0:00:01.370,0:00:07.120
Imagine you're in a bar, or a club,

0:00:07.120,0:00:10.130
and you start talking, and after a while,[br]the question comes up,

0:00:10.130,0:00:12.000
"So, what do you do for work?"

0:00:12.015,0:00:14.950
And since you think[br]your job is interesting,

0:00:14.950,0:00:19.230
you say, "I'm a mathematician."[br](Laughter)

0:00:19.690,0:00:22.080
And inevitably, during that conversation

0:00:22.080,0:00:25.750
one of these two phrases come up:

0:00:25.750,0:00:29.195
A) "I was terrible at math,[br]but it wasn't my fault.

0:00:29.195,0:00:32.613
It's because the teacher[br]was awful." (Laughter)

0:00:32.613,0:00:35.582
Or B) "But what is math really for?"

0:00:35.582,0:00:36.610
(Laughter)

0:00:36.610,0:00:38.955
I'll now address Case B.

0:00:38.955,0:00:40.510
(Laughter)

0:00:40.510,0:00:45.354
When someone asks you what math is for,[br]they're not asking you

0:00:45.354,0:00:48.203
about applications[br]of mathematical science.

0:00:48.203,0:00:49.554
They're asking you,

0:00:49.554,0:00:53.485
why did I have to study that bullshit[br]I never used in my life again? (Laughter)

0:00:53.485,0:00:55.924
That's what they're actually asking.

0:00:55.924,0:01:00.124
So when mathematicians are asked[br]what math is for,

0:01:00.124,0:01:02.404
they tend to fall into two groups:

0:01:02.404,0:01:07.739
54.51 percent of mathematicians[br]will assume an attacking position,

0:01:08.609,0:01:13.559
and 44.77 percent of mathematicians[br]will take a defensive position.

0:01:13.559,0:01:17.068
There's a strange 0.8 percent,[br]among which I include myself.

0:01:17.068,0:01:19.155
Who are the ones that attack?

0:01:19.155,0:01:21.902
The attacking ones are mathematicians[br]who would tell you

0:01:21.902,0:01:23.849
this question makes no sense,

0:01:23.849,0:01:26.597
because mathematics[br]have a meaning all their own --

0:01:26.597,0:01:29.144
a beautiful edifice with its own logic --

0:01:29.144,0:01:31.011
and that there's no point

0:01:31.011,0:01:33.558
in constantly searching[br]for all possible applications.

0:01:33.558,0:01:35.847
What's the use of poetry?[br]What's the use of love?

0:01:35.847,0:01:38.908
What's the use of life itself? [br]What kind of question is that?

0:01:38.908,0:01:40.529
(Laughter)

0:01:40.529,0:01:44.296
Hardy, for instance, was a model[br]of this type of attack.

0:01:44.296,0:01:46.242
And those who stand in defense tell you,

0:01:46.242,0:01:51.082
"Even if you don't realize it, friend,[br]math is behind everything."

0:01:51.082,0:01:52.340
(Laughter)

0:01:52.340,0:01:54.218
Those guys,

0:01:54.218,0:01:58.246
they always bring up[br]bridges and computers.

0:01:58.246,0:02:00.841
"If you don't know math,[br]your bridge will collapse."

0:02:00.841,0:02:02.286
(Laughter)

0:02:02.286,0:02:05.523
It's true, computers are all about math.

0:02:05.523,0:02:08.008
And now these guys[br]have also started saying

0:02:08.013,0:02:13.050
that behind information security[br]and credit cards are prime numbers.

0:02:13.710,0:02:17.379
These are the answers your math teacher[br]would give you if you asked him.

0:02:17.379,0:02:19.544
He's one of the defensive ones.

0:02:19.544,0:02:21.384
Okay, but who's right then?

0:02:21.384,0:02:23.990
Those who say that math[br]doesn't need to have a purpose,

0:02:23.990,0:02:26.849
or those who say that math[br]is behind everything we do?

0:02:26.849,0:02:28.520
Actually, both are right.

0:02:28.520,0:02:30.183
But remember I told you

0:02:30.183,0:02:33.726
I belong to that strange 0.8 percent[br]claiming something else?

0:02:33.726,0:02:36.929
So, go ahead, ask me what math is for.

0:02:36.929,0:02:39.858
Audience: What is math for?

0:02:39.858,0:02:44.673
Eduardo Sáenz de Cabezón: Okay,[br]76.34 percent of you asked the question,

0:02:44.673,0:02:47.600
23.41 percent didn't say anything,

0:02:47.600,0:02:48.827
and the 0.8 percent --

0:02:48.827,0:02:51.675
I'm not sure what those guys are doing.

0:02:51.675,0:02:55.175
Well, to my dear 76.31 percent --

0:02:55.175,0:02:59.815
it's true that math doesn't need[br]to serve a purpose,

0:02:59.815,0:03:02.685
it's true that it's[br]a beautiful structure, a logical one,

0:03:02.685,0:03:05.537
probably one[br]of the greatest collective efforts

0:03:05.537,0:03:07.633
ever achieved in human history.

0:03:07.633,0:03:09.732
But it's also true that there,

0:03:09.732,0:03:14.331
where scientists and technicians[br]are looking for mathematical theories

0:03:14.331,0:03:16.641
that allow them to advance,

0:03:16.641,0:03:20.438
they're within the structure of math,[br]which permeates everything.

0:03:20.438,0:03:23.585
It's true that we have to go[br]somewhat deeper,

0:03:23.585,0:03:25.308
to see what's behind science.

0:03:25.308,0:03:28.858
Science operates on intuition, creativity.

0:03:29.348,0:03:32.772
Math controls intuition[br]and tames creativity.

0:03:33.747,0:03:35.937
Almost everyone[br]who hasn't heard this before

0:03:35.937,0:03:38.647
is surprised when they hear[br]that if you take

0:03:38.647,0:03:43.187
a 0.1 millimeter thick sheet of paper,[br]the size we normally use,

0:03:43.187,0:03:46.505
and, if it were big enough,[br]fold it 50 times,

0:03:46.505,0:03:52.205
its thickness would extend almost[br]the distance from the Earth to the sun.

0:03:52.600,0:03:55.201
Your intuition tells you it's impossible.

0:03:55.201,0:03:57.622
Do the math and you'll see it's right.

0:03:57.622,0:04:00.135
That's what math is for.

0:04:00.135,0:04:03.917
It's true that science, all types[br]of science, only makes sense

0:04:03.917,0:04:07.288
because it makes us better understand[br]this beautiful world we live in.

0:04:07.288,0:04:08.669
And in doing that,

0:04:08.669,0:04:12.179
it helps us avoid the pitfalls[br]of this painful world we live in.

0:04:12.179,0:04:15.657
There are sciences that help us[br]in this way quite directly.

0:04:15.657,0:04:17.413
Oncological science, for example.

0:04:17.413,0:04:20.904
And there are others we look at from afar,[br]with envy sometimes,

0:04:20.904,0:04:23.464
but knowing that we are[br]what supports them.

0:04:23.464,0:04:26.213
All the basic sciences[br]support them,

0:04:26.213,0:04:28.649
including math.

0:04:28.649,0:04:32.366
All that makes science, science[br]is the rigor of math.

0:04:32.366,0:04:37.242
And that rigor factors in[br]because its results are eternal.

0:04:37.242,0:04:39.757
You probably said or were told[br]at some point

0:04:39.757,0:04:42.708
that diamonds are forever, right?

0:04:44.178,0:04:46.392
That depends on[br]your definition of forever!

0:04:46.392,0:04:48.883
A theorem -- that really is forever.

0:04:48.883,0:04:50.134
(Laughter)

0:04:50.134,0:04:53.486
The Pythagorean theorem is still true

0:04:53.486,0:04:56.601
even though Pythagoras is dead,[br]I assure you it's true. (Laughter)

0:04:56.601,0:04:57.946
Even if the world collapsed

0:04:57.946,0:05:00.391
the Pythagorean theorem[br]would still be true.

0:05:00.391,0:05:04.452
Wherever any two triangle sides[br]and a good hypotenuse get together

0:05:04.452,0:05:05.673
(Laughter)

0:05:05.673,0:05:08.534
the Pythagorean theorem goes all out.[br]It works like crazy.

0:05:08.534,0:05:11.355
(Applause)

0:05:15.535,0:05:19.407
Well, we mathematicians devote ourselves[br]to come up with theorems.

0:05:19.407,0:05:21.143
Eternal truths.

0:05:21.143,0:05:23.909
But it isn't always easy to know[br]the difference between

0:05:23.909,0:05:26.815
an eternal truth, or theorem,[br]and a mere conjecture.

0:05:26.815,0:05:29.829
You need proof.

0:05:29.829,0:05:31.596
For example,

0:05:31.596,0:05:36.423
let's say I have a big,[br]enormous, infinite field.

0:05:36.423,0:05:40.132
I want to cover it with equal pieces,[br]without leaving any gaps.

0:05:40.132,0:05:42.256
I could use squares, right?

0:05:42.256,0:05:46.222
I could use triangles.[br]Not circles, those leave little gaps.

0:05:46.777,0:05:49.134
Which is the best shape to use?

0:05:49.134,0:05:53.687
One that covers the same surface,[br]but has a smaller border.

0:05:53.687,0:05:58.396
In the year 300, Pappus of Alexandria[br]said the best is to use hexagons,

0:05:58.396,0:06:00.243
just like bees do.

0:06:00.243,0:06:01.990
But he didn't prove it.

0:06:01.990,0:06:04.688
The guy said, "Hexagons, great![br]Let's go with hexagons!"

0:06:04.688,0:06:07.656
He didn't prove it,[br]it remained a conjecture.

0:06:07.656,0:06:09.334
"Hexagons!"

0:06:09.334,0:06:12.964
And the world, as you know,[br]split into Pappists and anti-Pappists,

0:06:12.964,0:06:18.253
until 1700 years later

0:06:18.253,0:06:23.707
when in 1999, Thomas Hales proved

0:06:23.707,0:06:28.641
that Pappus and the bees were right --[br]the best shape to use was the hexagon.

0:06:28.641,0:06:31.123
And that became a theorem,[br]the honeycomb theorem,

0:06:31.123,0:06:33.183
that will be true forever and ever,

0:06:33.183,0:06:36.224
for longer than any diamond[br]you may have. (Laughter)

0:06:36.229,0:06:39.033
But what happens if we go[br]to three dimensions?

0:06:39.033,0:06:42.944
If I want to fill the space[br]with equal pieces,

0:06:43.464,0:06:44.805
without leaving any gaps,

0:06:44.805,0:06:46.638
I can use cubes, right?

0:06:46.638,0:06:49.994
Not spheres, those leave little gaps.[br](Laughter)

0:06:49.994,0:06:52.957
What is the best shape to use?

0:06:52.957,0:06:57.017
Lord Kelvin, of the famous[br]Kelvin degrees and all,

0:06:57.607,0:07:03.121
said that the best was to use[br]a truncated octahedron

0:07:04.791,0:07:07.507
which, as you all know --

0:07:07.507,0:07:09.035
(Laughter) --

0:07:09.035,0:07:10.814
is this thing here!

0:07:10.814,0:07:13.753
(Applause)

0:07:15.778,0:07:17.225
Come on.

0:07:18.025,0:07:20.862
Who doesn't have a truncated[br]octahedron at home? (Laughter)

0:07:20.862,0:07:22.089
Even a plastic one.

0:07:22.089,0:07:24.846
"Honey, get the truncated octahedron,[br]we're having guests."

0:07:24.846,0:07:26.240
Everybody has one![br](Laughter)

0:07:26.240,0:07:28.614
But Kelvin didn't prove it.

0:07:28.614,0:07:32.655
It remained a conjecture --[br]Kelvin's conjecture.

0:07:32.655,0:07:38.177
The world, as you know, then split into[br]Kelvinists and anti-Kelvinists

0:07:38.177,0:07:39.599
(Laughter)

0:07:39.599,0:07:43.496
until a hundred or so years later,

0:07:46.203,0:07:50.072
someone found a better structure.

0:07:50.917,0:07:56.026
Weaire and Phelan[br]found this little thing over here --

0:07:56.026,0:07:57.665
(Laughter) --

0:07:57.665,0:08:01.209
this structure to which they gave[br]the very clever name

0:08:01.209,0:08:03.375
"the Weaire-Phelan structure."

0:08:03.375,0:08:05.911
(Laughter)

0:08:05.911,0:08:08.568
It looks like a strange object,[br]but it isn't so strange,

0:08:08.568,0:08:10.239
it also exists in nature.

0:08:10.239,0:08:12.844
It's very interesting that this structure,

0:08:12.844,0:08:15.037
because of its geometric properties,

0:08:15.037,0:08:20.229
was used to build the Aquatics Center[br]for the Beijing Olympic Games.

0:08:20.969,0:08:23.714
There, Michael Phelps[br]won eight gold medals,

0:08:23.714,0:08:26.875
and became the best swimmer of all time.

0:08:26.875,0:08:30.616
Well, until someone better[br]comes along, right?

0:08:30.616,0:08:33.015
As may happen[br]with the Weaire-Phelan structure.

0:08:33.015,0:08:35.633
It's the best[br]until something better shows up.

0:08:35.633,0:08:40.225
But be careful, because this one[br]really stands a chance

0:08:40.225,0:08:45.205
that in a hundred or so years,[br]or even if it's in 1700 years,

0:08:45.205,0:08:50.603
that someone proves[br]it's the best possible shape for the job.

0:08:50.978,0:08:55.348
It will then become a theorem,[br]a truth, forever and ever.

0:08:55.348,0:08:58.302
For longer than any diamond.

0:08:58.837,0:09:02.567
So, if you want to tell someone

0:09:03.777,0:09:06.823
that you will love them forever

0:09:06.823,0:09:08.890
you can give them a diamond.

0:09:08.890,0:09:12.421
But if you want to tell them[br]that you'll love them forever and ever,

0:09:12.421,0:09:14.172
give them a theorem!

0:09:14.172,0:09:15.263
(Laughter)

0:09:15.263,0:09:17.853
But hang on a minute!

0:09:18.783,0:09:20.183
You'll have to prove it,

0:09:20.183,0:09:22.466
so your love doesn't remain

0:09:22.466,0:09:24.299
a conjecture.

0:09:24.299,0:09:27.543
(Applause)