0:00:01.458,0:00:06.260
Can you imagine,[br]you're in a bar, or a disco,

0:00:06.260,0:00:09.091
and you start talking to a girl,

0:00:09.951,0:00:14.542
and after a while this question come up:[br]"So, what do you do for work?"

0:00:14.553,0:00:17.867
And since you think[br]your job is interesting you say:

0:00:17.867,0:00:19.706
"I'm a mathematician."

0:00:19.706,0:00:21.725
(Laughter)

0:00:22.355,0:00:25.617
33.51 % of girls,

0:00:25.617,0:00:26.889
(Laughter)

0:00:26.889,0:00:30.772
in that moment, pretend[br]to get an urgent call and leave.

0:00:30.772,0:00:32.495
(Laughter)

0:00:32.495,0:00:35.806
And 64.69 % of girls

0:00:36.266,0:00:40.077
desperately try to change the topic and leave.

0:00:40.077,0:00:41.269
(Laughter)

0:00:41.269,0:00:44.494
There's a 0.8 % made up by your cousin,[br]your girlfriend and your mother,

0:00:44.494,0:00:45.629
(Laughter)

0:00:45.629,0:00:49.694
who know that you work in something weird[br]but don't remember what it is. (Laughter)

0:00:49.694,0:00:52.815
And there is 1 %[br]that actually follows the conversation.

0:00:52.815,0:00:55.080
When that conversation happens,

0:00:55.080,0:00:58.870
at some point, invariably,[br]one of these two phrases come up:

0:00:58.870,0:01:02.575
A: "I was terrible at math,[br]but it wasn't my fault,

0:01:02.575,0:01:05.614
it's that the teacher[br]was horrendous." (Laughter)

0:01:05.614,0:01:08.582
And B: "But what is math really for?"

0:01:08.582,0:01:09.930
(Laughter)

0:01:09.930,0:01:11.955
I'll deal with case B.

0:01:11.955,0:01:13.680
(Laughter)

0:01:13.680,0:01:18.484
When someone asks you what math is for,[br]they're not asking you

0:01:18.484,0:01:21.203
about the application[br]of mathematical science.

0:01:21.203,0:01:23.524
They're asking you:[br]"And why did I have to study

0:01:23.524,0:01:26.462
that bullshit I never used[br]again in my life?" (Laughter)

0:01:26.462,0:01:28.959
That's what they're actually asking.

0:01:28.994,0:01:33.124
So when mathematicians[br]are asked what math is for,

0:01:33.124,0:01:35.404
they tend to split into two groups.

0:01:35.404,0:01:40.739
54.51 % of mathematicians[br]will take an attacking posture

0:01:41.609,0:01:46.559
and 44.77 % of mathematicians[br]will take a defensive posture.

0:01:46.559,0:01:50.068
There's a strange 0.8 %,[br]among which I include myself.

0:01:50.068,0:01:52.155
Who are the ones that attack?

0:01:52.155,0:01:54.902
The attacking ones are mathematicians[br]who would tell you:

0:01:54.902,0:01:56.849
"This question makes no sense,

0:01:56.849,0:01:59.597
because mathematics[br]have a meaning on their own--

0:01:59.597,0:02:02.144
a beautiful edifice with its own logic--

0:02:02.144,0:02:04.011
and that there's no use

0:02:04.011,0:02:06.688
in constantly searching[br]for possible applications.

0:02:06.688,0:02:08.847
What's the use of poetry?[br]What's the use of love?

0:02:08.847,0:02:11.908
What's the use of life itself? [br]What kind of question is that?"

0:02:11.908,0:02:13.529
(Laughter)

0:02:13.529,0:02:17.296
Hardy, for instance, is a prime example[br]for this type of attack.

0:02:17.296,0:02:19.472
And those who stand in defense tell you:

0:02:19.472,0:02:24.082
"Even if you don't notice it, dear,[br]math is behind everything."

0:02:24.082,0:02:25.562
(Laughter)

0:02:25.562,0:02:27.724
They always--

0:02:27.724,0:02:31.666
always name bridges and computers.

0:02:31.666,0:02:34.041
"If you don't know math,[br]your bridge falls off."

0:02:34.041,0:02:35.566
(Laughter)

0:02:35.566,0:02:38.523
In reality, computers are all about math.

0:02:38.523,0:02:41.008
Now, these guys always happen to tell you

0:02:41.043,0:02:46.050
that behind information security[br]and credit cards are prime numbers.

0:02:46.710,0:02:50.219
These are the answers your math teacher[br]would give you if you asked him--

0:02:50.219,0:02:52.544
the defensive ones.

0:02:52.544,0:02:54.389
Okay, but, who's right then?

0:02:54.404,0:02:56.990
Those who say math[br]doesn't need to be useful at all,

0:02:56.990,0:02:59.849
or those who say[br]that it's really behind everything?

0:02:59.849,0:03:01.520
Actually, both are right.

0:03:01.520,0:03:03.183
But remember I told you

0:03:03.183,0:03:06.726
I belong to that strange 0.8 %[br]claiming something else.

0:03:06.726,0:03:09.929
So, go ahead, ask me what math is for.

0:03:09.929,0:03:12.858
Audience: What is math for?

0:03:12.858,0:03:17.183
Okay, so 76.34 % of you[br]asked the question,

0:03:17.783,0:03:20.720
23.41 % didn't say anything,

0:03:20.720,0:03:22.127
and 0.8 %--

0:03:22.127,0:03:24.675
not sure what those guys were doing.

0:03:24.675,0:03:26.985
Well, dear 76.31 %

0:03:29.035,0:03:32.815
it's true that math can be useless,

0:03:32.815,0:03:35.685
it's true that it's[br]a beautiful edification, a logical one,

0:03:35.685,0:03:38.537
probably one[br]of the greatest collective effort

0:03:38.537,0:03:40.633
the human race[br]has ever achieved in history.

0:03:40.633,0:03:42.522
But it's also true that there,

0:03:42.522,0:03:47.331
where scientists and technicians[br]are looking for mathematical theories,

0:03:47.331,0:03:49.641
models that allow them to advance,

0:03:49.641,0:03:53.708
they are in the edification of math,[br]which permeates everything.

0:03:53.708,0:03:56.585
It's true that we have to go[br]somewhat deeper,

0:03:56.585,0:03:58.308
to see what's behind science.

0:03:58.308,0:04:01.858
Science is based on intuition, creativity.

0:04:02.348,0:04:05.772
Math dominates intuition[br]and tames creativity.

0:04:06.747,0:04:09.717
Almost everyone[br]who hasn't heard it before

0:04:09.717,0:04:12.687
is surprised by the fact that if one took

0:04:12.687,0:04:15.657
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.