0:00:01.458,0:00:05.830
You can imagine: You're in a bar,[br]or, you know, a disco,

0:00:05.866,0:00:10.645
like that, and you start talking[br]to a girl, and after a while

0:00:10.680,0:00:14.213
this comes up in the conversation:[br]"and what do you do?"

0:00:14.248,0:00:22.045
And as you think your job is interesting[br]you say: "I'm a mathematician." (Laughter)

0:00:22.080,0:00:26.596
33.51 % of girls (Laughter)

0:00:26.631,0:00:32.142
in that moment pretend to get[br]an urgent call and leave. (Laughter)

0:00:32.177,0:00:40.340
And 64.69 % of girls desperately try[br]to change the topic and leave. (Laughter)

0:00:40.375,0:00:45.147
There's a 0.8 % made up by your cousin,[br]your girlfriend and your mother (Laughter)

0:00:45.183,0:00:49.626
that knows you work in something weird but[br]don't remember what (Laughter)

0:00:49.661,0:00:52.515
and there's a 1 % that[br]follows the conversation.

0:00:52.550,0:00:56.155
When that conversation[br]follows, invariably

0:00:56.190,0:00:58.560
in some moment, one of these[br]two phrases shows up:

0:00:58.595,0:01:02.065
A) "I was terrible at math,[br]but it wasn't my fault,

0:01:02.100,0:01:05.274
it's that the teacher[br]was horrendous." (Laughter)

0:01:05.309,0:01:09.253
And B) "But that math thing,[br]what is it for?" (Laughter)

0:01:09.288,0:01:13.289
I'll deal with case B.[br](Laughter)

0:01:13.324,0:01:16.875
When someone asks you what[br]math is for,

0:01:16.910,0:01:20.770
they're not asking you about the[br]applications of mathematical sciences.

0:01:20.805,0:01:23.264
They're asking you:[br]"And why did I have to study

0:01:23.299,0:01:26.272
that bullshit I never used[br]again in my life?" (Laughter)

0:01:26.307,0:01:28.959
That's what they're asking you really.

0:01:28.994,0:01:30.994
Given this, when they ask[br]a mathematician

0:01:31.029,0:01:34.914
what math is for, us[br]mathematicians split in two groups.

0:01:34.949,0:01:40.989
A 54.51 % of mathematicians[br]assumes an attacking posture,

0:01:41.024,0:01:46.109
and a 44.77 % of mathematicians[br]assumes a defensive posture.

0:01:46.144,0:01:49.788
There's a strange 0.8 %,[br]among which I include myself.

0:01:49.824,0:01:51.845
Who are the ones who attack?

0:01:51.880,0:01:54.966
The attacking ones are mathematicians[br]that tell you the question

0:01:55.001,0:01:59.197
makes no sense, because mathematics[br]have their own sense by themselves,

0:01:59.232,0:02:02.229
they're a beautiful edification with[br]its own logic built by itself

0:02:02.264,0:02:06.159
and that there's no use in one always[br]looking after the possible applications.

0:02:06.194,0:02:08.527
What's the use of poetry?[br]What's the use of love?

0:02:08.562,0:02:13.018
What's the use of life itself? [br]What kind of question is that? (Laughter)

0:02:13.053,0:02:17.311
Hardy, for example, is an[br]exponent of this attack.

0:02:17.346,0:02:18.602
And those who stand in [br]defense tell you that

0:02:18.637,0:02:25.068
even if you can't notice, dear,[br]math is behind everything. (Laughter)

0:02:25.103,0:02:30.993
They always name bridges[br]and computers, always.

0:02:31.028,0:02:35.079
If you don't know math,[br]your bridge falls off. (Laughter)

0:02:35.114,0:02:38.193
In reality computers[br]are all about math.

0:02:38.228,0:02:41.008
Now these guys always happen[br]to tell you that behind

0:02:41.043,0:02:45.600
information security and credit[br]cards are prime numbers.

0:02:45.635,0:02:49.989
These are the answers your math teacher[br]will give you if you ask him.

0:02:50.024,0:02:52.829
Those are the defensive ones.

0:02:52.864,0:02:54.389
Okay, but, who's right then?

0:02:54.424,0:02:56.760
Those who say math doesn't need[br]to be useful at all,

0:02:56.795,0:02:58.799
or those who say that it's really[br]behind everything?

0:02:58.834,0:03:01.330
In reality both are right.

0:03:01.365,0:03:05.475
But I told you I'm of that strange 0.8 %[br]that says something else, right?

0:03:05.510,0:03:09.329
So, go on, ask me[br]what math is for.

0:03:09.364,0:03:12.698
(Audience asks the question)

0:03:12.733,0:03:20.145
Okay! A 76.34 % of people[br]have asked, there's a 23.41 %

0:03:20.180,0:03:24.635
that shut up, and a 0.8 % that[br]I don't know what those guys are doing.

0:03:24.670,0:03:30.883
Well, dear 76.31 %, it's true[br]that math can be

0:03:30.918,0:03:34.605
useless, it's true that it's[br]a beautiful edification,

0:03:34.640,0:03:37.617
a logical one, one probably one of[br]the greatest collective efforts

0:03:37.652,0:03:40.303
the human being has ever made[br]along history.

0:03:40.338,0:03:44.165
But it's also true that there where[br]scientists, where technicians,

0:03:44.200,0:03:49.061
are looking for mathematical theories,[br]models that allow them to advance,

0:03:49.096,0:03:50.193
there they are, in the edification[br]of math, which permeate everything.

0:03:54.034,0:03:56.505
It's true that we have to go[br]somewhat deeper,

0:03:56.541,0:03:57.988
we're going to see what's[br]behind science.

0:03:58.024,0:04:02.288
Science works by intuition,[br]by creativity, and math

0:04:02.323,0:04:05.772
dominate intuition[br]and tame creativity.

0:04:05.807,0:04:10.415
Almost everyone who hasn't heard it before[br]is surprised by the fact that if one took

0:04:10.450,0:04:15.657
a sheet of paper 0.1 mm thick,[br]one of those we use normally,

0:04:15.692,0:04:19.075
big enough, and that I[br]could fold 50 times,

0:04:19.110,0:04:25.395
The thickness of that pile would take up[br]the distance from the Earth to the Sun.

0:04:25.430,0:04:30.196
Your intuition tells you: "Impossible."[br]Do the math and you'll see it's right.

0:04:30.231,0:04:31.845
That's what math is for.

0:04:31.880,0:04:36.067
It true that science, all science,[br]not only has a purpose

0:04:36.102,0:04:39.788
because it makes us understand better[br]the beautiful would we're in.

0:04:39.823,0:04:43.004
And because it does, it helps us[br]avoid the traps

0:04:43.039,0:04:44.799
of this painful world[br]we're in.

0:04:44.834,0:04:48.407
There are sciences that grasp[br]this very application.

0:04:48.442,0:04:50.003
Oncological science, for example.

0:04:50.038,0:04:53.495
And there are others we look[br]from afar, with some jealousy sometimes,

0:04:53.530,0:04:56.044
but knowing we are what supports them.

0:04:56.079,0:04:58.583
All the basic sciences[br]are the support of them,

0:04:58.618,0:05:01.359
and among these is math.

0:05:01.394,0:05:04.726
All that makes science be science[br]is the rigor of math.

0:05:04.761,0:05:09.572
And that rigor belongs to it[br]because its results are eternal.

0:05:09.607,0:05:12.037
Probably you said before,[br]or you were told sometime,

0:05:12.072,0:05:15.478
that diamonds are [br]forever, right?

0:05:15.513,0:05:18.892
It depends on what one[br]understands by forever!

0:05:18.927,0:05:22.569
A theorem, that really[br]is forever! (Laughter)

0:05:22.604,0:05:26.116
The Pythagorean theorem,[br]that is still true

0:05:26.151,0:05:29.221
even if Pythagoras is dead,[br]I'm telling you. (Laughter)

0:05:29.256,0:05:32.876
Even if the world collapsed the[br]Pythagorean theorem would still be true.

0:05:32.911,0:05:38.508
Wherever any two sides and a[br]good hypotenuse get together (Laughter)

0:05:38.543,0:05:48.574
the Pythagorean theorem works[br]to the max. (Applause)

0:05:48.609,0:05:51.997
Well, us mathematicians[br]devote ourselves to making theorems.

0:05:52.032,0:05:55.908
Eternal truths. But it isn't always[br]easy to know what is an

0:05:55.943,0:05:59.205
eternal truth, a theorem, and[br]what is a mere conjecture.

0:05:59.240,0:06:02.834
You need a demonstration.

0:06:02.869,0:06:08.949
For example: imagine you have[br]a big, enormous, infinite field.

0:06:08.984,0:06:12.702
I want to cover it with equal pieces,[br]without leaving any gaps.

0:06:12.737,0:06:14.836
I could use squares, right?

0:06:14.871,0:06:19.542
I could use triangles.[br]Not circles, those leave little gaps.

0:06:19.577,0:06:21.969
Which is the best piece I can use?

0:06:22.004,0:06:26.067
The one that to cover the same surface[br]has the smallest border.

0:06:26.102,0:06:31.056
Pappus of Alexandria, in the year 300[br]said the best was to use hexagons,

0:06:31.091,0:06:34.569
like bees do.[br]But he didn't demonstrate it!

0:06:34.604,0:06:37.538
The guy said "hexagons, great,[br]come on, hexagons, let's go with it!"

0:06:37.573,0:06:41.288
He didn't demonstrate it, he stayed[br]in a conjecture, he said "Hexagons!"

0:06:41.323,0:06:45.394
And the world, as you know, split into[br]pappists and anti-pappists,

0:06:45.429,0:06:51.195
until 1700 years later,[br]1700 years later,

0:06:51.230,0:06:57.212
in 1999 Thomas Hales[br]demonstrated that Pappus

0:06:57.247,0:07:01.321
and the bees were right,[br]the best was to use hexagons.

0:07:01.356,0:07:03.823
And that became a theorem,[br]the honeycomb theory,

0:07:03.858,0:07:05.993
that will be true forever[br]forever and ever,

0:07:06.028,0:07:09.224
for longer than any diamond[br]you may have. (Laughter)

0:07:09.259,0:07:11.683
But what happens if we go to 3 dimensions?

0:07:11.718,0:07:17.352
If I want to fill the space, with equal[br]pieces, without leaving any gaps,

0:07:17.387,0:07:18.998
I can use cubes, right?

0:07:19.033,0:07:23.019
Not spheres, those leave little gaps.[br](Laughter)

0:07:23.054,0:07:25.587
What is the best piece[br]I can use?

0:07:25.622,0:07:30.562
Lord Kelvin, the one of the Kelvin degrees[br]and all said, he said

0:07:30.597,0:07:38.139
that the best was to use a[br]truncated octahedron (Laughter)

0:07:38.174,0:07:49.069
that as you all know (Laughter)[br]is this thing over here! (Applause)

0:07:49.104,0:07:53.853
Come on! Who doesn't have a truncated[br]octahedron at home? (Laughter)

0:07:53.888,0:07:56.659
Even if it's plastic. Kid, bring[br]the truncated octahedron, we have guests.

0:07:56.694,0:08:01.243
Everybody has one! (Laughter)[br]But Kelvin didn't demonstrate it.

0:08:01.278,0:08:05.670
He stayed in a conjecture,[br]Kelvin's conjecture.

0:08:05.705,0:08:12.357
The world, as you know, split between[br]kelvinists and anti-kelvinists (Laughter)

0:08:12.392,0:08:18.823
until a hundred-and-something years later,[br]a hundred-and-something years later,

0:08:18.859,0:08:23.672
someone found a better structure.

0:08:23.707,0:08:28.626
Weaire and Phelan, Weaire and Phelan[br]found this little thing over here,

0:08:28.661,0:08:34.714
(Laughter) this structure they put the[br]imaginative name of

0:08:34.749,0:08:38.732
the Weaire-Phelan structure. (Laughter)

0:08:38.768,0:08:41.188
It seems like a strange thing[br]but it isn't that strange,

0:08:41.224,0:08:42.799
it's also present in nature.

0:08:42.835,0:08:47.399
It's very curious that this structure,[br]because of its geometric properties,

0:08:47.434,0:08:51.012
was used to build[br]the swimming building

0:08:51.047,0:08:53.824
in the Beijing Olympic Games.

0:08:53.859,0:08:57.089
There Michael Phelps won[br]8 gold medals, and became

0:08:57.124,0:08:59.645
the best swimmer of all times.

0:08:59.680,0:09:03.036
Well, of all times[br]until someone better comes along, no?

0:09:03.071,0:09:05.666
As it happens to the[br]Weaire-Phelan structure,

0:09:05.701,0:09:08.473
it's the best until something better[br]shows up.

0:09:08.508,0:09:12.645
But be careful, because this one[br]really has the opportunity,

0:09:12.680,0:09:17.775
that if a hundred-and-something years[br]pass, even if it's in 1700 years,

0:09:17.810,0:09:23.603
someone demonstrates that this[br]is the best piece possible.

0:09:23.638,0:09:27.898
And then it will be a theorem,[br]a truth forever, forever and ever.

0:09:27.933,0:09:31.552
For longer than any diamond.

0:09:31.587,0:09:39.835
So, well, if you want to tell someone[br]you'll love them forever (Laughter)

0:09:39.870,0:09:42.289
you can give them a diamond,[br]but if you want to tell them

0:09:42.324,0:09:47.933
that you'll love them forever and ever,[br]give them a theorem! (Laughter)

0:09:47.968,0:09:53.126
However, you'll have to demonstrate,

0:09:53.161,0:09:56.105
that your love doesn't stay a conjecture.

0:09:56.140,0:09:59.963
(Applause)

0:10:01.998,0:10:04.875
Thank you.