TED2016
Cédric Villani: What's so sexy about math?
塞德里克·维拉尼: 数学为何如此有性感？
Filmed:
Readability: 4.4
2,006,708 views
隐藏的真相在我们生活中无处不在；它们虽然没法被我们的感官直接捕捉，但数学让我们超越直觉去揭开它们神秘的面纱。在这个演讲中，菲尔兹奖得主塞德里克·维拉尼回顾了数学界的突破性发现，描述了探索过程的刺激感，并谈论了数学家有时令人费解的生活方式。“漂亮的数学解法并不只是为了一种满足感，”他如是说，“他们可以改变人类对世界的认知。”
Cédric Villani - Mathematician
Cédric Villani tackles perplexing problems in mathematical physics, analysis and geometry with rigor, wit and a signature personal style. Full bio
Cédric Villani tackles perplexing problems in mathematical physics, analysis and geometry with rigor, wit and a signature personal style. Full bio
Double-click the English transcript below to play the video.
00:12
What is it that French people
do better than all the others?
do better than all the others?
0
804
4412
法国人在什么方面做得比别人好呢？
00:18
If you would take polls,
1
6454
1926
如果你去做个投票调查，
排名前三的或许是：
00:20
the top three answers might be:
2
8404
1807
爱情，红酒，发牢骚。
00:22
love, wine and whining.
3
10235
4039
（笑声）
00:26
(Laughter)
4
14298
1301
可能吧。
00:27
Maybe.
5
15623
1159
00:29
But let me suggest a fourth one:
6
17530
2338
但我还想提出第四个答案：
数学。
00:31
mathematics.
7
19892
1190
00:33
Did you know that Paris
has more mathematicians
has more mathematicians
8
21760
2853
你们知道巴黎的数学家比世界上
其它任何一个城市
其它任何一个城市
都要多吗？
00:36
than any other city in the world?
9
24637
1801
00:38
And more streets
with mathematicians' names, too.
with mathematicians' names, too.
10
26801
2494
而且以数学家的名字命名的街道数量也更多。
00:42
And if you look at the statistics
of the Fields Medal,
of the Fields Medal,
11
30215
3449
如果你查查菲尔兹奖的统计，
它也经常被称作“诺贝尔数学奖”，
00:45
often called the Nobel Prize
for mathematics,
for mathematics,
12
33688
2493
只授予40岁以下的数学家，
00:48
and always awarded to mathematicians
below the age of 40,
below the age of 40,
13
36205
3932
你会发现，就人均获奖数量来说，
00:52
you will find that France has more
Fields medalists per inhabitant
Fields medalists per inhabitant
14
40161
3887
法国是世界第一。
00:56
than any other country.
15
44072
1168
00:58
What is it that we find so sexy in math?
16
46286
2954
我们在数学中到底
发现了什么让人着迷的东西？
发现了什么让人着迷的东西？
01:02
After all, it seems to be
dull and abstract,
dull and abstract,
17
50153
3204
毕竟它看上去那么无聊、抽象，
只是数字、计算、定理而已。
01:05
just numbers and computations
and rules to apply.
and rules to apply.
18
53381
3483
01:10
Mathematics may be abstract,
19
58518
2112
数学可能很抽象，
但是它并不无聊，
01:12
but it's not dull
20
60654
1151
而且它并不都是计算。
01:13
and it's not about computing.
21
61829
1729
01:16
It is about reasoning
22
64178
1747
它是有关逻辑的推理，
让我们的所作所为都有理有据。
01:17
and proving our core activity.
23
65949
2260
01:20
It is about imagination,
24
68513
1522
它有关丰富的想象，
我们最常歌颂的人类天赋。
01:22
the talent which we most praise.
25
70059
2019
它还有关真理的追寻。
01:24
It is about finding the truth.
26
72102
2101
01:27
There's nothing like the feeling
which invades you
which invades you
27
75613
2737
当你苦思冥想数月之后，
终于找到问题的正确解法那一刻，
01:30
when after months of hard thinking,
28
78374
2171
那种感受真的无与伦比。
01:32
you finally understand the right
reasoning to solve your problem.
reasoning to solve your problem.
29
80569
3298
01:37
The great mathematician
André Weil likened this --
André Weil likened this --
30
85042
3576
伟大的数学家安德雷·韦依
把这种感受比作——
把这种感受比作——
不开玩笑——
01:40
no kidding --
31
88642
1151
比作性快感。
01:41
to sexual pleasure.
32
89817
1589
01:44
But noted that this feeling
can last for hours, or even days.
can last for hours, or even days.
33
92197
5341
但是他还说这种感受
可以持续数小时甚至数天。
可以持续数小时甚至数天。
01:50
The reward may be big.
34
98804
1853
这种回报可能难以估量。
01:53
Hidden mathematical truths
permeate our whole physical world.
permeate our whole physical world.
35
101325
3864
隐藏的数学规律
渗透在我们整个物质世界中。
渗透在我们整个物质世界中。
01:57
They are inaccessible to our senses
36
105680
2670
我们的感官不能捕捉它们，
但可以通过数学的放大镜观察到。
02:00
but can be seen
through mathematical lenses.
through mathematical lenses.
37
108374
2724
02:04
Close your eyes for moment
38
112092
1592
闭上眼睛一小会儿，
想一想你周围此时此刻正在发生的事。
02:05
and think of what is occurring
right now around you.
right now around you.
39
113708
3475
02:10
Invisible particles from the air
around are bumping on you
around are bumping on you
40
118337
3493
看不见的空气分子
在不断地撞击你，
在不断地撞击你，
02:13
by the billions and billions
at each second,
at each second,
41
121854
2733
每秒钟数十亿次，
完全是混乱无序的状态。
02:16
all in complete chaos.
42
124611
2063
02:19
And still,
43
127049
1151
然而，
它们的行为可以被数学物理学精准地预测。
02:20
their statistics can be accurately
predicted by mathematical physics.
predicted by mathematical physics.
44
128224
4688
02:25
And open your eyes now
45
133715
2792
睁开你的双眼，
看看这些分子的速率分布统计。
02:28
to the statistics of the velocities
of these particles.
of these particles.
46
136531
3310
02:32
The famous bell-shaped Gauss Curve,
47
140510
3240
这是著名的钟形高斯曲线，
也可以叫做误差律——
02:35
or the Law of Errors --
48
143774
2181
描述分子平均行为的一些偏差。
02:37
of deviations with respect
to the mean behavior.
to the mean behavior.
49
145979
2722
02:41
This curve tells about the statistics
of velocities of particles
of velocities of particles
50
149550
4302
这条曲线告诉我们
粒子的速率分布情况，
粒子的速率分布情况，
正如一条人口统计曲线
02:45
in the same way as a demographic curve
51
153876
2539
能够告诉我们人口的年龄分布情况。
02:48
would tell about the statistics
of ages of individuals.
of ages of individuals.
52
156439
3841
02:52
It's one of the most
important curves ever.
important curves ever.
53
160884
2650
它是最重要的一条曲线之一。
02:56
It keeps on occurring again and again,
54
164137
3186
它的规律不断地重复，
在诸多理论与实验中呈现，
02:59
from many theories and many experiments,
55
167347
2403
它是数学的普适性的体现，
03:01
as a great example of the universality
56
169774
3281
而这种性质对我们数学家至关重要。
03:05
which is so dear to us mathematicians.
57
173079
3552
03:09
Of this curve,
58
177694
1227
关于这个曲线，
著名的科学家弗朗西斯·高尔顿说：
03:10
the famous scientist Francis Galton said,
59
178945
3049
“如果古希腊人知道这个规律，
他们一定会把它神化的。
他们一定会把它神化的。
03:14
"It would have been deified by the Greeks
if they had known it.
if they had known it.
60
182018
4524
03:19
It is the supreme law of unreason."
61
187064
3351
它是无理性的至高准则。”
03:23
And there's no better way to materialize
that supreme goddess than Galton's Board.
that supreme goddess than Galton's Board.
62
191818
6602
高尔顿板就是
把这个“神灵”实体化的最佳体现。
把这个“神灵”实体化的最佳体现。
03:31
Inside this board are narrow tunnels
63
199774
3197
在这个板子里有一些狭道，
一些掉落的小球会随机通过这里，
03:34
through which tiny balls
will fall down randomly,
will fall down randomly,
64
202995
4628
03:40
going right or left, or left, etc.
65
208295
5387
有些往右，有些往左。
03:46
All in complete randomness and chaos.
66
214139
3251
完全是随机的、混乱的。
03:50
Let's see what happens when we look
at all these random trajectories together.
at all these random trajectories together.
67
218085
6080
让我们看看这些随机路线
会呈现怎样的规律。
会呈现怎样的规律。
（板子摇动）
03:56
(Board shaking)
68
224189
5435
这其实算是锻炼身体，
04:01
This is a bit of a sport,
69
229648
2844
因为我们得疏通一些拥堵的状况。
04:04
because we need to resolve
some traffic jams in there.
some traffic jams in there.
70
232516
4870
04:11
Aha.
71
239715
1150
啊哈。
04:13
We think that randomness
is going to play me a trick on stage.
is going to play me a trick on stage.
72
241313
3587
看来随机性要在这个舞台上
跟我开个小玩笑了。
跟我开个小玩笑了。
04:19
There it is.
73
247609
1463
好了！
04:22
Our supreme goddess of unreason.
74
250382
2583
这个无理性的至高无上的神，
高斯曲线，
04:24
the Gauss Curve,
75
252989
1519
被囚禁在了这个透明的盒子里，
就像《睡魔》漫画里的梦魇一样。
就像《睡魔》漫画里的梦魇一样。
04:26
trapped here inside this transparent box
as Dream in "The Sandman" comics.
as Dream in "The Sandman" comics.
76
254532
6452
04:34
For you I have shown it,
77
262623
2698
我向各位展示了这个规律，
04:37
but to my students I explain why
it could not be any other curve.
it could not be any other curve.
78
265345
5285
但向我的学生，我要解释
为什么它不可能是任何其它的曲线。
为什么它不可能是任何其它的曲线。
04:43
And this is touching
the mystery of that goddess,
the mystery of that goddess,
79
271128
2870
这就近乎揭开了这个神灵的面纱，
把一个美丽的巧合
变成一个赏心悦目的数学解释。
变成一个赏心悦目的数学解释。
04:46
replacing a beautiful coincidence
by a beautiful explanation.
by a beautiful explanation.
80
274022
4701
04:51
All of science is like this.
81
279027
2333
一切的科学都是这样的。
04:54
And beautiful mathematical explanations
are not only for our pleasure.
are not only for our pleasure.
82
282213
5348
漂亮的数学解法并不只是
为了我们自己开心。
为了我们自己开心。
它们同样改变了我们看世界的视角。
04:59
They also change our vision of the world.
83
287585
2660
05:03
For instance,
84
291040
1237
举个例子，
爱因斯坦、
05:04
Einstein,
85
292301
1150
佩兰、
05:05
Perrin,
86
293476
1150
斯莫鲁霍夫斯基，
05:06
Smoluchowski,
87
294651
1150
他们对粒子的随机轨迹
进行了数学分析，
进行了数学分析，
05:07
they used the mathematical analysis
of random trajectories
of random trajectories
88
295826
3559
再加上高斯曲线，
05:11
and the Gauss Curve
89
299409
2037
他们解释并证明了
我们的世界由原子组成。
我们的世界由原子组成。
05:13
to explain and prove that our
world is made of atoms.
world is made of atoms.
90
301470
4928
05:19
It was not the first time
91
307524
1802
这并不是第一次，
数学已经多次颠覆了我们的世界观。
05:21
that mathematics was revolutionizing
our view of the world.
our view of the world.
92
309350
3390
05:25
More than 2,000 years ago,
93
313555
2212
两千多年前，
在古希腊的时代，
05:27
at the time of the ancient Greeks,
94
315791
2610
05:31
it already occurred.
95
319502
1479
颠覆已经发生了。
05:33
In those days,
96
321827
1286
在那个时代，
人们只探索了世界的很小一部分，
05:35
only a small fraction of the world
had been explored,
had been explored,
97
323137
3283
而地球看上去无边无际。
05:38
and the Earth might have seemed infinite.
98
326444
3042
05:42
But clever Eratosthenes,
99
330034
1767
但是聪明的埃拉托色尼
利用数学工具，
05:43
using mathematics,
100
331825
1417
成功的测量了地球的大小，
误差只有惊人的2%。
误差只有惊人的2%。
05:45
was able to measure the Earth
with an amazing accuracy of two percent.
with an amazing accuracy of two percent.
101
333266
5111
05:51
Here's another example.
102
339969
1416
还有另一个例子。
05:54
In 1673, Jean Richer noticed
103
342238
3805
在1673年，让·里谢注意到
一个单摆在卡宴（译注：南美法属圭亚那首都，
近赤道）比在巴黎摆动得稍稍慢一些。
近赤道）比在巴黎摆动得稍稍慢一些。
05:58
that a pendulum swings slightly
slower in Cayenne than in Paris.
slower in Cayenne than in Paris.
104
346067
6912
06:06
From this observation alone,
and clever mathematics,
and clever mathematics,
105
354350
4400
只用这一个现象，
以及一些巧妙的数学推导，
以及一些巧妙的数学推导，
牛顿正确地推断出
06:10
Newton rightly deduced
106
358774
2306
地球在两极地区稍稍扁一些，
06:13
that the Earth is a wee bit
flattened at the poles,
flattened at the poles,
107
361104
5541
大概只有0.3%，
06:18
like 0.3 percent --
108
366669
1601
06:20
so tiny that you wouldn't even
notice it on the real view of the Earth.
notice it on the real view of the Earth.
109
368843
4413
这种细微的差别在
观察地球全貌时根本无法发现。
观察地球全貌时根本无法发现。
06:26
These stories show that mathematics
110
374276
3928
这些故事说明了，
数学能够让我们超越自己的直觉，
06:30
is able to make us go out of our intuition
111
378228
4762
06:35
measure the Earth which seems infinite,
112
383512
3485
测量看似不可测的地球尺寸，
观察看不见的原子，
06:39
see atoms which are invisible
113
387021
2294
或是检测肉眼不可识别的微小形变。
06:41
or detect an imperceptible
variation of shape.
variation of shape.
114
389339
3381
如果你们只能从我的演讲中
了解到一样东西，
了解到一样东西，
06:44
And if there is just one thing that you
should take home from this talk,
should take home from this talk,
115
392744
3847
那应该是这个：
06:48
it is this:
116
396615
1194
数学让我们超越人类直觉，
06:49
mathematics allows us
to go beyond the intuition
to go beyond the intuition
117
397833
4378
并且探索我们所无法触及的领域。
06:54
and explore territories
which do not fit within our grasp.
which do not fit within our grasp.
118
402235
4249
06:59
Here's a modern example
you will all relate to:
you will all relate to:
119
407609
2999
这有个例子各位都非常熟悉：
07:03
searching the Internet.
120
411362
1667
网上搜索。
07:06
The World Wide Web,
121
414037
1342
万维网，
有着超过十亿个网页，
07:07
more than one billion web pages --
122
415403
1804
难道你想全部搜索一遍吗？
07:09
do you want to go through them all?
123
417231
1674
07:11
Computing power helps,
124
419660
1802
计算机可能有帮助，
但是如果没有了数学模型，
它就是一堆废铁，
它就是一堆废铁，
07:13
but it would be useless without
the mathematical modeling
the mathematical modeling
125
421486
3186
无法搜寻数据中隐藏的信息。
07:16
to find the information
hidden in the data.
hidden in the data.
126
424696
2563
07:20
Let's work out a baby problem.
127
428491
2379
让我们做一道很简单的题。
07:23
Imagine that you're a detective
working on a crime case,
working on a crime case,
128
431872
3807
想象你是一个侦探，
正在调查一个犯罪案件，
正在调查一个犯罪案件，
很多人参与其中，并且各执一词。
07:27
and there are many people
who have their version of the facts.
who have their version of the facts.
129
435703
3788
07:32
Who do you want to interview first?
130
440032
1745
你想先询问谁呢？
07:34
Sensible answer:
131
442681
1915
合理的答案是：
主要的目击者。
07:36
prime witnesses.
132
444620
1437
07:38
You see,
133
446878
1234
想想看，
假设有一位7号证人，
07:40
suppose that there is person number seven,
134
448136
4220
告诉了你一件事情，
07:44
tells you a story,
135
452380
1151
但当你问他从哪里听说的，
07:45
but when you ask where he got if from,
136
453555
2014
他说3号证人是消息来源。
07:47
he points to person
number three as a source.
number three as a source.
137
455593
3036
有可能3号证人
07:50
And maybe person number three, in turn,
138
458653
2068
也相应地指向1号证人作为主要消息来源。
07:52
points at person number one
as the primary source.
as the primary source.
139
460745
3696
现在1号证人是主要目击者了，
07:56
Now number one is a prime witness,
140
464465
1661
所以我一定想要先去采访他。
07:58
so I definitely want
to interview him -- priority
to interview him -- priority
141
466150
3238
08:02
And from the graph
142
470148
1151
从这幅图中，
我们同样看到4号证人
是一位主要目击者。
是一位主要目击者。
08:03
we also see that person
number four is a prime witness.
number four is a prime witness.
143
471323
3228
我可能更想先去采访他，
08:06
And maybe I even want
to interview him first,
to interview him first,
144
474575
2443
因为他被提及的次数比1号还要多。
08:09
because there are more
people who refer to him.
people who refer to him.
145
477042
2359
08:12
OK, that was easy,
146
480354
2664
好吧，这还算简单的，
但是如果有一大堆要作证的人，
那该怎么办呢？
那该怎么办呢？
08:15
but now what about if you have
a big bunch of people who will testify?
a big bunch of people who will testify?
147
483042
5246
08:20
And this graph,
148
488864
1352
在这幅图中，
我可以把它当作
一件复杂案件的所有证人，
一件复杂案件的所有证人，
08:22
I may think of it as all people
who testify in a complicated crime case,
who testify in a complicated crime case,
149
490240
5619
但也可以把它看作是
互相链接的网页，
互相链接的网页，
08:27
but it may just as well be web pages
pointing to each other,
pointing to each other,
150
495883
4022
08:31
referring to each other for contents.
151
499929
2071
互相引用其中的内容。
08:34
Which ones are the most authoritative?
152
502878
2336
哪些网页最有权威性呢？
08:37
Not so clear.
153
505587
1334
还不太清楚。
08:40
Enter PageRank,
154
508091
1900
于是PageRank问世了，
它是谷歌最早的基石之一。
08:42
one of the early cornerstones of Google.
155
510015
2536
08:45
This algorithm uses the laws
of mathematical randomness
of mathematical randomness
156
513337
4242
这种算法运用了
数学随机性的定律，
数学随机性的定律，
来自动判断哪些网页关联最多，
08:49
to determine automatically
the most relevant web pages,
the most relevant web pages,
157
517603
3857
与我们在高尔顿板实验中
运用随机性的方法一样。
运用随机性的方法一样。
08:53
in the same way as we used randomness
in the Galton Board experiment.
in the Galton Board experiment.
158
521484
5062
08:59
So let's send into this graph
159
527341
2341
那就把一堆小小的数码玻璃珠
放到这个图表中，
09:01
a bunch of tiny, digital marbles
160
529706
2850
让它们随机的在图中穿行。
09:04
and let them go randomly
through the graph.
through the graph.
161
532580
3749
每当它们到达某个网页，
09:08
Each time they arrive at some site,
162
536353
1667
它们就会随机选择一个链接，
然后跳转到另一页。
然后跳转到另一页。
09:10
they will go out through some link
chosen at random to the next one.
chosen at random to the next one.
163
538044
4166
一遍又一遍重复。
09:14
And again, and again, and again.
164
542234
1753
09:16
And with small, growing piles,
165
544358
1628
用这些小小的光点，
我们记录下每个网页
被访问的次数，
被访问的次数，
09:18
we'll keep the record of how many
times each site has been visited
times each site has been visited
166
546010
3753
就用这些数码珠子。
09:21
by these digital marbles.
167
549787
1945
09:24
Here we go.
168
552243
1151
开始喽。
一切随机。
09:25
Randomness, randomness.
169
553418
1848
09:27
And from time to time,
170
555811
1448
随着时间推移，
为了增强趣味性，
这些跳跃是完全随机的。
这些跳跃是完全随机的。
09:29
also let's make jumps completely
randomly to increase the fun.
randomly to increase the fun.
171
557283
3952
09:34
And look at this:
172
562471
1216
看看这个：
09:36
from the chaos will emerge the solution.
173
564358
2785
在一片混乱中产生了一个答案。
09:39
The highest piles
correspond to those sites
correspond to those sites
174
567483
2485
这里最高的几堆对应着
那些相对来说链接更多的网页，
09:41
which somehow are better
connected than the others,
connected than the others,
175
569992
3511
被引用更多次的网页。
09:45
more pointed at than the others.
176
573527
2273
在这里我们清晰地看到，
09:47
And here we see clearly
177
575824
1722
哪一些是我们最想先看的网页。
09:49
which are the web pages
we want to first try.
we want to first try.
178
577570
3032
09:53
Once again,
179
581507
1151
再一次，
问题的解答来源于随机性。
09:54
the solution emerges from the randomness.
180
582682
2460
09:57
Of course, since that time,
181
585775
2251
当然，从那以来，
谷歌已经发明出
数不胜数的复杂算法，
数不胜数的复杂算法，
10:00
Google has come up with much more
sophisticated algorithms,
sophisticated algorithms,
182
588050
3707
但是这个算法已经很漂亮了。
10:03
but already this was beautiful.
183
591781
2280
10:06
And still,
184
594981
1476
然而，
这只是沧海一粟。
10:08
just one problem in a million.
185
596481
1611
10:10
With the advent of digital area,
186
598734
2270
随着数字领域的飞速发展，
越来越多的问题
需要用数学分析来解决，
需要用数学分析来解决，
10:13
more and more problems lend
themselves to mathematical analysis,
themselves to mathematical analysis,
187
601028
5016
让数学家这个工作
变得越来越实用，
变得越来越实用，
10:18
making the job of mathematician
a more and more useful one,
a more and more useful one,
188
606068
4365
10:23
to the extent that a few years ago,
189
611166
2722
以至于大约几年前，
它在数百个职业中排名第一，
10:25
it was ranked number one
among hundreds of jobs
among hundreds of jobs
190
613912
3779
这份排名是有关最好和最差的职业，
10:29
in a study about the best and worst jobs
191
617715
3968
由华尔街日报在2009年发表。
10:33
published by the Wall Street
Journal in 2009.
Journal in 2009.
192
621707
2975
10:37
Mathematician --
193
625445
1852
数学家——
世界上最好的工作。
10:39
best job in the world.
194
627321
1433
10:41
That's because of the applications:
195
629646
3068
这是因为它应用广泛：
通讯理论、
10:44
communication theory,
196
632738
2139
信息理论、
10:46
information theory,
197
634901
1820
博弈论、
10:48
game theory,
198
636745
1260
压缩传感、
10:50
compressed sensing,
199
638029
1446
机器学习、
10:51
machine learning,
200
639499
1562
图表分析、
10:53
graph analysis,
201
641085
1567
谐波分析。
10:54
harmonic analysis.
202
642676
1742
还有随机过程、
10:56
And why not stochastic processes,
203
644442
2640
线性编程、
10:59
linear programming,
204
647106
1630
或者是流体模拟。
11:00
or fluid simulation?
205
648760
2028
11:03
Each of these fields have
monster industrial applications.
monster industrial applications.
206
651292
3895
以上每一个领域都有
规模巨大的工业应用。
规模巨大的工业应用。
透过它们可以看出，
11:07
And through them,
207
655211
1151
数学的商机是无限的。
11:08
there is big money in mathematics.
208
656386
1999
11:11
And let me concede
209
659400
2040
我必须承认，
谈到从数学中赚钱，
11:13
that when it comes to making
money from the math,
money from the math,
210
661464
2477
美国人可是遥遥领先全世界，
11:15
the Americans are by a long shot
the world champions,
the world champions,
211
663965
3824
有一群标志性绝顶聪明的领导者，
还有让人大开眼界的商业巨头，
还有让人大开眼界的商业巨头，
11:19
with clever, emblematic billionaires
and amazing, giant companies,
and amazing, giant companies,
212
667813
4619
归根结底都不约而同地依赖好的算法。
11:24
all resting, ultimately,
on good algorithm.
on good algorithm.
213
672456
3280
11:29
Now with all this beauty,
usefulness and wealth,
usefulness and wealth,
214
677091
3972
数学兼具着美、实用性，
以及无限商机，
以及无限商机，
它似乎的确更有魅力了。
11:33
mathematics does look more sexy.
215
681087
2284
11:36
But don't you think
216
684399
1617
但是你千万别以为
数学家的生活很轻松。
11:38
that the life a mathematical
researcher is an easy one.
researcher is an easy one.
217
686040
4120
11:42
It is filled with perplexity,
218
690959
2741
这种生活满是混乱，
11:46
frustration,
219
694347
1150
满是沮丧，
11:48
a desperate fight for understanding.
220
696172
2445
是追求真知的绝望之战。
11:51
Let me evoke for you
221
699955
2140
让我向各位讲述
我的数学生涯中最特别的一天。
11:54
one of the most striking days
in my mathematician's life.
in my mathematician's life.
222
702119
4380
或者我应该说，
11:58
Or should I say,
223
706523
1151
最特别的一晚。
11:59
one of the most striking nights.
224
707698
1737
12:02
At that time,
225
710713
1151
那个时候，
我待在普林斯顿大学的
高等研究所里，
高等研究所里，
12:03
I was staying at the Institute
for Advanced Studies in Princeton --
for Advanced Studies in Princeton --
226
711888
3151
这里曾是爱因斯坦多年的家，
12:07
for many years, the home
of Albert Einstein
of Albert Einstein
227
715063
2139
也很可能是世界上
数学研究的神圣之颠。
数学研究的神圣之颠。
12:09
and arguably the most holy place
for mathematical research in the world.
for mathematical research in the world.
228
717226
4428
12:14
And that night I was working
and working on an elusive proof,
and working on an elusive proof,
229
722878
3844
在那个晚上我苦思冥想，
寻找一个非常隐晦的证明，
寻找一个非常隐晦的证明，
它十分的不完整。
12:18
which was incomplete.
230
726746
1378
12:21
It was all about understanding
231
729304
2208
它都是有关于了解
等离子体的矛盾稳定特性，
12:23
the paradoxical stability
property of plasmas,
property of plasmas,
232
731536
3823
这里指的是一团电子云。
12:27
which are a crowd of electrons.
233
735383
1958
12:30
In the perfect world of plasma,
234
738423
2736
在等离子体的理想世界，
是没有任何碰撞的，
12:33
there are no collisions
235
741183
1778
而且没有任何摩擦力，
使其像我们习惯的那么稳定。
使其像我们习惯的那么稳定。
12:34
and no friction to provide
the stability like we are used to.
the stability like we are used to.
236
742985
3658
12:39
But still,
237
747392
1151
然而，
如果你轻微打破等离子体平衡，
12:40
if you slightly perturb
a plasma equilibrium,
a plasma equilibrium,
238
748567
3033
你会发现相应产生的电场
12:43
you will find that the
resulting electric shield
resulting electric shield
239
751624
2688
会自发的消失，
12:46
spontaneously vanishes,
240
754336
2339
或者是减弱，
12:48
or damps out,
241
756699
1975
好像受到了某种神秘摩擦力的影响。
12:50
as if by some mysterious friction force.
242
758698
3294
12:54
This paradoxical effect,
243
762728
1835
这种矛盾的特性，
叫做朗道阻尼，
12:56
called the Landau damping,
244
764587
1477
是等离子物理中
最重要的现象之一，
最重要的现象之一，
12:58
is one of the most important
in plasma physics,
in plasma physics,
245
766088
2989
而且它是由数学思想推导出来的。
13:01
and it was discovered
through mathematical ideas.
through mathematical ideas.
246
769101
3002
13:04
But still,
247
772970
1151
然而，
对此现象的完整数学理解还不完善。
13:06
a full mathematical understanding
of this phenomenon was missing.
of this phenomenon was missing.
248
774145
4230
我和我的前学生、主要合作者
克莱蒙·穆奥合作，
克莱蒙·穆奥合作，
13:10
And together with my former student
and main collaborator Clément Mouhot,
and main collaborator Clément Mouhot,
249
778399
4786
我们那时在巴黎，
13:15
in Paris at the time,
250
783209
1492
我们为了寻找这个证法
已经工作了好几个月。
已经工作了好几个月。
13:16
we had been working for months
and months on such a proof.
and months on such a proof.
251
784725
4086
13:21
Actually,
252
789832
1335
实际上，
我还错误地宣布
我们可以解决这个问题。
我们可以解决这个问题。
13:23
I had already announced by mistake
that we could solve it.
that we could solve it.
253
791191
4746
然而事实上，
13:27
But the truth is,
254
795961
1725
那种证法完全无效。
13:29
the proof was just not working.
255
797710
2147
13:32
In spite of more than 100 pages
of complicated, mathematical arguments,
of complicated, mathematical arguments,
256
800196
4349
即使是一百多页的复杂数学推导，
还有一大堆的新发现，
13:36
and a bunch discoveries,
257
804569
1690
巨大的计算量，
13:38
and huge calculation,
258
806283
1267
依然得不出个所以然。
13:39
it was not working.
259
807574
1169
13:41
And that night in Princeton,
260
809290
1681
在普林斯顿的那个晚上，
证明中的一个小缺口让我近乎疯狂。
13:42
a certain gap in the chain of arguments
was driving me crazy.
was driving me crazy.
261
810995
4301
13:47
I was putting in there all my energy
and experience and tricks,
and experience and tricks,
262
815658
4593
我对它使出浑身解数，
但是依旧没有进展。
13:52
and still nothing was working.
263
820275
1742
13:54
1 a.m., 2 a.m., 3 a.m.,
264
822553
3882
凌晨一点、两点、三点，
毫无进展。
13:58
not working.
265
826459
1308
14:00
Around 4 a.m., I go to bed in low spirits.
266
828545
4321
大概凌晨四点的时候，
我无精打采的上床。
我无精打采的上床。
14:05
Then a few hours later,
267
833915
2460
然而几个小时后，
我从床上爬起来，
14:08
waking up and go,
268
836399
1151
“啊，该送孩子们上学了。”……
14:09
"Ah, it's time to get
the kids to school --"
the kids to school --"
269
837574
3357
这是什么？
14:12
What is this?
270
840955
1151
我发誓，我的脑袋里有个声音。
14:14
There was this voice in my head, I swear.
271
842130
2142
14:16
"Take the second term to the other side,
272
844894
1913
“把第二项移到等式另一边，
“傅里叶展开然后在L2域反变换。”
14:18
Fourier transform and invert in L2."
273
846831
1919
14:21
(Laughter)
274
849257
1151
（笑声）
可恶！
14:22
Damn it,
275
850432
1702
这就是解法的开始啊！
14:24
that was the start of the solution!
276
852158
2113
14:27
You see,
277
855519
1151
你们看到，
我觉得我自己在休息，
14:28
I thought I had taken some rest,
278
856694
2283
但实际上我的大脑还在持续思考。
14:31
but really my brain had
continued to work on it.
continued to work on it.
279
859001
3388
14:35
In those moments,
280
863008
1597
在那些时刻，
你不会想到你的职业生涯
或是你的同事，
或是你的同事，
14:36
you don't think of your career
or your colleagues,
or your colleagues,
281
864629
2601
这只是你自己与问题之间的斗争。
14:39
it's just a complete battle
between the problem and you.
between the problem and you.
282
867254
3690
14:44
That being said,
283
872098
1328
但说到这里，
你因为工作努力而受到奖赏
当然是很好的事情。
当然是很好的事情。
14:45
it does not harm when you do get
a promotion in reward for your hard work.
a promotion in reward for your hard work.
284
873450
3949
14:49
And after we completed our huge
analysis of the Landau damping,
analysis of the Landau damping,
285
877808
5160
在我们完成了朗道阻尼方面的
重大研究后，
重大研究后，
我很幸运地
14:54
I was lucky enough
286
882992
1615
获得了我梦寐以求的菲尔兹奖，
14:56
to get the most coveted Fields Medal
287
884631
3030
我从印度总统手中接过此奖，
14:59
from the hands of the President of India,
288
887685
2867
那是在2010年8月19日，
在海德拉巴城——
在海德拉巴城——
15:02
in Hyderabad on 19 August, 2010 --
289
890576
3920
15:07
an honor that mathematicians
never dare to dream,
never dare to dream,
290
895453
3251
这是一个数学家不敢奢望的奖项，
我也会将这天永远铭记在心。
15:10
a day that I will remember until I live.
291
898728
2399
15:14
What do you think,
292
902366
1447
对于这样的情况，
你们觉得怎样呢？
15:15
on such an occasion?
293
903837
2141
很自豪，对吧？
15:18
Pride, yes?
294
906002
1150
15:19
And gratitude to the man collaborators
who made this possible.
who made this possible.
295
907791
3640
还有对主要合作者的感激之情。
15:24
And because it was a collective adventure,
296
912304
2212
而且因为这是一个集体研究，
你需要把成果公开，
而非只是与合作者共享。
而非只是与合作者共享。
15:26
you need to share it,
not just with your collaborators.
not just with your collaborators.
297
914540
4142
15:31
I believe that everybody can appreciate
the thrill of mathematical research,
the thrill of mathematical research,
298
919548
5692
我相信每个人都可以欣赏
数学研究的刺激感，
数学研究的刺激感，
并且分享精彩研究过程中的人和事。
15:37
and share the passionate stories
of humans and ideas behind it.
of humans and ideas behind it.
299
925264
4318
15:42
And I've been working with my staff
at Institut Henri Poincaré,
at Institut Henri Poincaré,
300
930494
4774
我在昂利·庞加莱研究所
与我的团队工作，
与我的团队工作，
还有一些其他的合伙人、
世界各地的数学交流艺术家，
世界各地的数学交流艺术家，
15:47
together with partners and artists
of mathematical communication worldwide,
of mathematical communication worldwide,
301
935292
5181
于是我们就可以创立我们自己的，
特殊的数学博物馆。
特殊的数学博物馆。
15:52
so that we can found our own,
very special museum of mathematics there.
very special museum of mathematics there.
302
940497
4587
15:58
So in a few years,
303
946537
1777
再过几年，
16:00
when you come to Paris,
304
948885
1577
当你到巴黎来，
在你们品尝过美味酥脆的
法国长面包和马卡龙（蛋白杏仁饼甜点）之后，
法国长面包和马卡龙（蛋白杏仁饼甜点）之后，
16:02
after tasting the great, crispy
baguette and macaroon,
baguette and macaroon,
305
950486
5658
请各位也来我们的
昂利·庞加莱研究所转一转，
昂利·庞加莱研究所转一转，
16:08
please come and visit us
at Institut Henri Poincaré,
at Institut Henri Poincaré,
306
956168
3663
与我们共享一个数学的梦。
16:11
and share the mathematical dream with us.
307
959856
2515
谢谢。
16:14
Thank you.
308
962395
1151
（掌声）
16:15
(Applause)
309
963570
7000
ABOUT THE SPEAKER
Cédric Villani - MathematicianCédric Villani tackles perplexing problems in mathematical physics, analysis and geometry with rigor, wit and a signature personal style.
Why you should listen
His Byronesque hair, colorful ascots and spider brooches have earned Cédric Villani the nickname “the Lady Gaga of Mathematics.” But this moniker has not obscured Villani’s deeper, serious mission: inspiring students to delve into the mysteries of mathematics.
Villani’s fame is based on his work resolving difficult problems of kinetic theory, for which he received the Fields Medal in 2010. His book Birth of a Theorem is an exhilarating journey into the nocturnal dilemmas of mathematicians hot on the trail of discovery.
Villani was elected to the French National Assembly in June 2017.
Cédric Villani | Speaker | TED.com