0:00:22.995,0:00:25.080
And inevitably, during that conversation

0:00:25.080,0:00:28.750
one of these two phrases come up:

0:00:28.750,0:00:32.195
A) "I was terrible at math,[br]but it wasn't my fault.

0:00:32.195,0:00:35.614
It's because the teacher[br]was awful." (Laughter)

0:00:35.614,0:00:38.582
Or B) "But what is math really for?"

0:00:38.582,0:00:39.610
(Laughter)

0:00:39.610,0:00:41.955
I'll now address Case B.

0:00:41.955,0:00:43.510
(Laughter)

0:00:43.510,0:00:48.354
When someone asks you what math is for,[br]they're not asking you

0:00:48.354,0:00:51.203
about applications[br]of mathematical science.

0:00:51.203,0:00:52.554
They're asking you,

0:00:52.554,0:00:56.485
why did I have to study that bullshit[br]I never used in my life again? (Laughter)

0:00:56.485,0:00:58.924
That's what they're actually asking.

0:00:58.924,0:01:03.124
So when mathematicians are asked[br]what math is for,

0:01:03.124,0:01:05.404
they tend to fall into two groups:

0:01:05.404,0:01:10.739
54.51 percent of mathematicians[br]will assume an attacking position,

0:01:11.609,0:01:16.559
and 44.77 percent of mathematicians[br]will take a defensive position.

0:01:16.559,0:01:20.068
There's a strange 0.8 percent,[br]among which I include myself.

0:01:20.068,0:01:22.155
Who are the ones that attack?

0:01:22.155,0:01:24.902
The attacking ones are mathematicians[br]who would tell you

0:01:24.902,0:01:26.849
this question makes no sense,

0:01:26.849,0:01:29.597
because mathematics[br]have a meaning all their own --

0:01:29.597,0:01:32.144
a beautiful edifice with its own logic --

0:01:32.144,0:01:34.011
and that there's no point

0:01:34.011,0:01:36.558
in constantly searching[br]for all possible applications.

0:01:36.558,0:01:38.847
What's the use of poetry?[br]What's the use of love?

0:01:38.847,0:01:41.908
What's the use of life itself? [br]What kind of question is that?

0:01:41.908,0:01:43.529
(Laughter)

0:01:43.529,0:01:47.296
Hardy, for instance, was a model[br]of this type of attack.

0:01:47.296,0:01:49.242
And those who stand in defense tell you,

0:01:49.242,0:01:54.082
"Even if you don't realize it, friend,[br]math is behind everything."

0:01:54.082,0:01:55.340
(Laughter)

0:01:55.340,0:01:57.218
Those guys,

0:01:57.218,0:02:01.246
they always bring up[br]bridges and computers.

0:02:01.246,0:02:03.841
"If you don't know math,[br]your bridge will collapse."

0:02:03.841,0:02:05.286
(Laughter)

0:02:05.286,0:02:08.523
It's true, computers are all about math.

0:02:08.523,0:02:11.008
And now these guys[br]have also started saying

0:02:11.013,0:02:16.050
that behind information security[br]and credit cards are prime numbers.

0:02:16.710,0:02:20.379
These are the answers your math teacher[br]would give you if you asked him.

0:02:20.379,0:02:22.544
He's one of the defensive ones.

0:02:22.544,0:02:24.384
Okay, but who's right then?

0:02:24.384,0:02:26.990
Those who say that math[br]doesn't need to have a purpose,

0:02:26.990,0:02:29.849
or those who say that math[br]is behind everything we do?

0:02:29.849,0:02:31.520
Actually, both are right.

0:02:31.520,0:02:33.183
But remember I told you

0:02:33.183,0:02:36.726
I belong to that strange 0.8 percent[br]claiming something else?

0:02:36.726,0:02:39.929
So, go ahead, ask me what math is for.

0:02:39.929,0:02:42.858
Audience: What is math for?

0:02:42.858,0:02:47.673
Eduardo Sáenz de Cabezón: Okay,[br]76.34 percent of you asked the question,

0:02:47.673,0:02:50.600
23.41 percent didn't say anything,

0:02:50.600,0:02:51.827
and the 0.8 percent --

0:02:51.827,0:02:54.675
I'm not sure what those guys are doing.

0:02:54.675,0:02:58.175
Well, to my dear 76.31 percent --

0:02:58.175,0:03:02.815
it's true that math doesn't need[br]to serve a purpose,

0:03:02.815,0:03:05.685
it's true that it's[br]a beautiful structure, a logical one,

0:03:05.685,0:03:08.537
probably one[br]of the greatest collective efforts

0:03:08.537,0:03:10.633
ever achieved in human history.

0:03:10.633,0:03:12.732
But it's also true that there,

0:03:12.732,0:03:17.331
where scientists and technicians[br]are looking for mathematical theories

0:03:17.331,0:03:19.641
that allow them to advance,

0:03:19.641,0:03:23.438
they're within the structure of math,[br]which permeates everything.

0:03:23.438,0:03:26.585
It's true that we have to go[br]somewhat deeper,

0:03:26.585,0:03:28.308
to see what's behind science.

0:03:28.308,0:03:31.858
Science operates on intuition, creativity.

0:03:32.348,0:03:35.772
Math controls intuition[br]and tames creativity.

0:03:36.747,0:03:38.937
Almost everyone[br]who hasn't heard this before

0:03:38.937,0:03:41.647
is surprised when they hear[br]that if you take

0:03:41.647,0:03:46.187
a 0.1 millimeter thick sheet of paper,[br]the size we normally use,

0:03:46.187,0:03:49.505
and, if it were big enough,[br]fold it 50 times,

0:03:49.505,0:03:55.205
its thickness would extend almost[br]the distance from the Earth to the sun.

0:03:55.600,0:03:58.201
Your intuition tells you it's impossible.

0:03:58.201,0:04:00.622
Do the math and you'll see it's right.

0:04:00.622,0:04:03.135
That's what math is for.

0:04:03.135,0:04:06.917
It's true that science, all types[br]of science, only makes sense

0:04:06.917,0:04:10.288
because it makes us better understand[br]this beautiful world we live in.

0:04:10.288,0:04:11.669
And in doing that,

0:04:11.669,0:04:15.179
it helps us avoid the pitfalls[br]of this painful world we live in.

0:04:15.179,0:04:18.656
There are sciences that help us[br]in this way quite directly.

0:04:18.656,0:04:20.413
Oncological science, for example.

0:04:20.413,0:04:23.905
And there are others we look at from afar,[br]with envy sometimes,

0:04:23.905,0:04:26.464
but knowing that we are[br]what supports them.

0:04:26.464,0:04:29.213
All the basic sciences[br]support them,

0:04:29.213,0:04:31.649
including math.

0:04:31.649,0:04:35.366
All that makes science, science[br]is the rigor of math.

0:04:35.366,0:04:40.242
And that rigor factors in[br]because its results are eternal.

0:04:40.242,0:04:42.757
You probably said or were told[br]at some point

0:04:42.757,0:04:45.708
that diamonds are forever, right?

0:04:47.178,0:04:49.392
That depends on[br]your definition of forever!

0:04:49.392,0:04:51.883
A theorem -- that really is forever.

0:04:51.883,0:04:53.134
(Laughter)

0:04:53.134,0:04:56.486
The Pythagorean theorem is still true

0:04:56.486,0:04:59.601
even though Pythagoras is dead,[br]I assure you it's true. (Laughter)

0:04:59.601,0:05:00.946
Even if the world collapsed

0:05:00.946,0:05:03.391
the Pythagorean theorem[br]would still be true.

0:05:03.391,0:05:07.452
Wherever any two triangle sides[br]and a good hypotenuse get together

0:05:07.452,0:05:08.673
(Laughter)

0:05:08.673,0:05:11.534
the Pythagorean theorem goes all out.[br]It works like crazy.

0:05:11.534,0:05:14.355
(Applause)

0:05:18.535,0:05:22.407
Well, we mathematicians devote ourselves[br]to come up with theorems.

0:05:22.407,0:05:24.143
Eternal truths.

0:05:24.143,0:05:26.909
But it isn't always easy to know[br]the difference between

0:05:26.909,0:05:29.815
an eternal truth, or theorem,[br]and a mere conjecture.

0:05:29.815,0:05:32.829
You need proof.

0:05:32.829,0:05:34.596
For example,

0:05:34.596,0:05:39.423
let's say I have a big,[br]enormous, infinite field.

0:05:39.423,0:05:43.132
I want to cover it with equal pieces,[br]without leaving any gaps.

0:05:43.132,0:05:45.256
I could use squares, right?

0:05:45.256,0:05:49.222
I could use triangles.[br]Not circles, those leave little gaps.

0:05:49.777,0:05:52.134
Which is the best shape to use?

0:05:52.134,0:05:56.687
One that covers the same surface,[br]but has a smaller border.

0:05:56.687,0:06:01.396
In the year 300, Pappus of Alexandria[br]said the best is to use hexagons,

0:06:01.396,0:06:03.243
just like bees do.

0:06:03.243,0:06:04.990
But he didn't prove it.

0:06:04.990,0:06:07.688
The guy said, "Hexagons, great![br]Let's go with hexagons!"

0:06:07.688,0:06:10.656
He didn't prove it,[br]it remained a conjecture.

0:06:10.656,0:06:12.334
"Hexagons!"

0:06:12.334,0:06:15.964
And the world, as you know,[br]split into Pappists and anti-Pappists,

0:06:15.964,0:06:21.253
until 1700 years later

0:06:21.253,0:06:26.707
when in 1999, Thomas Hales proved

0:06:26.707,0:06:31.641
that Pappus and the bees were right --[br]the best shape to use was the hexagon.

0:06:31.641,0:06:34.123
And that became a theorem,[br]the honeycomb theorem,

0:06:34.123,0:06:36.183
that will be true forever and ever,

0:06:36.183,0:06:39.224
for longer than any diamond[br]you may have. (Laughter)

0:06:39.229,0:06:42.033
But what happens if we go[br]to three dimensions?

0:06:42.033,0:06:45.944
If I want to fill the space[br]with equal pieces,

0:06:46.464,0:06:47.805
without leaving any gaps,

0:06:47.805,0:06:49.638
I can use cubes, right?

0:06:49.638,0:06:52.994
Not spheres, those leave little gaps.[br](Laughter)

0:06:52.994,0:06:55.957
What is the best shape to use?

0:06:55.957,0:07:00.017
Lord Kelvin, of the famous[br]Kelvin degrees and all,

0:07:00.607,0:07:06.121
said that the best was to use[br]a truncated octahedron

0:07:07.791,0:07:10.507
which, as you all know --

0:07:10.507,0:07:12.035
(Laughter) --

0:07:12.035,0:07:13.814
is this thing here!

0:07:13.814,0:07:16.753
(Applause)

0:07:18.778,0:07:20.225
Come on.

0:07:21.025,0:07:23.862
Who doesn't have a truncated[br]octahedron at home? (Laughter)

0:07:23.862,0:07:25.089
Even a plastic one.

0:07:25.089,0:07:27.846
"Honey, get the truncated octahedron,[br]we're having guests."

0:07:27.846,0:07:29.240
Everybody has one![br](Laughter)

0:07:29.240,0:07:31.614
But Kelvin didn't prove it.

0:07:31.614,0:07:35.655
It remained a conjecture --[br]Kelvin's conjecture.

0:07:35.655,0:07:41.177
The world, as you know, then split into[br]Kelvinists and anti-Kelvinists

0:07:41.177,0:07:42.599
(Laughter)

0:07:42.599,0:07:46.496
until a hundred or so years later,

0:07:49.203,0:07:53.072
someone found a better structure.

0:07:53.917,0:07:59.026
Weaire and Phelan[br]found this little thing over here --

0:07:59.026,0:08:00.665
(Laughter) --

0:08:00.665,0:08:04.209
this structure to which they gave[br]the very clever name

0:08:04.209,0:08:06.375
"the Weaire-Phelan structure."

0:08:06.375,0:08:08.911
(Laughter)

0:08:08.911,0:08:11.568
It looks like a strange object,[br]but it isn't so strange,

0:08:11.568,0:08:13.239
it also exists in nature.

0:08:13.239,0:08:15.844
It's very interesting that this structure,

0:08:15.844,0:08:18.037
because of its geometric properties,

0:08:18.037,0:08:23.229
was used to build the Aquatics Center[br]for the Beijing Olympic Games.

0:08:23.969,0:08:26.714
There, Michael Phelps[br]won eight gold medals,

0:08:26.714,0:08:29.875
and became the best swimmer of all time.

0:08:29.875,0:08:33.616
Well, until someone better[br]comes along, right?

0:08:33.616,0:08:36.015
As may happen[br]with the Weaire-Phelan structure.

0:08:36.015,0:08:38.633
It's the best[br]until something better shows up.

0:08:38.633,0:08:43.225
But be careful, because this one[br]really stands a chance

0:08:43.225,0:08:48.205
that in a hundred or so years,[br]or even if it's in 1700 years,

0:08:48.205,0:08:53.603
that someone proves[br]it's the best possible shape for the job.

0:08:53.978,0:08:58.348
It will then become a theorem,[br]a truth, forever and ever.

0:08:58.348,0:09:01.302
For longer than any diamond.

0:09:01.837,0:09:05.567
So, if you want to tell someone

0:09:06.777,0:09:09.823
that you will love them forever

0:09:09.823,0:09:11.890
you can give them a diamond.

0:09:11.890,0:09:15.421
But if you want to tell them[br]that you'll love them forever and ever,

0:09:15.421,0:09:17.172
give them a theorem!

0:09:17.172,0:09:18.263
(Laughter)

0:09:18.263,0:09:20.853
But hang on a minute!

0:09:21.783,0:09:23.183
You'll have to prove it,

0:09:23.183,0:09:25.466
so your love doesn't remain

0:09:25.466,0:09:27.299
a conjecture.

0:09:27.299,0:09:30.543
(Applause)