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And inevitably, during that conversation

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00:00:25,080 --> 00:00:28,750
one of these two phrases come up:

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00:00:28,750 --> 00:00:32,195
A) "I was terrible at math,
but it wasn't my fault.

4
00:00:32,195 --> 00:00:35,614
It's because the teacher
was awful." (Laughter)

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00:00:35,614 --> 00:00:38,582
Or B) "But what is math really for?"

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00:00:38,582 --> 00:00:39,610
(Laughter)

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00:00:39,610 --> 00:00:41,955
I'll now address Case B.

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00:00:41,955 --> 00:00:43,510
(Laughter)

9
00:00:43,510 --> 00:00:48,354
When someone asks you what math is for,
they're not asking you

10
00:00:48,354 --> 00:00:51,203
about applications
of mathematical science.

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00:00:51,203 --> 00:00:52,554
They're asking you,

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00:00:52,554 --> 00:00:56,485
why did I have to study that bullshit
I never used in my life again? (Laughter)

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00:00:56,485 --> 00:00:58,924
That's what they're actually asking.

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00:00:58,924 --> 00:01:03,124
So when mathematicians are asked
what math is for,

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00:01:03,124 --> 00:01:05,404
they tend to fall into two groups:

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00:01:05,404 --> 00:01:10,739
54.51 percent of mathematicians
will assume an attacking position,

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00:01:11,609 --> 00:01:16,559
and 44.77 percent of mathematicians
will take a defensive position.

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00:01:16,559 --> 00:01:20,068
There's a strange 0.8 percent,
among which I include myself.

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00:01:20,068 --> 00:01:22,155
Who are the ones that attack?

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00:01:22,155 --> 00:01:24,902
The attacking ones are mathematicians
who would tell you

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00:01:24,902 --> 00:01:26,849
this question makes no sense,

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00:01:26,849 --> 00:01:29,597
because mathematics
have a meaning all their own --

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00:01:29,597 --> 00:01:32,144
a beautiful edifice with its own logic --

24
00:01:32,144 --> 00:01:34,011
and that there's no point

25
00:01:34,011 --> 00:01:36,558
in constantly searching
for all possible applications.

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00:01:36,558 --> 00:01:38,847
What's the use of poetry?
What's the use of love?

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00:01:38,847 --> 00:01:41,908
What's the use of life itself? 
What kind of question is that?

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00:01:41,908 --> 00:01:43,529
(Laughter)

29
00:01:43,529 --> 00:01:47,296
Hardy, for instance, was a model
of this type of attack.

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00:01:47,296 --> 00:01:49,242
And those who stand in defense tell you,

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"Even if you don't realize it, friend,
math is behind everything."

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00:01:54,082 --> 00:01:55,340
(Laughter)

33
00:01:55,340 --> 00:01:57,218
Those guys,

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00:01:57,218 --> 00:02:01,246
they always bring up
bridges and computers.

35
00:02:01,246 --> 00:02:03,841
"If you don't know math,
your bridge will collapse."

36
00:02:03,841 --> 00:02:05,286
(Laughter)

37
00:02:05,286 --> 00:02:08,523
It's true, computers are all about math.

38
00:02:08,523 --> 00:02:11,008
And now these guys
have also started saying

39
00:02:11,013 --> 00:02:16,050
that behind information security
and credit cards are prime numbers.

40
00:02:16,710 --> 00:02:20,379
These are the answers your math teacher
would give you if you asked him.

41
00:02:20,379 --> 00:02:22,544
He's one of the defensive ones.

42
00:02:22,544 --> 00:02:24,384
Okay, but who's right then?

43
00:02:24,384 --> 00:02:26,990
Those who say that math
doesn't need to have a purpose,

44
00:02:26,990 --> 00:02:29,849
or those who say that math
is behind everything we do?

45
00:02:29,849 --> 00:02:31,520
Actually, both are right.

46
00:02:31,520 --> 00:02:33,183
But remember I told you

47
00:02:33,183 --> 00:02:36,726
I belong to that strange 0.8 percent
claiming something else?

48
00:02:36,726 --> 00:02:39,929
So, go ahead, ask me what math is for.

49
00:02:39,929 --> 00:02:42,858
Audience: What is math for?

50
00:02:42,858 --> 00:02:47,673
Eduardo Sáenz de Cabezón: Okay,
76.34 percent of you asked the question,

51
00:02:47,673 --> 00:02:50,600
23.41 percent didn't say anything,

52
00:02:50,600 --> 00:02:51,827
and the 0.8 percent --

53
00:02:51,827 --> 00:02:54,675
I'm not sure what those guys are doing.

54
00:02:54,675 --> 00:02:58,175
Well, to my dear 76.31 percent --

55
00:02:58,175 --> 00:03:02,815
it's true that math doesn't need
to serve a purpose,

56
00:03:02,815 --> 00:03:05,685
it's true that it's
a beautiful structure, a logical one,

57
00:03:05,685 --> 00:03:08,537
probably one
of the greatest collective efforts

58
00:03:08,537 --> 00:03:10,633
ever achieved in human history.

59
00:03:10,633 --> 00:03:12,732
But it's also true that there,

60
00:03:12,732 --> 00:03:17,331
where scientists and technicians
are looking for mathematical theories

61
00:03:17,331 --> 00:03:19,641
that allow them to advance,

62
00:03:19,641 --> 00:03:23,438
they're within the structure of math,
which permeates everything.

63
00:03:23,438 --> 00:03:26,585
It's true that we have to go
somewhat deeper,

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00:03:26,585 --> 00:03:28,308
to see what's behind science.

65
00:03:28,308 --> 00:03:31,858
Science operates on intuition, creativity.

66
00:03:32,348 --> 00:03:35,772
Math controls intuition
and tames creativity.

67
00:03:36,747 --> 00:03:38,937
Almost everyone
who hasn't heard this before

68
00:03:38,937 --> 00:03:41,647
is surprised when they hear
that if you take

69
00:03:41,647 --> 00:03:46,187
a 0.1 millimeter thick sheet of paper,
the size we normally use,

70
00:03:46,187 --> 00:03:49,505
and, if it were big enough,
fold it 50 times,

71
00:03:49,505 --> 00:03:55,205
its thickness would extend almost
the distance from the Earth to the sun.

72
00:03:55,600 --> 00:03:58,201
Your intuition tells you it's impossible.

73
00:03:58,201 --> 00:04:00,622
Do the math and you'll see it's right.

74
00:04:00,622 --> 00:04:03,135
That's what math is for.

75
00:04:03,135 --> 00:04:06,917
It's true that science, all types
of science, only makes sense

76
00:04:06,917 --> 00:04:10,288
because it makes us better understand
this beautiful world we live in.

77
00:04:10,288 --> 00:04:11,669
And in doing that,

78
00:04:11,669 --> 00:04:15,179
it helps us avoid the pitfalls
of this painful world we live in.

79
00:04:15,179 --> 00:04:18,656
There are sciences that help us
in this way quite directly.

80
00:04:18,656 --> 00:04:20,413
Oncological science, for example.

81
00:04:20,413 --> 00:04:23,905
And there are others we look at from afar,
with envy sometimes,

82
00:04:23,905 --> 00:04:26,464
but knowing that we are
what supports them.

83
00:04:26,464 --> 00:04:29,213
All the basic sciences
support them,

84
00:04:29,213 --> 00:04:31,649
including math.

85
00:04:31,649 --> 00:04:35,366
All that makes science, science
is the rigor of math.

86
00:04:35,366 --> 00:04:40,242
And that rigor factors in
because its results are eternal.

87
00:04:40,242 --> 00:04:42,757
You probably said or were told
at some point

88
00:04:42,757 --> 00:04:45,708
that diamonds are forever, right?

89
00:04:47,178 --> 00:04:49,392
That depends on
your definition of forever!

90
00:04:49,392 --> 00:04:51,883
A theorem -- that really is forever.

91
00:04:51,883 --> 00:04:53,134
(Laughter)

92
00:04:53,134 --> 00:04:56,486
The Pythagorean theorem is still true

93
00:04:56,486 --> 00:04:59,601
even though Pythagoras is dead,
I assure you it's true. (Laughter)

94
00:04:59,601 --> 00:05:00,946
Even if the world collapsed

95
00:05:00,946 --> 00:05:03,391
the Pythagorean theorem
would still be true.

96
00:05:03,391 --> 00:05:07,452
Wherever any two triangle sides
and a good hypotenuse get together

97
00:05:07,452 --> 00:05:08,673
(Laughter)

98
00:05:08,673 --> 00:05:11,534
the Pythagorean theorem goes all out.
It works like crazy.

99
00:05:11,534 --> 00:05:14,355
(Applause)

100
00:05:18,535 --> 00:05:22,407
Well, we mathematicians devote ourselves
to come up with theorems.

101
00:05:22,407 --> 00:05:24,143
Eternal truths.

102
00:05:24,143 --> 00:05:26,909
But it isn't always easy to know
the difference between

103
00:05:26,909 --> 00:05:29,815
an eternal truth, or theorem,
and a mere conjecture.

104
00:05:29,815 --> 00:05:32,829
You need proof.

105
00:05:32,829 --> 00:05:34,596
For example,

106
00:05:34,596 --> 00:05:39,423
let's say I have a big,
enormous, infinite field.

107
00:05:39,423 --> 00:05:43,132
I want to cover it with equal pieces,
without leaving any gaps.

108
00:05:43,132 --> 00:05:45,256
I could use squares, right?

109
00:05:45,256 --> 00:05:49,222
I could use triangles.
Not circles, those leave little gaps.

110
00:05:49,777 --> 00:05:52,134
Which is the best shape to use?

111
00:05:52,134 --> 00:05:56,687
One that covers the same surface,
but has a smaller border.

112
00:05:56,687 --> 00:06:01,396
In the year 300, Pappus of Alexandria
said the best is to use hexagons,

113
00:06:01,396 --> 00:06:03,243
just like bees do.

114
00:06:03,243 --> 00:06:04,990
But he didn't prove it.

115
00:06:04,990 --> 00:06:07,688
The guy said, "Hexagons, great!
Let's go with hexagons!"

116
00:06:07,688 --> 00:06:10,656
He didn't prove it,
it remained a conjecture.

117
00:06:10,656 --> 00:06:12,334
"Hexagons!"

118
00:06:12,334 --> 00:06:15,964
And the world, as you know,
split into Pappists and anti-Pappists,

119
00:06:15,964 --> 00:06:21,253
until 1700 years later

120
00:06:21,253 --> 00:06:26,707
when in 1999, Thomas Hales proved

121
00:06:26,707 --> 00:06:31,641
that Pappus and the bees were right --
the best shape to use was the hexagon.

122
00:06:31,641 --> 00:06:34,123
And that became a theorem,
the honeycomb theorem,

123
00:06:34,123 --> 00:06:36,183
that will be true forever and ever,

124
00:06:36,183 --> 00:06:39,224
for longer than any diamond
you may have. (Laughter)

125
00:06:39,229 --> 00:06:42,033
But what happens if we go
to three dimensions?

126
00:06:42,033 --> 00:06:45,944
If I want to fill the space
with equal pieces,

127
00:06:46,464 --> 00:06:47,805
without leaving any gaps,

128
00:06:47,805 --> 00:06:49,638
I can use cubes, right?

129
00:06:49,638 --> 00:06:52,994
Not spheres, those leave little gaps.
(Laughter)

130
00:06:52,994 --> 00:06:55,957
What is the best shape to use?

131
00:06:55,957 --> 00:07:00,017
Lord Kelvin, of the famous
Kelvin degrees and all,

132
00:07:00,607 --> 00:07:06,121
said that the best was to use
a truncated octahedron

133
00:07:07,791 --> 00:07:10,507
which, as you all know --

134
00:07:10,507 --> 00:07:12,035
(Laughter) --

135
00:07:12,035 --> 00:07:13,814
is this thing here!

136
00:07:13,814 --> 00:07:16,753
(Applause)

137
00:07:18,778 --> 00:07:20,225
Come on.

138
00:07:21,025 --> 00:07:23,862
Who doesn't have a truncated
octahedron at home? (Laughter)

139
00:07:23,862 --> 00:07:25,089
Even a plastic one.

140
00:07:25,089 --> 00:07:27,846
"Honey, get the truncated octahedron,
we're having guests."

141
00:07:27,846 --> 00:07:29,240
Everybody has one!
(Laughter)

142
00:07:29,240 --> 00:07:31,614
But Kelvin didn't prove it.

143
00:07:31,614 --> 00:07:35,655
It remained a conjecture --
Kelvin's conjecture.

144
00:07:35,655 --> 00:07:41,177
The world, as you know, then split into
Kelvinists and anti-Kelvinists

145
00:07:41,177 --> 00:07:42,599
(Laughter)

146
00:07:42,599 --> 00:07:46,496
until a hundred or so years later,

147
00:07:49,203 --> 00:07:53,072
someone found a better structure.

148
00:07:53,917 --> 00:07:59,026
Weaire and Phelan
found this little thing over here --

149
00:07:59,026 --> 00:08:00,665
(Laughter) --

150
00:08:00,665 --> 00:08:04,209
this structure to which they gave
the very clever name

151
00:08:04,209 --> 00:08:06,375
"the Weaire-Phelan structure."

152
00:08:06,375 --> 00:08:08,911
(Laughter)

153
00:08:08,911 --> 00:08:11,568
It looks like a strange object,
but it isn't so strange,

154
00:08:11,568 --> 00:08:13,239
it also exists in nature.

155
00:08:13,239 --> 00:08:15,844
It's very interesting that this structure,

156
00:08:15,844 --> 00:08:18,037
because of its geometric properties,

157
00:08:18,037 --> 00:08:23,229
was used to build the Aquatics Center
for the Beijing Olympic Games.

158
00:08:23,969 --> 00:08:26,714
There, Michael Phelps
won eight gold medals,

159
00:08:26,714 --> 00:08:29,875
and became the best swimmer of all time.

160
00:08:29,875 --> 00:08:33,616
Well, until someone better
comes along, right?

161
00:08:33,616 --> 00:08:36,015
As may happen
with the Weaire-Phelan structure.

162
00:08:36,015 --> 00:08:38,633
It's the best
until something better shows up.

163
00:08:38,633 --> 00:08:43,225
But be careful, because this one
really stands a chance

164
00:08:43,225 --> 00:08:48,205
that in a hundred or so years,
or even if it's in 1700 years,

165
00:08:48,205 --> 00:08:53,603
that someone proves
it's the best possible shape for the job.

166
00:08:53,978 --> 00:08:58,348
It will then become a theorem,
a truth, forever and ever.

167
00:08:58,348 --> 00:09:01,302
For longer than any diamond.

168
00:09:01,837 --> 00:09:05,567
So, if you want to tell someone

169
00:09:06,777 --> 00:09:09,823
that you will love them forever

170
00:09:09,823 --> 00:09:11,890
you can give them a diamond.

171
00:09:11,890 --> 00:09:15,421
But if you want to tell them
that you'll love them forever and ever,

172
00:09:15,421 --> 00:09:17,172
give them a theorem!

173
00:09:17,172 --> 00:09:18,263
(Laughter)

174
00:09:18,263 --> 00:09:20,853
But hang on a minute!

175
00:09:21,783 --> 00:09:23,183
You'll have to prove it,

176
00:09:23,183 --> 00:09:25,466
so your love doesn't remain

177
00:09:25,466 --> 00:09:27,299
a conjecture.

178
00:09:27,299 --> 00:09:30,543
(Applause)