WEBVTT

00:00:01.458 --> 00:00:06.260
Imagine you're in a bar, or a club,

00:00:06.910 --> 00:00:09.591
and you start talking to a girl,

00:00:09.951 --> 00:00:14.542
and after a while this question come up:
"So, what do you do for work?"

00:00:14.553 --> 00:00:17.867
And since you think
your job is interesting you say:

00:00:17.867 --> 00:00:19.706
"I'm a mathematician."

00:00:19.706 --> 00:00:21.725
(Laughter)

00:00:22.355 --> 00:00:25.617
33.51 % of girls,

00:00:25.617 --> 00:00:26.889
(Laughter)

00:00:26.889 --> 00:00:30.772
in that moment, pretend
to get an urgent call and leave.

00:00:30.772 --> 00:00:32.495
(Laughter)

00:00:32.495 --> 00:00:35.806
And 64.69 % of girls

00:00:36.266 --> 00:00:40.077
desperately try to change the topic and leave.

00:00:40.077 --> 00:00:41.269
(Laughter)

00:00:41.269 --> 00:00:44.494
There's 0.8 % made up by your cousin,
your girlfriend and your mother,

00:00:44.494 --> 00:00:45.629
(Laughter)

00:00:45.629 --> 00:00:49.694
who know that you work in something weird
but don't remember what it is. (Laughter)

00:00:49.694 --> 00:00:52.815
And there is 1 %
that actually follows the conversation.

00:00:52.815 --> 00:00:55.080
When that conversation happens,

00:00:55.080 --> 00:00:59.230
at some point, invariably,
one of these two phrases come up:

00:00:59.230 --> 00:01:02.575
A: "I was terrible at math,
but it wasn't my fault,

00:01:02.575 --> 00:01:05.614
it's that the teacher
was horrendous." (Laughter)

00:01:05.614 --> 00:01:08.582
And B: "But what is math really for?"

00:01:08.582 --> 00:01:09.930
(Laughter)

00:01:09.930 --> 00:01:11.955
I'll deal with case B.

00:01:11.955 --> 00:01:13.680
(Laughter)

00:01:13.680 --> 00:01:18.484
When someone asks you what math is for,
they're not asking you

00:01:18.484 --> 00:01:21.203
about the application
of mathematical science.

00:01:21.203 --> 00:01:22.734
They're asking you:

00:01:22.734 --> 00:01:26.915
"Why did I have to study that bullshit
I never used in my life again?" (Laughter)

00:01:26.915 --> 00:01:28.959
That's what they're actually asking.

00:01:28.994 --> 00:01:33.124
So when mathematicians are asked
what math is for,

00:01:33.124 --> 00:01:35.404
they tend to split into two groups.

00:01:35.404 --> 00:01:40.739
54.51 % of mathematicians
will assume an attacking posture,

00:01:41.609 --> 00:01:46.559
and 44.77 % of mathematicians
will take a defensive posture.

00:01:46.559 --> 00:01:50.068
There's a strange 0.8 %,
among which I include myself.

00:01:50.068 --> 00:01:52.155
Who are the ones that attack?

00:01:52.155 --> 00:01:54.902
The attacking ones are mathematicians
who would tell you:

00:01:54.902 --> 00:01:56.849
"This question makes no sense,

00:01:56.849 --> 00:01:59.597
because mathematics
have a meaning on their own--

00:01:59.597 --> 00:02:02.144
a beautiful edifice with its own logic--

00:02:02.144 --> 00:02:04.011
and that there's no point

00:02:04.011 --> 00:02:06.688
in constantly searching
for all possible applications.

00:02:06.688 --> 00:02:08.847
What's the use of poetry?
What's the use of love?

00:02:08.847 --> 00:02:11.908
What's the use of life itself? 
What kind of question is that?"

00:02:11.908 --> 00:02:13.529
(Laughter)

00:02:13.529 --> 00:02:17.296
Hardy, for instance, is a prime example
for this type of attack.

00:02:17.296 --> 00:02:19.652
And those who stand in defense tell you:

00:02:19.652 --> 00:02:24.082
"Even if you don't notice it, buddy,
math is behind everything."

00:02:24.082 --> 00:02:25.562
(Laughter)

00:02:25.562 --> 00:02:27.724
They always--

00:02:27.724 --> 00:02:31.666
always name bridges and computers.

00:02:31.666 --> 00:02:34.041
"If you don't know math,
your bridge falls off."

00:02:34.041 --> 00:02:35.566
(Laughter)

00:02:35.566 --> 00:02:38.523
In reality, computers are all about math.

00:02:38.523 --> 00:02:41.008
Now, these guys always happen to tell you

00:02:41.043 --> 00:02:46.050
that behind information security
and credit cards are prime numbers.

00:02:46.710 --> 00:02:50.379
These are the answers your math teacher
would give you if you asked him--

00:02:50.379 --> 00:02:52.544
the defensive ones.

00:02:52.544 --> 00:02:54.389
Okay, but, who's right then?

00:02:54.404 --> 00:02:56.990
Those who say math
doesn't need to be useful at all,

00:02:56.990 --> 00:02:59.849
or those who say
that it's really behind everything?

00:02:59.849 --> 00:03:01.520
Actually, both are right.

00:03:01.520 --> 00:03:03.183
But remember I told you

00:03:03.183 --> 00:03:06.726
I belong to that strange 0.8 %
claiming something else.

00:03:06.726 --> 00:03:09.929
So, go ahead, ask me what math is for.

00:03:09.929 --> 00:03:12.858
Audience: What is math for?

00:03:12.858 --> 00:03:17.183
Okay, so 76.34 % of you
asked the question,

00:03:17.783 --> 00:03:20.720
23.41 % didn't say anything,

00:03:20.720 --> 00:03:22.127
and 0.8 %--

00:03:22.127 --> 00:03:24.675
not sure what those guys were doing.

00:03:24.675 --> 00:03:26.985
Well, dear 76.31 %

00:03:29.035 --> 00:03:32.815
it's true that math can be useless,

00:03:32.815 --> 00:03:35.685
it's true that it's
a beautiful edification, a logical one,

00:03:35.685 --> 00:03:38.537
probably one
of the greatest collective effort

00:03:38.537 --> 00:03:40.633
the human race
has ever achieved in history.

00:03:40.633 --> 00:03:42.732
But it's also true that there,

00:03:42.732 --> 00:03:47.331
where scientists and technicians
are looking for mathematical theories

00:03:47.331 --> 00:03:49.641
that allow them to advance,

00:03:49.641 --> 00:03:53.708
they are in the edification of math,
which permeates everything.

00:03:53.708 --> 00:03:56.585
It's true that we have to go
somewhat deeper,

00:03:56.585 --> 00:03:58.308
to see what's behind science.

00:03:58.308 --> 00:04:01.858
Science is based on intuition, creativity.

00:04:02.348 --> 00:04:05.772
Math dominates intuition
and tames creativity.

00:04:06.747 --> 00:04:09.437
Almost every person
who hasn't heard this before

00:04:09.437 --> 00:04:11.647
is surprised when they hear

00:04:11.647 --> 00:04:16.187
that a 0.1 mm thick sheet of paper--
one that we normally use--

00:04:16.187 --> 00:04:19.505
is big enough, that if you fold 50 times,

00:04:19.505 --> 00:04:25.205
the thickness of that pile would take up
the distance from the Earth to the Sun.

00:04:25.600 --> 00:04:28.201
Your intuition tells you it's impossible.

00:04:28.201 --> 00:04:30.622
Do the math and you'll see it's right.

00:04:30.622 --> 00:04:33.135
That's what math is for.

00:04:33.135 --> 00:04:36.917
It's true that the main purpose
of science, of all types of science,

00:04:36.917 --> 00:04:40.288
is to make us better understand
the beautiful world we live in.

00:04:40.288 --> 00:04:41.669
And because it does so,

00:04:41.669 --> 00:04:45.179
it can help us avoid the traps
of this painful world we live in.

00:04:45.179 --> 00:04:48.657
There are sciences
that grasp this very application.

00:04:48.657 --> 00:04:50.413
Oncological science, for example.

00:04:50.413 --> 00:04:53.905
And there are others we look at from afar,
with jealousy sometimes,

00:04:53.905 --> 00:04:56.464
but knowing we are what supports them.

00:04:56.464 --> 00:04:59.213
All the basic sciences
are the support of them,

00:04:59.213 --> 00:05:01.649
and among these is math.

00:05:01.649 --> 00:05:05.366
All that makes science, science,
is the rigor of math.

00:05:05.366 --> 00:05:10.062
And that rigor belongs to it
because the results are eternal.

00:05:10.062 --> 00:05:12.757
You probably said or were told
at some point,

00:05:12.757 --> 00:05:15.708
that diamonds are forever, right?

00:05:17.178 --> 00:05:19.392
It depends on
what you understand by "forever"!

00:05:19.392 --> 00:05:21.883
A theorem-- that really is forever!

00:05:21.883 --> 00:05:23.134
(Laughter)

00:05:23.134 --> 00:05:26.486
The Pythagorean theorem is still true

00:05:26.486 --> 00:05:29.431
even though Pythagoras is dead,
I'm telling you. (Laughter)

00:05:29.431 --> 00:05:30.946
Even if the world collapsed

00:05:30.946 --> 00:05:33.391
the Pythagorean theorem
would still be true.

00:05:33.391 --> 00:05:37.452
Wherever any two sides
and a good hypotenuse get together

00:05:37.452 --> 00:05:38.673
(Laughter)

00:05:38.673 --> 00:05:41.364
the Pythagorean theorem
works at its the max.

00:05:41.364 --> 00:05:44.355
(Applause)

00:05:48.785 --> 00:05:52.407
Well, us mathematicians devote ourselves
to come up with theorems.

00:05:52.407 --> 00:05:54.143
Eternal truths.

00:05:54.143 --> 00:05:58.139
But it isn't always easy to know
what an eternal truth, a theorem, is

00:05:58.139 --> 00:06:00.045
compared to a mere conjecture.

00:06:00.045 --> 00:06:02.834
You need demonstration.

00:06:02.869 --> 00:06:04.596
For example,

00:06:04.596 --> 00:06:09.423
imagine you have a big,
enormous, infinite field.

00:06:09.423 --> 00:06:13.132
I want to cover it with equal pieces,
without leaving any gaps.

00:06:13.132 --> 00:06:15.256
I could use squares, right?

00:06:15.256 --> 00:06:19.222
I could use triangles.
Not circles, those leave little gaps.

00:06:19.777 --> 00:06:22.004
Which is the best piece I can use?

00:06:22.004 --> 00:06:26.687
The one that covers the same surface
has the smallest border.

00:06:26.687 --> 00:06:31.396
In the year 300, Pappus of Alexandria
said the best is to use hexagons,

00:06:31.396 --> 00:06:33.243
just like bees do.

00:06:33.243 --> 00:06:34.990
But he didn't demonstrate it.

00:06:34.990 --> 00:06:37.688
The guy said, "Hexagons, great!
Let's go with hexagons!"

00:06:37.688 --> 00:06:40.656
He didn't demonstrate it,
he stayed in a conjecture.

00:06:40.656 --> 00:06:42.334
"Hexagons!"

00:06:42.334 --> 00:06:45.964
And the world, as you know,
split into pappists and anti-pappists,

00:06:45.964 --> 00:06:49.713
until 1700 years later--

00:06:49.713 --> 00:06:51.892
1700 years later--

00:06:51.892 --> 00:06:56.497
in 1999 Thomas Hales demonstrated

00:06:57.047 --> 00:07:02.001
that Pappus and the bees were right,
the best was to use hexagons.

00:07:02.001 --> 00:07:03.823
And that became a theorem,
the honeycomb theory,

00:07:03.858 --> 00:07:05.993
that will be true forever
forever and ever,

00:07:06.028 --> 00:07:09.224
for longer than any diamond
you may have. (Laughter)

00:07:09.259 --> 00:07:11.683
But what happens if we go to 3 dimensions?

00:07:11.718 --> 00:07:17.352
If I want to fill the space, with equal
pieces, without leaving any gaps,

00:07:17.387 --> 00:07:18.998
I can use cubes, right?

00:07:19.033 --> 00:07:23.019
Not spheres, those leave little gaps.
(Laughter)

00:07:23.054 --> 00:07:25.587
What is the best piece
I can use?

00:07:25.622 --> 00:07:30.562
Lord Kelvin, the one of the Kelvin degrees
and all said, he said

00:07:30.597 --> 00:07:38.139
that the best was to use a
truncated octahedron (Laughter)

00:07:38.174 --> 00:07:49.069
that as you all know (Laughter)
is this thing over here! (Applause)

00:07:49.104 --> 00:07:53.853
Come on! Who doesn't have a truncated
octahedron at home? (Laughter)

00:07:53.888 --> 00:07:56.659
Even if it's plastic. Kid, bring
the truncated octahedron, we have guests.

00:07:56.694 --> 00:08:01.243
Everybody has one! (Laughter)
But Kelvin didn't demonstrate it.

00:08:01.278 --> 00:08:05.670
He stayed in a conjecture,
Kelvin's conjecture.

00:08:05.705 --> 00:08:12.357
The world, as you know, split between
kelvinists and anti-kelvinists (Laughter)

00:08:12.392 --> 00:08:18.823
until a hundred-and-something years later,
a hundred-and-something years later,

00:08:18.859 --> 00:08:23.672
someone found a better structure.

00:08:23.707 --> 00:08:28.626
Weaire and Phelan, Weaire and Phelan
found this little thing over here,

00:08:28.661 --> 00:08:34.714
(Laughter) this structure they put the
imaginative name of

00:08:34.749 --> 00:08:38.732
the Weaire-Phelan structure. (Laughter)

00:08:38.768 --> 00:08:41.188
It seems like a strange thing
but it isn't that strange,

00:08:41.224 --> 00:08:42.799
it's also present in nature.

00:08:42.835 --> 00:08:47.399
It's very curious that this structure,
because of its geometric properties,

00:08:47.434 --> 00:08:51.012
was used to build
the swimming building

00:08:51.047 --> 00:08:53.824
in the Beijing Olympic Games.

00:08:53.859 --> 00:08:57.089
There Michael Phelps won
8 gold medals, and became

00:08:57.124 --> 00:08:59.645
the best swimmer of all times.

00:08:59.680 --> 00:09:03.036
Well, of all times
until someone better comes along, no?

00:09:03.071 --> 00:09:05.666
As it happens to the
Weaire-Phelan structure,

00:09:05.701 --> 00:09:08.473
it's the best until something better
shows up.

00:09:08.508 --> 00:09:12.645
But be careful, because this one
really has the opportunity,

00:09:12.680 --> 00:09:17.775
that if a hundred-and-something years
pass, even if it's in 1700 years,

00:09:17.810 --> 00:09:23.603
someone demonstrates that this
is the best piece possible.

00:09:23.638 --> 00:09:27.898
And then it will be a theorem,
a truth forever, forever and ever.

00:09:27.933 --> 00:09:31.552
For longer than any diamond.

00:09:31.587 --> 00:09:39.835
So, well, if you want to tell someone
you'll love them forever (Laughter)

00:09:39.870 --> 00:09:42.289
you can give them a diamond,
but if you want to tell them

00:09:42.324 --> 00:09:47.933
that you'll love them forever and ever,
give them a theorem! (Laughter)

00:09:47.968 --> 00:09:53.126
However, you'll have to demonstrate,

00:09:53.161 --> 00:09:56.105
that your love doesn't stay a conjecture.

00:09:56.140 --> 00:09:59.963
(Applause)

00:10:01.998 --> 00:10:04.875
Thank you.