Eduardo Sáenz de Cabezón: Math is forever (with English subtitles) | TED

190,450 views ・ 2015-04-07

TED


Please double-click on the English subtitles below to play the video.

00:00
Translator: Tomás Guarna Reviewer: Sebastian Betti
0
0
7000
00:13
Imagine you're in a bar, or a club,
1
13370
5750
00:19
and you start talking, and after a while, the question comes up,
2
19120
3010
00:22
"So, what do you do for work?"
3
22130
1870
00:24
And since you think your job is interesting,
4
24015
2935
00:26
you say, "I'm a mathematician." (Laughter)
5
26950
4280
00:31
And inevitably, during that conversation
6
31690
2390
00:34
one of these two phrases come up:
7
34080
3670
00:37
A) "I was terrible at math, but it wasn't my fault.
8
37750
3445
00:41
It's because the teacher was awful." (Laughter)
9
41195
3418
00:44
Or B) "But what is math really for?"
10
44613
2969
00:47
(Laughter)
11
47582
1028
00:48
I'll now address Case B.
12
48610
2345
00:50
(Laughter)
13
50955
1555
00:52
When someone asks you what math is for, they're not asking you
14
52510
4844
00:57
about applications of mathematical science.
15
57354
2849
01:00
They're asking you,
16
60203
1351
01:01
why did I have to study that bullshit I never used in my life again? (Laughter)
17
61554
3931
01:05
That's what they're actually asking.
18
65485
2439
01:07
So when mathematicians are asked what math is for,
19
67924
4200
01:12
they tend to fall into two groups:
20
72124
2280
01:14
54.51 percent of mathematicians will assume an attacking position,
21
74404
5335
01:20
and 44.77 percent of mathematicians will take a defensive position.
22
80609
4950
01:25
There's a strange 0.8 percent, among which I include myself.
23
85559
3509
01:29
Who are the ones that attack?
24
89068
2087
01:31
The attacking ones are mathematicians who would tell you
25
91155
2747
01:33
this question makes no sense,
26
93902
1947
01:35
because mathematics have a meaning all their own --
27
95849
2748
01:38
a beautiful edifice with its own logic --
28
98597
2547
01:41
and that there's no point
29
101144
1867
01:43
in constantly searching for all possible applications.
30
103011
2547
01:45
What's the use of poetry? What's the use of love?
31
105558
2289
01:47
What's the use of life itself? What kind of question is that?
32
107847
3061
01:50
(Laughter)
33
110908
1621
01:52
Hardy, for instance, was a model of this type of attack.
34
112529
3767
01:56
And those who stand in defense tell you,
35
116296
1946
01:58
"Even if you don't realize it, friend, math is behind everything."
36
118242
4840
02:03
(Laughter)
37
123082
1258
02:04
Those guys,
38
124340
1878
02:06
they always bring up bridges and computers.
39
126218
4028
02:10
"If you don't know math, your bridge will collapse."
40
130246
2595
02:12
(Laughter)
41
132841
1445
02:14
It's true, computers are all about math.
42
134286
3237
02:17
And now these guys have also started saying
43
137523
2485
02:20
that behind information security and credit cards are prime numbers.
44
140013
5037
02:25
These are the answers your math teacher would give you if you asked him.
45
145710
3669
02:29
He's one of the defensive ones.
46
149379
2165
02:31
Okay, but who's right then?
47
151544
1840
02:33
Those who say that math doesn't need to have a purpose,
48
153384
2606
02:35
or those who say that math is behind everything we do?
49
155990
2859
02:38
Actually, both are right.
50
158849
1671
02:40
But remember I told you
51
160520
1663
02:42
I belong to that strange 0.8 percent claiming something else?
52
162183
3543
02:45
So, go ahead, ask me what math is for.
53
165726
3203
02:48
Audience: What is math for?
54
168929
2929
02:51
Eduardo Sáenz de Cabezón: Okay, 76.34 percent of you asked the question,
55
171858
4815
02:56
23.41 percent didn't say anything,
56
176673
2927
02:59
and the 0.8 percent --
57
179600
1227
03:00
I'm not sure what those guys are doing.
58
180827
2848
03:03
Well, to my dear 76.31 percent --
59
183675
3500
03:07
it's true that math doesn't need to serve a purpose,
60
187175
4640
03:11
it's true that it's a beautiful structure, a logical one,
61
191815
2870
03:14
probably one of the greatest collective efforts
62
194685
2852
03:17
ever achieved in human history.
63
197537
2096
03:19
But it's also true that there,
64
199633
2099
03:21
where scientists and technicians are looking for mathematical theories
65
201732
4599
03:26
that allow them to advance,
66
206331
2310
03:28
they're within the structure of math, which permeates everything.
67
208641
3797
03:32
It's true that we have to go somewhat deeper,
68
212438
3147
03:35
to see what's behind science.
69
215585
1723
03:37
Science operates on intuition, creativity.
70
217308
3550
03:41
Math controls intuition and tames creativity.
71
221348
3424
03:45
Almost everyone who hasn't heard this before
72
225747
2190
03:47
is surprised when they hear that if you take
73
227937
2710
03:50
a 0.1 millimeter thick sheet of paper, the size we normally use,
74
230647
4540
03:55
and, if it were big enough, fold it 50 times,
75
235187
3318
03:58
its thickness would extend almost the distance from the Earth to the sun.
76
238505
5700
04:04
Your intuition tells you it's impossible.
77
244600
2601
04:07
Do the math and you'll see it's right.
78
247201
2421
04:09
That's what math is for.
79
249622
2513
04:12
It's true that science, all types of science, only makes sense
80
252135
3782
04:15
because it makes us better understand this beautiful world we live in.
81
255917
3371
04:19
And in doing that,
82
259288
1381
04:20
it helps us avoid the pitfalls of this painful world we live in.
83
260669
3510
04:24
There are sciences that help us in this way quite directly.
84
264179
3478
04:27
Oncological science, for example.
85
267657
1756
04:29
And there are others we look at from afar, with envy sometimes,
86
269413
3491
04:32
but knowing that we are what supports them.
87
272904
2560
04:35
All the basic sciences support them,
88
275464
2749
04:38
including math.
89
278213
2436
04:40
All that makes science, science is the rigor of math.
90
280649
3717
04:44
And that rigor factors in because its results are eternal.
91
284366
4876
04:49
You probably said or were told at some point
92
289242
2515
04:51
that diamonds are forever, right?
93
291757
2951
04:56
That depends on your definition of forever!
94
296178
2214
04:58
A theorem -- that really is forever.
95
298392
2491
05:00
(Laughter)
96
300883
1251
05:02
The Pythagorean theorem is still true
97
302134
3352
05:05
even though Pythagoras is dead, I assure you it's true. (Laughter)
98
305486
3115
05:08
Even if the world collapsed
99
308601
1345
05:09
the Pythagorean theorem would still be true.
100
309946
2445
05:12
Wherever any two triangle sides and a good hypotenuse get together
101
312391
4061
05:16
(Laughter)
102
316452
1221
05:17
the Pythagorean theorem goes all out. It works like crazy.
103
317673
2861
05:20
(Applause)
104
320534
2821
05:27
Well, we mathematicians devote ourselves to come up with theorems.
105
327535
3872
05:31
Eternal truths.
106
331407
1736
05:33
But it isn't always easy to know the difference between
107
333143
2766
05:35
an eternal truth, or theorem, and a mere conjecture.
108
335909
2906
05:38
You need proof.
109
338815
3014
05:41
For example,
110
341829
1767
05:43
let's say I have a big, enormous, infinite field.
111
343596
4827
05:48
I want to cover it with equal pieces, without leaving any gaps.
112
348423
3709
05:52
I could use squares, right?
113
352132
2124
05:54
I could use triangles. Not circles, those leave little gaps.
114
354256
3966
05:58
Which is the best shape to use?
115
358777
2357
06:01
One that covers the same surface, but has a smaller border.
116
361134
4553
06:05
In the year 300, Pappus of Alexandria said the best is to use hexagons,
117
365687
4709
06:10
just like bees do.
118
370396
1847
06:12
But he didn't prove it.
119
372243
1747
06:13
The guy said, "Hexagons, great! Let's go with hexagons!"
120
373990
2698
06:16
He didn't prove it, it remained a conjecture.
121
376688
2968
06:19
"Hexagons!"
122
379656
1678
06:21
And the world, as you know, split into Pappists and anti-Pappists,
123
381334
3630
06:24
until 1700 years later
124
384964
5289
06:30
when in 1999, Thomas Hales proved
125
390253
5454
06:35
that Pappus and the bees were right -- the best shape to use was the hexagon.
126
395707
4934
06:40
And that became a theorem, the honeycomb theorem,
127
400641
2482
06:43
that will be true forever and ever,
128
403123
2060
06:45
for longer than any diamond you may have. (Laughter)
129
405183
3041
06:48
But what happens if we go to three dimensions?
130
408229
2804
06:51
If I want to fill the space with equal pieces,
131
411033
3911
06:55
without leaving any gaps,
132
415464
1341
06:56
I can use cubes, right?
133
416805
1833
06:58
Not spheres, those leave little gaps. (Laughter)
134
418638
3356
07:01
What is the best shape to use?
135
421994
2963
07:04
Lord Kelvin, of the famous Kelvin degrees and all,
136
424957
4060
07:09
said that the best was to use a truncated octahedron
137
429607
5514
07:16
which, as you all know --
138
436791
2716
07:19
(Laughter) --
139
439507
1528
07:21
is this thing here!
140
441035
1779
07:22
(Applause)
141
442814
2939
07:27
Come on.
142
447778
1447
07:30
Who doesn't have a truncated octahedron at home? (Laughter)
143
450025
2837
07:32
Even a plastic one.
144
452862
1227
07:34
"Honey, get the truncated octahedron, we're having guests."
145
454089
2757
07:36
Everybody has one! (Laughter)
146
456846
1394
07:38
But Kelvin didn't prove it.
147
458240
2374
07:40
It remained a conjecture -- Kelvin's conjecture.
148
460614
4041
07:44
The world, as you know, then split into Kelvinists and anti-Kelvinists
149
464655
5522
07:50
(Laughter)
150
470177
1422
07:51
until a hundred or so years later,
151
471599
3897
07:58
someone found a better structure.
152
478203
3869
08:02
Weaire and Phelan found this little thing over here --
153
482917
5109
08:08
(Laughter) --
154
488026
1639
08:09
this structure to which they gave the very clever name
155
489665
3544
08:13
"the Weaire-€“Phelan structure."
156
493209
2166
08:15
(Laughter)
157
495375
2536
08:17
It looks like a strange object, but it isn't so strange,
158
497911
2657
08:20
it also exists in nature.
159
500568
1671
08:22
It's very interesting that this structure,
160
502239
2605
08:24
because of its geometric properties,
161
504844
2193
08:27
was used to build the Aquatics Center for the Beijing Olympic Games.
162
507037
5192
08:32
There, Michael Phelps won eight gold medals,
163
512969
2745
08:35
and became the best swimmer of all time.
164
515714
3161
08:38
Well, until someone better comes along, right?
165
518875
3741
08:42
As may happen with the Weaire-€“Phelan structure.
166
522616
2399
08:45
It's the best until something better shows up.
167
525015
2618
08:47
But be careful, because this one really stands a chance
168
527633
4592
08:52
that in a hundred or so years, or even if it's in 1700 years,
169
532225
4980
08:57
that someone proves it's the best possible shape for the job.
170
537205
5398
09:02
It will then become a theorem, a truth, forever and ever.
171
542978
4370
09:07
For longer than any diamond.
172
547348
2954
09:10
So, if you want to tell someone
173
550837
3730
09:15
that you will love them forever
174
555777
3046
09:18
you can give them a diamond.
175
558823
2067
09:20
But if you want to tell them that you'll love them forever and ever,
176
560890
3531
09:24
give them a theorem!
177
564421
1751
09:26
(Laughter)
178
566172
1091
09:27
But hang on a minute!
179
567263
2590
09:30
You'll have to prove it,
180
570783
1400
09:32
so your love doesn't remain
181
572183
2283
09:34
a conjecture.
182
574466
1833
09:36
(Applause)
183
576299
3244
About this website

This site will introduce you to YouTube videos that are useful for learning English. You will see English lessons taught by top-notch teachers from around the world. Double-click on the English subtitles displayed on each video page to play the video from there. The subtitles scroll in sync with the video playback. If you have any comments or requests, please contact us using this contact form.

https://forms.gle/WvT1wiN1qDtmnspy7