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 Saenz de Cabezon: 数学恒久远

Filmed:
1,878,468 views

数学是用来干嘛的?这是那些一想到数学就昏昏欲睡的学生想破头也想不明白的问题,数学家Eduardo Sáenz de Cabezón以幽默而优雅的方式进行了回答。作为任何科学的基础,数学之美被Eduardo展现得淋漓尽致,而且,钻石未必长久,数学定理才是真正的恒久远。
- 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俱乐部,
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设想这样一个场景,在酒吧,或是俱乐部里,
你跟一位女士搭讪,
00:19
and you start开始 talking, and after a while,
the question comes up,
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不久聊到了这个问题,「你做什么工作的?」
00:22
"So, what do you do for work?"
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00:24
And since以来 you think
your job工作 is interesting有趣,
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你觉得你的工作蛮有趣的,因此你说,
00:26
you say, "I'm a mathematician数学家."
(Laughter笑声)
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「我是一位数学家。」
00:31
And inevitably必将, during that conversation会话
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(笑声)
00:34
one of these two phrases短语 come up:
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有33.51%的女士,
00:37
A) "I was terrible可怕 at math数学,
but it wasn't my fault故障.
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听到这句话之后,
会假装接到了紧急电话而离开。
00:41
It's because the teacher老师
was awful可怕." (Laughter笑声)
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(笑声)
有64.69%的女士会感到绝望,
00:44
Or B) "But what is math数学 really for?"
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00:47
(Laughter笑声)
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赶紧转换话题,然后离开。
00:48
I'll now address地址 Case案件 B.
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00:50
(Laughter笑声)
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(笑声)
00:52
When someone有人 asks you what math数学 is for,
they're not asking you
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还有0.8%的人,即你的姐妹、女朋友和母亲,
00:57
about applications应用
of mathematical数学的 science科学.
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她们知道你做的是一份奇怪的工作,
但却想不起来具体是什么了。(笑声)
01:00
They're asking you,
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01:01
why did I have to study研究 that bullshit废话
I never used in my life again? (Laughter笑声)
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还有1%的人仍然想继续这段对话。
不可避免地是,后面的对话中
01:05
That's what they're actually其实 asking.
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会出现这两句之一:
01:07
So when mathematicians数学家 are asked
what math数学 is for,
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A) 「我数学很差,但不是我的错,
01:12
they tend趋向 to fall秋季 into two groups:
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我老师教得太差了。」(笑声)
01:14
54.51 percent百分 of mathematicians数学家
will assume承担 an attacking进攻 position位置,
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或B) 「数学到底是干什么用的呢?」
(笑声)
01:20
and 44.77 percent百分 of mathematicians数学家
will take a defensive防御性 position位置.
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下面我就谈谈B这种情况
(笑声)
当有人问你数学是用来干什么的,
他们并不是在问你
01:25
There's a strange奇怪 0.8 percent百分,
among其中 which哪一个 I include包括 myself.
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01:29
Who are the ones那些 that attack攻击?
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数学科学的应用。
01:31
The attacking进攻 ones那些 are mathematicians数学家
who would tell you
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他们是在问你,
01:33
this question makes品牌 no sense,
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为什么我不得不学这些
一辈子都不会再用到的垃圾?(笑声)
01:35
because mathematics数学
have a meaning含义 all their own拥有 --
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这才是他们真正想知道的。
01:38
a beautiful美丽 edifice大厦 with its own拥有 logic逻辑 --
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当数学家被问起来这个问题,
01:41
and that there's no point
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01:43
in constantly经常 searching搜索
for all possible可能 applications应用.
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他们的回应可分为两类:
01:45
What's the use of poetry诗歌?
What's the use of love?
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54.51%的数学家会为之争辩,
01:47
What's the use of life itself本身?
What kind of question is that?
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01:50
(Laughter笑声)
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01:52
Hardy哈迪, for instance, was a model模型
of this type类型 of attack攻击.
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44.77%的数学家会为自己辩护。
01:56
And those who stand in defense防御 tell you,
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01:58
"Even if you don't realize实现 it, friend朋友,
math数学 is behind背后 everything."
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还有0.8%奇怪的数学家,我也属于这一类。
这些为之争辩的数学家是谁?
02:03
(Laughter笑声)
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他们会告诉你这个问题
02:04
Those guys,
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02:06
they always bring带来 up
bridges桥梁 and computers电脑.
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没有意义,
因为数学自身就是全部意义所在——
02:10
"If you don't know math数学,
your bridge will collapse坍方."
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由逻辑搭建起的美丽的建筑——
02:12
(Laughter笑声)
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一直寻找其用处
02:14
It's true真正, computers电脑 are all about math数学.
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是没有意义的。
02:17
And now these guys
have also started开始 saying
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诗歌有什么用处?爱有什么用处?
02:20
that behind背后 information信息 security安全
and credit信用 cards are prime主要 numbers数字.
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生命本身的用处是什么?这是个什么问题?
(笑声)
Hardy,举个例子,就是这类人。
02:25
These are the answers答案 your math数学 teacher老师
would give you if you asked him.
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那些回护自己的数学家会告诉你,
02:29
He's one of the defensive防御性 ones那些.
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「即便你没有意识到,
朋友,数学无处不在。」
02:31
Okay, but who's谁是 right then?
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02:33
Those who say that math数学
doesn't need to have a purpose目的,
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02:35
or those who say that math数学
is behind背后 everything we do?
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(笑声)
那些人,
02:38
Actually其实, both are right.
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就是用数学来建造桥梁和发明计算机的。
02:40
But remember记得 I told you
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02:42
I belong属于 to that strange奇怪 0.8 percent百分
claiming自称 something else其他?
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「如果你不懂数学,你造的桥就会塌。」
02:45
So, go ahead, ask me what math数学 is for.
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(笑声)
没错,计算机要应用到数学。
02:48
Audience听众: What is math数学 for?
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那些人还会说
02:51
Eduardo爱德华多enz恩茨 de CabezCabezón: Okay,
76.34 percent百分 of you asked the question,
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信息安全和信用卡背后是质数。
02:56
23.41 percent百分 didn't say anything,
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如果你问你的数学老师,他会给你这些答案。
02:59
and the 0.8 percent百分 --
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03:00
I'm not sure what those guys are doing.
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他属于回护这一类的。
03:03
Well, to my dear 76.31 percent百分 --
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哪种说法是对的呢?
是那些说数学没必要有意义的人,
03:07
it's true真正 that math数学 doesn't need
to serve服务 a purpose目的,
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还是那些说数学无处不在的人?
03:11
it's true真正 that it's
a beautiful美丽 structure结构体, a logical合乎逻辑 one,
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事实上,两种说法都对。
但你们应该还记得,
03:14
probably大概 one
of the greatest最大 collective集体 efforts努力
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我告诉过你们我属于那有其他观点的奇怪的0.8%。
03:17
ever achieved实现 in human人的 history历史.
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来吧,问我数学是干什么用的。
03:19
But it's also true真正 that there,
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03:21
where scientists科学家们 and technicians技师
are looking for mathematical数学的 theories理论
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观众:数学是干什么用的?
Eduardo: 好,76.34%的人问了这个问题,
03:26
that allow允许 them to advance提前,
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03:28
they're within the structure结构体 of math数学,
which哪一个 permeates渗透 everything.
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23.41%什么都没说,
03:32
It's true真正 that we have to go
somewhat有些 deeper更深,
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还有0.8%——
我不知道这些家伙在干什么。
03:35
to see what's behind背后 science科学.
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好,至亲爱的这76.34%的人——
03:37
Science科学 operates操作 on intuition直觉, creativity创造力.
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诚然,数学不需要为某个目的而存在,
03:41
Math数学 controls控制 intuition直觉
and tames驯服 creativity创造力.
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数学的确是有一个逻辑的、美丽的构造,
03:45
Almost几乎 everyone大家
who hasn't有没有 heard听说 this before
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数学很可能是人类历史上最伟大的
03:47
is surprised诧异 when they hear
that if you take
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集众人之力的成就之一。
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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但这种说法也是无可厚非的:
科学家和工程师不断利用数学理论
03:55
and, if it were big enough足够,
fold it 50 times,
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03:58
its thickness厚度 would extend延伸 almost几乎
the distance距离 from the Earth地球 to the sun太阳.
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来进行研究,
这些理论是属于数学架构的,而数学无处不在;
04:04
Your intuition直觉 tells告诉 you it's impossible不可能.
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我们需要深入思考,
04:07
Do the math数学 and you'll你会 see it's right.
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去探索科学背后的奇妙。
04:09
That's what math数学 is for.
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科学需要直觉和创造力,
04:12
It's true真正 that science科学, all types类型
of science科学, only makes品牌 sense
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而数学会将直觉和创造力转变为非对即错的事实。
04:15
because it makes品牌 us better understand理解
this beautiful美丽 world世界 we live生活 in.
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下面这个事实,当第一次听到时,
04:19
And in doing that,
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04:20
it helps帮助 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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几乎所有人都会觉得不可思议:
如果你拿一张0.1毫米厚的纸张,
平常用的纸就这么厚,
04:24
There are sciences科学 that help us
in this way quite相当 directly.
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04:27
Oncological肿瘤学 science科学, for example.
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如果它足够大,对折50次,
04:29
And there are others其他 we look at from afar,
with envy羡慕 sometimes有时,
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纸的厚度几乎相当于地球到太阳的距离。
04:32
but knowing会心 that we are
what supports支持 them.
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04:35
All the basic基本 sciences科学
support支持 them,
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你的直觉告诉你这不可能。
04:38
including包含 math数学.
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但用数学算一下,你就知道这是事实。
04:40
All that makes品牌 science科学, science科学
is the rigor严格 of math数学.
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这就是数学的用处。
04:44
And that rigor严格 factors因素 in
because its results结果 are eternal永恒.
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科学,所有科学,
让我们更好地理解世界——
我们生活的这个美丽的世界。
正因此,科学才有意义。
04:49
You probably大概 said or were told
at some point
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04:51
that diamonds钻石 are forever永远, right?
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在赋予我们对这个世界的理解时,
科学帮助我们避免在这个世界里受苦受难。
04:56
That depends依靠 on
your definition定义 of forever永远!
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有诸多科学是以非常直接地方式帮助我们,
04:58
A theorem定理 -- that really is forever永远.
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如肿瘤学;
05:00
(Laughter笑声)
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05:02
The Pythagorean毕达哥拉斯 theorem定理 is still true真正
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还有一些科学我们只能遥看,
有时心怀嫉妒,
05:05
even though虽然 Pythagoras毕达哥拉斯 is dead,
I assure保证 you it's true真正. (Laughter笑声)
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但知道是我们在推动科学的进步。
所有的基础科学都在推动它们,
05:08
Even if the world世界 collapsed倒塌
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05:09
the Pythagorean毕达哥拉斯 theorem定理
would still be true真正.
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包括数学。
05:12
Wherever哪里 any two triangle三角形 sides双方
and a good hypotenuse斜边 get together一起
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所有的都是科学,科学是严谨的数学表达。
05:16
(Laughter笑声)
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把严谨考虑在内是因为其结果是永恒的。
05:17
the Pythagorean毕达哥拉斯 theorem定理 goes all out.
It works作品 like crazy.
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05:20
(Applause掌声)
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你或许说过,也可能听过这样的说法,
即钻石恒久远,是吧?
05:27
Well, we mathematicians数学家 devote奉献 ourselves我们自己
to come up with theorems定理.
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这取决于你对永恒的定义!
定理——才是真正的永恒。
05:31
Eternal永恒 truths真理.
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05:33
But it isn't always easy简单 to know
the difference区别 between之间
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(笑声)
虽然毕达哥拉斯已经死了,
05:35
an eternal永恒 truth真相, or theorem定理,
and a mere conjecture推测.
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但勾股定律依然是正确的,
我可以向你保证。(笑声)
05:38
You need proof证明.
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即便世界消亡了,
05:41
For example,
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勾股定律还是正确的。
05:43
let's say I have a big,
enormous巨大, infinite无穷 field领域.
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每当两个直角边和一个合适的斜边聚在一起,
05:48
I want to cover it with equal等于 pieces,
without leaving离开 any gaps空白.
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(笑声)
勾股定律就能适用。简直太好用了。
05:52
I could use squares广场, right?
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(掌声)
05:54
I could use triangles三角形.
Not circles, those leave离开 little gaps空白.
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05:58
Which哪一个 is the best最好 shape形状 to use?
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我们数学家为定理投入了大量精力,
06:01
One that covers盖子 the same相同 surface表面,
but has a smaller border边境.
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这永恒的事实。
06:05
In the year 300, Pappus冠毛 of Alexandria亚历山大
said the best最好 is to use hexagons六边形,
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但弄清永恒的真理,或定理,
与猜想之间的差别不总是容易的。
06:10
just like bees蜜蜂 do.
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需要证明。
06:12
But he didn't prove证明 it.
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06:13
The guy said, "Hexagons六角形, great!
Let's go with hexagons六边形!"
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比如说,
有一个巨大的,无限大的二维平面,
06:16
He didn't prove证明 it,
it remained保持 a conjecture推测.
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06:19
"Hexagons六角形!"
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06:21
And the world世界, as you know,
split分裂 into PappistsPappists and anti-Pappists抗Pappists,
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我想用相同的片状物覆盖住它,
不留任何空隙。
06:24
until直到 1700 years年份 later后来
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我可以用正方形,对吧?
我可以用三角形。
圆不行,会留下空隙。
06:30
when in 1999, Thomas托马斯 Hales海尔斯 proved证实
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最好的形状是什么呢?
覆盖住最大的面积,而边长最小。
06:35
that Pappus冠毛 and the bees蜜蜂 were right --
the best最好 shape形状 to use was the hexagon六边形.
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在公元300年,亚历山大的帕普斯
说六边形最好,
06:40
And that became成为 a theorem定理,
the honeycomb蜂窝 theorem定理,
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06:43
that will be true真正 forever永远 and ever,
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就像蜜蜂那样。
06:45
for longer than any diamond钻石
you may可能 have. (Laughter笑声)
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但他没有证明这个说法。
他说,「六边形,伟大!
让我们用六边形吧!」
06:48
But what happens发生 if we go
to three dimensions尺寸?
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他没有证明它,这只是一个猜想。
06:51
If I want to fill the space空间
with equal等于 pieces,
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「六边形!」
你们也知道,这个世界分成了
帕普斯和反帕普斯两派,
06:55
without leaving离开 any gaps空白,
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06:56
I can use cubes立方体, right?
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直到1700年后的1999年,
06:58
Not spheres, those leave离开 little gaps空白.
(Laughter笑声)
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07:01
What is the best最好 shape形状 to use?
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Thomas Hales证明
07:04
Lord Kelvin, of the famous著名
Kelvin degrees and all,
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帕普斯和蜜蜂是正确的——
最佳的形状是六边形。
07:09
said that the best最好 was to use
a truncated octahedron八面体
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这变成了一个定理,
即蜂窝定理,
永恒的真理,
07:16
which哪一个, as you all know --
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要比任何钻石都长久远。(笑声)
07:19
(Laughter笑声) --
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07:21
is this thing here!
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如果是三维空间呢?
07:22
(Applause掌声)
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如果我们想用相同的结构填满空间,
07:27
Come on.
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不留任何空隙,
我可以用立方体,对吧?
07:30
Who doesn't have a truncated
octahedron八面体 at home? (Laughter笑声)
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不能用曲面体,会留下空隙。(笑声)
07:32
Even a plastic塑料 one.
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07:34
"Honey蜜糖, get the truncated octahedron八面体,
we're having guests宾客."
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最佳的结构是什么呢?
07:36
Everybody每个人 has one!
(Laughter笑声)
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开尔文爵士,就是开氏温度的开氏,
07:38
But Kelvin didn't prove证明 it.
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07:40
It remained保持 a conjecture推测 --
Kelvin's开尔文 conjecture推测.
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说最佳的是结构是截角八面体,
07:44
The world世界, as you know, then split分裂 into
KelvinistsKelvinists and anti-Kelvinists抗Kelvinists
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你们都知道的——
07:50
(Laughter笑声)
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07:51
until直到 a hundred or so years年份 later后来,
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(笑声)——
就是这个东西!
(掌声)
07:58
someone有人 found发现 a better structure结构体.
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拜托,
08:02
WeaireWeaire and Phelan费伦
found发现 this little thing over here --
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谁家没有截角八面体?(笑声)
塑料的更别提了。
「亲爱的,把截角八面体拿来,
客人要来了。」
08:08
(Laughter笑声) --
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08:09
this structure结构体 to which哪一个 they gave
the very clever聪明 name名称
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每个人都有!(笑声)
但开尔文没有证实这个理论。
08:13
"the Weaire-Weaire-€“Phelan费伦 structure结构体."
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这是一个猜想——开尔文猜想。
08:15
(Laughter笑声)
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你们都知道的,世界分成了
开尔文派和反开尔文派,
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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08:20
it also exists存在 in nature性质.
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08:22
It's very interesting有趣 that this structure结构体,
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(笑声)
直到大约一百年后,
08:24
because of its geometric几何 properties性能,
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08:27
was used to build建立 the Aquatics水上运动 Center中央
for the Beijing北京 Olympic奥林匹克 Games游戏.
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有人发现了更好的结构。
08:32
There, Michael迈克尔 Phelps菲尔普斯
won韩元 eight gold medals奖牌,
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08:35
and became成为 the best最好 swimmer游泳者 of all time.
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威尔勒和菲兰发现这个小东西——
08:38
Well, until直到 someone有人 better
comes along沿, right?
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(笑声)——
08:42
As may可能 happen发生
with the Weaire-Weaire-€“Phelan费伦 structure结构体.
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他们很聪明地将其称之为
08:45
It's the best最好
until直到 something better shows节目 up.
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「威尔勒-菲兰多面体」。
08:47
But be careful小心, because this one
really stands站立 a chance机会
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(笑声)
它看起来很奇怪,但其实并没那么奇怪,
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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自然中可以见到它的身影。
其结构非常有趣,
08:57
that someone有人 proves证明
it's the best最好 possible可能 shape形状 for the job工作.
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鉴于它的几何特性,
北京奥运会的水立方场馆的设计
就是采用的该结构。
09:02
It will then become成为 a theorem定理,
a truth真相, forever永远 and ever.
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在这个场馆中,
迈克尔•菲利普斯赢得了8枚金牌,
09:07
For longer than any diamond钻石.
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成为史上最佳游泳健将。
09:10
So, if you want to tell someone有人
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直到有人发现更好的结构,没错吧?
威尔勒-菲兰多面体可能也无出其右。
09:15
that you will love them forever永远
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在有人发现更好的之前,
它一直会是最佳的结构。
09:18
you can give them a diamond钻石.
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但要注意,很有可能
09:20
But if you want to tell them
that you'll你会 love them forever永远 and ever,
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09:24
give them a theorem定理!
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在100年左右的时间之内,
甚至是1700年后,
09:26
(Laughter笑声)
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09:27
But hang on a minute分钟!
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有人证明它是最佳的填满空间的结构,
09:30
You'll你会 have to prove证明 it,
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09:32
so your love doesn't remain
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09:34
a conjecture推测.
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它就会成为定理,永远正确,
09:36
(Applause掌声)
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比钻石还要久远。
所以,如果你想告诉另一位
你会永远爱Ta,
你可以给Ta一颗钻石。
但如果你想告诉Ta你对Ta的爱真正永永远远,
就给他一个定理!
(笑声)
但稍等片刻!
你要证明这个定理,
这样你的爱才不是一个猜想。
(掌声)
Translated by Yumeng Guo
Reviewed by Sabrina 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