TEDxRiodelaPlata
Eduardo Sáenz de Cabezón: Math is forever
Eduardo Saenz de Cabezon: 数学恒久远
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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。
Eduardo Sáenz de Cabezón - Math educator
Eduardo Sáenz de Cabezón links science with humor and stories. Full bio
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 you're in a bar, or a club,
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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 talking, and after a while,
the question comes up,
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 you think
your job is interesting,
your job is interesting,
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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."
(Laughter)
(Laughter)
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「我是一位数学家。」
00:31
And inevitably, during that conversation
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（笑声）
00:34
one of these two phrases come up:
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有33.51%的女士，
00:37
A) "I was terrible at math,
but it wasn't my fault.
but it wasn't my fault.
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听到这句话之后，
会假装接到了紧急电话而离开。
会假装接到了紧急电话而离开。
00:41
It's because the teacher
was awful." (Laughter)
was awful." (Laughter)
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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 really for?"
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00:47
(Laughter)
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赶紧转换话题，然后离开。
00:48
I'll now address Case B.
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00:50
(Laughter)
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（笑声）
00:52
When someone asks you what math is for,
they're not asking you
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
of mathematical science.
of mathematical science.
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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）
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 that bullshit
I never used in my life again? (Laughter)
I never used in my life again? (Laughter)
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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 asking.
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会出现这两句之一：
01:07
So when mathematicians are asked
what math is for,
what math is for,
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A) 「我数学很差，但不是我的错，
01:12
they tend to fall into two groups:
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我老师教得太差了。」（笑声）
01:14
54.51 percent of mathematicians
will assume an attacking position,
will assume an attacking position,
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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 of mathematicians
will take a defensive position.
will take a defensive position.
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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
他们并不是在问你
01:25
There's a strange 0.8 percent,
among which I include myself.
among which I include myself.
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01:29
Who are the ones that attack?
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数学科学的应用。
01:31
The attacking ones are mathematicians
who would tell you
who would tell you
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他们是在问你，
01:33
this question makes 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）
一辈子都不会再用到的垃圾？（笑声）
01:35
because mathematics
have a meaning all their own --
have a meaning all their own --
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这才是他们真正想知道的。
01:38
a beautiful edifice with its own logic --
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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 searching
for all possible applications.
for all possible applications.
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他们的回应可分为两类：
01:45
What's the use of poetry?
What's the use of love?
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?
What kind of question is that?
What kind of question is that?
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01:50
(Laughter)
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01:52
Hardy, for instance, was a model
of this type of attack.
of this type of attack.
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44.77%的数学家会为自己辩护。
01:56
And those who stand in defense tell you,
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01:58
"Even if you don't realize it, friend,
math is behind everything."
math is behind 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)
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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 up
bridges and computers.
bridges and computers.
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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,
your bridge will collapse."
your bridge will collapse."
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由逻辑搭建起的美丽的建筑——
02:12
(Laughter)
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一直寻找其用处
02:14
It's true, computers are all about math.
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是没有意义的。
02:17
And now these guys
have also started saying
have also started saying
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诗歌有什么用处？爱有什么用处？
02:20
that behind information security
and credit cards are prime numbers.
and credit cards are prime numbers.
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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 your math teacher
would give you if you asked him.
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 ones.
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「即便你没有意识到，
朋友，数学无处不在。」
朋友，数学无处不在。」
02:31
Okay, but who's right then?
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02:33
Those who say that math
doesn't need to have a purpose,
doesn't need to have a purpose,
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02:35
or those who say that math
is behind everything we do?
is behind everything we do?
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(笑声）
那些人，
02:38
Actually, 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 I told you
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02:42
I belong to that strange 0.8 percent
claiming something else?
claiming something else?
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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 is for.
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（笑声）
没错，计算机要应用到数学。
02:48
Audience: What is math for?
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那些人还会说
02:51
Eduardo Sáenz de Cabezón: Okay,
76.34 percent of you asked the question,
76.34 percent 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 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 --
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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 --
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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 that math doesn't need
to serve a purpose,
to serve a purpose,
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还是那些说数学无处不在的人？
03:11
it's true that it's
a beautiful structure, a logical one,
a beautiful structure, a logical 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 one
of the greatest collective efforts
of the greatest collective efforts
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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 in human history.
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来吧，问我数学是干什么用的。
03:19
But it's also true that there,
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03:21
where scientists and technicians
are looking for mathematical theories
are looking for mathematical theories
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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 them to advance,
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03:28
they're within the structure of math,
which permeates everything.
which permeates everything.
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23.41%什么都没说，
03:32
It's true that we have to go
somewhat deeper,
somewhat deeper,
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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 science.
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好，至亲爱的这76.34%的人——
03:37
Science operates on intuition, creativity.
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诚然，数学不需要为某个目的而存在，
03:41
Math controls intuition
and tames creativity.
and tames creativity.
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数学的确是有一个逻辑的、美丽的构造，
03:45
Almost everyone
who hasn't heard this before
who hasn't heard 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 when they hear
that if you take
that if you take
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集众人之力的成就之一。
03:50
a 0.1 millimeter thick sheet of paper,
the size we normally use,
the size we normally 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,
fold it 50 times,
fold it 50 times,
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03:58
its thickness would extend almost
the distance from the Earth to the sun.
the distance from the Earth to the sun.
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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 tells you it's impossible.
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我们需要深入思考，
04:07
Do the math and you'll see it's right.
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去探索科学背后的奇妙。
04:09
That's what math is for.
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科学需要直觉和创造力，
04:12
It's true that science, all types
of science, only makes sense
of science, only makes 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 us better understand
this beautiful world we live in.
this beautiful world we live 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 us avoid the pitfalls
of this painful world we live in.
of this painful world we live 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，
平常用的纸就这么厚，
04:24
There are sciences that help us
in this way quite directly.
in this way quite directly.
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04:27
Oncological science, for example.
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如果它足够大，对折50次，
04:29
And there are others we look at from afar,
with envy sometimes,
with envy sometimes,
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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 that we are
what supports them.
what supports them.
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04:35
All the basic sciences
support them,
support them,
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你的直觉告诉你这不可能。
04:38
including math.
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但用数学算一下，你就知道这是事实。
04:40
All that makes science, science
is the rigor of math.
is the rigor of math.
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这就是数学的用处。
04:44
And that rigor factors in
because its results are eternal.
because its results are eternal.
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科学，所有科学，
让我们更好地理解世界——
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。
正因此，科学才有意义。
04:49
You probably said or were told
at some point
at some point
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04:51
that diamonds are forever, 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 on
your definition of forever!
your definition of forever!
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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 -- that really is forever.
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如肿瘤学；
05:00
(Laughter)
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05:02
The Pythagorean theorem is still true
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还有一些科学我们只能遥看，
有时心怀嫉妒，
有时心怀嫉妒，
05:05
even though Pythagoras is dead,
I assure you it's true. (Laughter)
I assure you it's true. (Laughter)
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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 collapsed
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05:09
the Pythagorean theorem
would still be true.
would still be true.
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包括数学。
05:12
Wherever any two triangle sides
and a good hypotenuse get together
and a good hypotenuse get together
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所有的都是科学，科学是严谨的数学表达。
05:16
(Laughter)
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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 theorem goes all out.
It works like crazy.
It works like crazy.
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05:20
(Applause)
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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 devote ourselves
to come up with theorems.
to come up with theorems.
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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 truths.
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05:33
But it isn't always easy to know
the difference between
the difference between
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（笑声）
虽然毕达哥拉斯已经死了，
05:35
an eternal truth, or theorem,
and a mere conjecture.
and a mere conjecture.
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但勾股定律依然是正确的，
我可以向你保证。（笑声）
我可以向你保证。（笑声）
05:38
You need proof.
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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, infinite field.
enormous, infinite field.
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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 pieces,
without leaving any gaps.
without leaving any gaps.
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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, right?
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（掌声）
05:54
I could use triangles.
Not circles, those leave little gaps.
Not circles, those leave little gaps.
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05:58
Which is the best shape 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 the same surface,
but has a smaller border.
but has a smaller border.
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这永恒的事实。
06:05
In the year 300, Pappus of Alexandria
said the best is to use hexagons,
said the best is to use hexagons,
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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 do.
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需要证明。
06:12
But he didn't prove it.
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06:13
The guy said, "Hexagons, great!
Let's go with hexagons!"
Let's go with hexagons!"
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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 it,
it remained a conjecture.
it remained a conjecture.
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06:19
"Hexagons!"
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06:21
And the world, as you know,
split into Pappists and anti-Pappists,
split into Pappists and anti-Pappists,
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我想用相同的片状物覆盖住它，
不留任何空隙。
不留任何空隙。
06:24
until 1700 years later
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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。
圆不行，会留下空隙。
06:30
when in 1999, Thomas Hales proved
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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 and the bees were right --
the best shape to use was the hexagon.
the best shape to use was the hexagon.
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在公元300年，亚历山大的帕普斯
说六边形最好，
说六边形最好，
06:40
And that became a theorem,
the honeycomb theorem,
the honeycomb theorem,
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06:43
that will be true forever and ever,
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就像蜜蜂那样。
06:45
for longer than any diamond
you may have. (Laughter)
you may have. (Laughter)
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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！」
让我们用六边形吧！」
06:48
But what happens if we go
to three dimensions?
to three dimensions?
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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
with equal pieces,
with equal 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，
帕普斯和反帕普斯两派，
06:55
without leaving any gaps,
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06:56
I can use cubes, right?
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直到1700年后的1999年，
06:58
Not spheres, those leave little gaps.
(Laughter)
(Laughter)
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07:01
What is the best shape to use?
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Thomas Hales证明
07:04
Lord Kelvin, of the famous
Kelvin degrees and all,
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。
最佳的形状是六边形。
07:09
said that the best was to use
a truncated octahedron
a truncated octahedron
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这变成了一个定理，
即蜂窝定理，
即蜂窝定理，
永恒的真理，
07:16
which, as you all know --
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要比任何钻石都长久远。（笑声）
07:19
(Laughter) --
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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)
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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 at home? (Laughter)
octahedron at home? (Laughter)
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不能用曲面体，会留下空隙。（笑声）
07:32
Even a plastic one.
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07:34
"Honey, get the truncated octahedron,
we're having guests."
we're having guests."
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最佳的结构是什么呢？
07:36
Everybody has one!
(Laughter)
(Laughter)
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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 it.
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07:40
It remained a conjecture --
Kelvin's conjecture.
Kelvin's conjecture.
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说最佳的是结构是截角八面体，
07:44
The world, as you know, then split into
Kelvinists and anti-Kelvinists
Kelvinists and anti-Kelvinists
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你们都知道的——
07:50
(Laughter)
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07:51
until a hundred or so years later,
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（笑声）——
就是这个东西！
（掌声）
07:58
someone found a better structure.
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拜托，
08:02
Weaire and Phelan
found this little thing over here --
found 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。」
客人要来了。」
08:08
(Laughter) --
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08:09
this structure to which they gave
the very clever name
the very clever name
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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-Phelan structure."
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这是一个猜想——开尔文猜想。
08:15
(Laughter)
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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，
开尔文派和反开尔文派，
08:17
It looks like a strange object,
but it isn't so strange,
but it isn't so strange,
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08:20
it also exists in nature.
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08:22
It's very interesting that this structure,
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（笑声）
直到大约一百年后，
08:24
because of its geometric properties,
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08:27
was used to build the Aquatics Center
for the Beijing Olympic Games.
for the Beijing Olympic Games.
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有人发现了更好的结构。
08:32
There, Michael Phelps
won eight gold medals,
won eight gold medals,
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08:35
and became the best swimmer of all time.
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威尔勒和菲兰发现这个小东西——
08:38
Well, until someone better
comes along, right?
comes along, right?
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（笑声）——
08:42
As may happen
with the Weaire-Phelan structure.
with the Weaire-Phelan structure.
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他们很聪明地将其称之为
08:45
It's the best
until something better shows up.
until something better shows up.
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「威尔勒-菲兰多面体」。
08:47
But be careful, because this one
really stands a chance
really stands a chance
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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,
or even if it's in 1700 years,
or even if it's in 1700 years,
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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 proves
it's the best possible shape for the job.
it's the best possible shape for the job.
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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。
就是采用的该结构。
09:02
It will then become a theorem,
a truth, forever and ever.
a truth, forever 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，
迈克尔•菲利普斯赢得了8枚金牌，
09:07
For longer than any diamond.
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成为史上最佳游泳健将。
09:10
So, if you want to tell someone
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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
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在有人发现更好的之前，
它一直会是最佳的结构。
它一直会是最佳的结构。
09:18
you can give them a diamond.
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但要注意，很有可能
09:20
But if you want to tell them
that you'll love them forever and ever,
that you'll love them forever and ever,
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09:24
give them a theorem!
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在100年左右的时间之内，
甚至是1700年后，
甚至是1700年后，
09:26
(Laughter)
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09:27
But hang on a minute!
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有人证明它是最佳的填满空间的结构，
09:30
You'll have to prove it,
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09:32
so your love doesn't remain
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09:34
a conjecture.
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它就会成为定理，永远正确，
09:36
(Applause)
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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）
ABOUT THE SPEAKER
Eduardo Sáenz de Cabezón - Math educatorEduardo 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.
Eduardo Sáenz de Cabezón | Speaker | TED.com