隙,
06:55
without leaving離開 any gaps空白,
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06:56
I can use cubes立方體, right?
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我可以使用立方體,對不對?
06:58
Not spheres, those leave離開 little gaps空白.
(Laughter笑聲)
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不能用球體,那會留下小缺口。(笑聲)
07:01
What is the best最好 shape形狀 to use?
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什麼形狀是最好的?
07:04
Lord Kelvin, of the famous著名
Kelvin degrees and all,
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以克氏溫標聞名的克爾文爵士,
07:09
said that the best最好 was to use
a truncated octahedron八面體
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說,最好使用截角八面體
07:16
which哪一個, as you all know --
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因為,因為大家都知道
07:19
(Laughter笑聲) --
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(笑聲)
07:21
is this thing here!
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就是這個東西!
07:22
(Applause掌聲)
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(掌聲)
07:27
Come on.
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拜託。
07:30
Who doesn't have a truncated
octahedron八面體 at home? (Laughter笑聲)
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誰家沒有截角八面體? (笑聲)
07:32
Even a plastic塑料 one.
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即使是塑膠的。
07:34
"Honey蜜糖, get the truncated octahedron八面體,
we're having guests賓客."
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“親愛的,去拿截角八面體,我們有客人來了。“
07:36
Everybody每個人 has one!
(Laughter笑聲)
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每個人都有!(笑聲)
07:38
But Kelvin didn't prove證明 it.
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但克爾文並沒有證明它。
07:40
It remained保持 a conjecture推測 --
Kelvin's開爾文 conjecture推測.
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它仍然是一個猜想 - 克爾文的猜想。
07:44
The world世界, as you know, then split分裂 into
KelvinistsKelvinists and anti-Kelvinists抗Kelvinists
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而這世界,你也知道,
分成克爾文幫和反克爾文幫,
07:50
(Laughter笑聲)
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(笑聲)
07:51
until直到 a hundred or so years年份 later後來,
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直到一百年多年後,
有人找到了更好的立方體。
07:58
someone有人 found發現 a better structure結構體.
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Weaire和Phelan發現了這個小東西 -
08:02
WeaireWeaire and Phelan費倫
found發現 this little thing over here --
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(笑聲)
08:08
(Laughter笑聲) --
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08:09
this structure結構體 to which哪一個 they gave
the very clever聰明 name名稱
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他們給這種立方結構取了個非常聰明的名字
08:13
"the Weaire-Weaire-€“Phelan費倫 structure結構體."
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就是“Weaire - Phelan的結構”。
(笑聲)
08:15
(Laughter笑聲)
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08:17
It looks容貌 like a strange奇怪 object目的,
but it isn't so strange奇怪,
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它看起來像一個奇怪的物體,
但它不是那麼的陌生,
08:20
it also exists存在 in nature性質.
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因為它也存在於自然界。
08:22
It's very interesting有趣 that this structure結構體,
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這種結構是非常有趣的,
08:24
because of its geometric幾何 properties性能,
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因為它的幾何特性,
被用來在北京奧運會設計游泳中心。
08:27
was used to build建立 the Aquatics水上運動 Center中央
for the Beijing北京 Olympic奧林匹克 Games遊戲.
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08:32
There, Michael邁克爾 Phelps菲爾普斯
won韓元 eight gold medals獎牌,
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在那裡,菲爾普斯贏得了八面奧運金牌,
08:35
and became成為 the best最好 swimmer游泳者 of all time.
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並成為有史以來最好的游泳運動員。
08:38
Well, until直到 someone有人 better
comes along沿, right?
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好吧,直到有人發現更好的結構,對不對?
08:42
As may可能 happen發生
with the Weaire-Weaire-€“Phelan費倫 structure結構體.
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就像是Weaire - Phelan結構。
直到更好的東西出現。
08:45
It's the best最好
until直到 something better shows節目 up.
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08:47
But be careful小心, because this one
really stands站立 a chance機會
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但注意,因為這個是很有可能的
08:52
that in a hundred or so years年份,
or even if it's in 1700 years年份,
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在100年左右,或者是在1700年後,
有人會證明這是最好的結構。
08:57
that someone有人 proves證明
it's the best最好 possible可能 shape形狀 for the job工作.
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09:02
It will then become成為 a theorem定理,
a truth真相, forever永遠 and ever.
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然後,它會成為一個定理,一個真理,直到永遠。
比鑽石活得更久。
09:07
For longer than any diamond鑽石.
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09:10
So, if you want to tell someone有人
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所以,如果你想告訴別人
09:15
that you will love them forever永遠
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你會永遠愛他們,
09:18
you can give them a diamond鑽石.
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你可以給他們鑽石。
09:20
But if you want to tell them
that you'll你會 love them forever永遠 and ever,
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但是,如果你要告訴他們,
你一定會永永遠遠的喜歡他們,
給他們一個定理!
09:24
give them a theorem定理!
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(笑聲)
09:26
(Laughter笑聲)
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09:27
But hang on a minute分鐘!
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等一下!
09:30
You'll你會 have to prove證明 it,
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你必須要證明它,
09:32
so your love doesn't remain
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讓你的愛不只是
一個猜想。
09:34
a conjecture推測.
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09:36
(Applause掌聲)
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(掌聲)
Translated by Xueling Sun
Reviewed by Karen SONG

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ABOUT THE SPEAKER
Eduardo Sáenz de Cabezón - Math educator
Eduardo Sáenz de Cabezón links science with humor and stories.

Why you should listen

Eduardo Sáenz de Cabezón links science with humor and stories. He studied theology and has a PhD in mathematics from the University of La Rioja. He speaks on these two topics in universities and secondary schools as a storyteller for children, youth and adults. Sáenz de Cabezón has also been a professor of Computer Information Systems, Discrete Mathematics and Algebra at the University of La Rioja since 2010.

He won the FameLab contest for scientific monologues in Spain in 2013.

More profile about the speaker
Eduardo Sáenz de Cabezón | Speaker | TED.com