0:00:01.458,0:00:06.260
Imagine you're in a bar, or a club,

0:00:06.910,0:00:09.591
and you start talking to a girl,

0:00:09.951,0:00:14.542
and after a while this question comes 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 subject[br]and leave.

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

0:00:41.269,0:00:44.494
Another 0.8% consists of your cousin,[br]your girlfriend and your mom,

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 then there's 1%[br]that actually follow the conversation.

0:00:52.815,0:00:55.080
And inevitably, during that conversation

0:00:55.080,0:00:59.230
one of these two phrases come up:

0:00:59.230,0:01:02.575
A: "I was terrible at math,[br]but it wasn't my fault.

0:01:02.575,0:01:05.614
It's because the teacher[br]was awful." (Laughter)

0:01:05.614,0:01:08.582
Or 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 address 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.

0:01:21.203,0:01:22.734
They're asking you:

0:01:22.734,0:01:26.915
"Why did I have to study that bullshit[br]I never used in my life again?" (Laughter)

0:01:26.915,0:01:28.959
That's what they're actually asking.

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

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

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

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

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 all 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 point

0:02:04.011,0:02:06.688
in constantly searching[br]for all 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, was a prime candidate[br]for this type of attack.

0:02:17.296,0:02:19.652
And those who stand in defense tell you:

0:02:19.652,0:02:24.082
"Even if you don't realize it, buddy,[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 bring up bridges and computers.

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

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

0:02:35.566,0:02:38.523
It's true, computers are all about math.

0:02:38.523,0:02:41.008
And now these guys[br]have also started saying

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

0:02:46.710,0:02:50.379
These are the answers your math teacher[br]would give you if you asked him.

0:02:50.379,0:02:52.544
He's one of 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 that math[br]doesn't need to have a purpose,

0:02:56.990,0:02:59.849
or those who say that math[br]is behind everything we do?

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
I'm not sure what those guys were doing.

0:03:24.675,0:03:26.985
Well, to my dear 76.31% --

0:03:29.035,0:03:32.815
it's true that math doesn't need[br]to serve a purpose,

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

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

0:03:38.537,0:03:40.633
ever achieved in human history.

0:03:40.633,0:03:42.732
But it's also true that there,

0:03:42.732,0:03:47.331
where scientists and technicians[br]are looking for mathematical theories

0:03:47.331,0:03:49.641
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 controls intuition[br]and tames creativity.

0:04:06.747,0:04:09.437
Almost everyone[br]who hasn't heard this before

0:04:09.437,0:04:11.647
is surprised when they hear[br]that if you take

0:04:11.647,0:04:16.187
a 0.1 mm thick sheet of paper--[br]the size we normally use--

0:04:16.187,0:04:19.505
and, if it were big enough,[br]fold it 50 times,

0:04:19.505,0:04:25.205
the thickness of that pile would extend[br]the distance from the Earth to the Sun.

0:04:25.600,0:04:28.201
Your intuition tells you it's impossible.

0:04:28.201,0:04:30.622
Do the math and you'll see it's right.

0:04:30.622,0:04:33.135
That's what math is for.

0:04:33.135,0:04:36.917
It's true that science, all types[br]of science, only makes sense

0:04:36.917,0:04:40.288
because it makes us better understand[br]the beautiful world we live in.

0:04:40.288,0:04:41.669
And in doing that,

0:04:41.669,0:04:45.179
it helps us avoid the traps[br]of this painful world we live in.

0:04:45.179,0:04:48.657
There are sciences[br]that grasp this very application.

0:04:48.657,0:04:50.413
Oncological science, for example.

0:04:50.413,0:04:53.905
And there are others we look at from afar,[br]with envy sometimes,

0:04:53.905,0:04:56.464
but knowing we are what supports them.

0:04:56.464,0:04:59.213
All the basic sciences[br]support them,

0:04:59.213,0:05:01.649
including math.

0:05:01.649,0:05:05.366
All that makes science, science,[br]is the rigor of math.

0:05:05.366,0:05:10.062
And that rigor factors in[br]because its results are eternal.

0:05:10.062,0:05:12.757
You probably said or were told[br]at some point,

0:05:12.757,0:05:15.708
that diamonds are forever, right?

0:05:17.178,0:05:19.392
That depends on[br]your definition of "forever"!

0:05:19.392,0:05:21.883
A theorem-- that really is forever!

0:05:21.883,0:05:23.134
(Laughter)

0:05:23.134,0:05:26.486
The Pythagorean theorem is still true

0:05:26.486,0:05:29.431
even though Pythagoras is dead,[br]I assure it's true. (Laughter)

0:05:29.431,0:05:30.946
Even if the world collapsed

0:05:30.946,0:05:33.391
the Pythagorean theorem[br]would still be true.

0:05:33.391,0:05:37.452
Wherever any two triangle sides[br]and a good hypotenuse get together

0:05:37.452,0:05:38.673
(Laughter)

0:05:38.673,0:05:41.364
the Pythagorean theorem[br]goes all out, works like crazy.

0:05:41.364,0:05:44.355
(Applause)

0:05:48.785,0:05:52.407
Well, we mathematicians devote ourselves[br]to come up with theorems.

0:05:52.407,0:05:54.143
Eternal truths.

0:05:54.143,0:05:58.139
But it isn't always easy to know[br]the difference between

0:05:58.139,0:06:00.045
an eternal truth, or theorem,[br]and a mere conjecture.

0:06:00.045,0:06:02.834
You need proof.

0:06:02.869,0:06:04.596
For example,

0:06:04.596,0:06:09.423
imagine you have a big,[br]enormous, infinite field.

0:06:09.423,0:06:13.132
I want to cover it with equal pieces,[br]without leaving any gaps.

0:06:13.132,0:06:15.256
I could use squares, right?

0:06:15.256,0:06:19.222
I could use triangles.[br]Not circles, those leave little gaps.

0:06:19.777,0:06:22.134
Which is the best shape to use?

0:06:22.134,0:06:26.687
One that covers the same surface,[br]but has a smaller border.

0:06:26.687,0:06:31.396
In the year 300, Pappus of Alexandria[br]said the best is to use hexagons,

0:06:31.396,0:06:33.243
just like bees do.

0:06:33.243,0:06:34.990
But he didn't prove it.

0:06:34.990,0:06:37.688
The guy said, "Hexagons, great![br]Let's go with hexagons!"

0:06:37.688,0:06:40.656
He didn't prove it,[br]it remained a conjecture.

0:06:40.656,0:06:42.334
"Hexagons!"

0:06:42.334,0:06:45.964
And the world, as you know,[br]split into Pappists and anti-Pappists,

0:06:45.964,0:06:49.713
until 1700 years later--

0:06:49.713,0:06:51.892
1700 years later--

0:06:51.892,0:06:56.497
in 1999 Thomas Hales proved

0:06:57.047,0:07:01.641
that Pappus and the bees were right,[br]the best shape to use was the hexagon.

0:07:01.641,0:07:04.123
And that became a theorem,[br]the honeycomb theorem,

0:07:04.123,0:07:06.183
that will be true forever and ever,

0:07:06.183,0:07:09.224
for longer than any diamond[br]you may have. (Laughter)

0:07:09.259,0:07:12.033
But what happens if we go to 3 dimensions?

0:07:12.033,0:07:15.944
If I want to fill the space,[br]with equal pieces,

0:07:16.464,0:07:18.065
without leaving any gaps,

0:07:18.065,0:07:19.638
I can use cubes, right?

0:07:19.638,0:07:23.019
Not spheres, those leave little gaps.[br](Laughter)

0:07:23.054,0:07:25.957
What is the best piece I can use?

0:07:25.957,0:07:27.727
Lord Kelvin, of the famous[br]Kelvin degrees and all,

0:07:30.607,0:07:34.451
said that the best was to use[br]a truncated octahedron

0:07:36.511,0:07:38.425
(Laughter)

0:07:38.425,0:07:40.507
which as you all know

0:07:40.507,0:07:42.035
(Laughter)

0:07:42.035,0:07:43.814
is this thing over here!

0:07:43.814,0:07:46.753
(Applause)

0:07:49.948,0:07:51.395
Come on!

0:07:51.395,0:07:54.182
Who doesn't have a truncated[br]octahedron at home? (Laughter)

0:07:54.182,0:07:55.299
Even if it's plastic.

0:07:55.299,0:07:57.766
"Kid, get the truncated octahedron,[br]we're having guests."

0:07:57.766,0:07:59.680
Everybody has one! (Laughter)

0:07:59.680,0:08:01.614
But Kelvin didn't prove it.

0:08:01.614,0:08:05.670
It remained a conjecture--[br]Kelvin's conjecture.

0:08:05.705,0:08:11.177
The world, as you know, split into[br]Kelvinists and anti-Kelvinists

0:08:11.177,0:08:12.909
(Laughter)

0:08:12.909,0:08:16.496
until a hundred-and-something years later,

0:08:17.216,0:08:19.653
a hundred-and-something years later,

0:08:19.653,0:08:23.072
someone found a better structure.

0:08:24.097,0:08:29.026
Weaire and Phelan[br]found this little thing over here,

0:08:29.026,0:08:30.665
(Laughter)

0:08:30.665,0:08:34.209
this structure to which they gave[br]the imaginative name

0:08:34.209,0:08:36.375
of the Weaire-Phelan structure.

0:08:36.375,0:08:39.041
(Laughter)

0:08:39.041,0:08:41.768
It looks like a strange object,[br]but it isn't so strange,

0:08:41.768,0:08:43.389
it also exists in nature.

0:08:43.389,0:08:45.844
It's very interesting that this structure,

0:08:45.844,0:08:48.037
because of its geometric properties,

0:08:48.037,0:08:53.229
was used to build the Aquatics Center[br]for the Beijing Olympic Games.

0:08:53.969,0:08:57.089
There, Michael Phelps[br]won eight gold medals,

0:08:57.124,0:08:59.875
and became the best swimmer of all time.

0:08:59.875,0:09:03.616
Well, until someone better[br]comes along, right?

0:09:03.616,0:09:06.016
As it may happen[br]to the Weaire-Phelan structure.

0:09:06.016,0:09:08.633
It's the best[br]until something better shows up.

0:09:08.633,0:09:13.225
But be careful, because this one[br]really has the chance

0:09:13.225,0:09:18.205
that in a hundred or so years,[br]or even if it's in 1700 years,

0:09:18.205,0:09:23.603
that someone proves[br]that it's the best possible piece.

0:09:23.978,0:09:28.348
It will then become a theorem,[br]a truth, forever and ever.

0:09:28.348,0:09:31.552
For longer than any diamond.

0:09:32.057,0:09:35.637
So, if you want to tell someone

0:09:36.777,0:09:39.293
that you will love them forever

0:09:39.293,0:09:40.699
(Laughter)

0:09:40.699,0:09:42.430
you can give them a diamond,

0:09:42.430,0:09:45.571
but if you want to tell them[br]that you'll love them forever and ever,

0:09:45.571,0:09:47.172
give them a theorem!

0:09:47.172,0:09:48.683
(Laughter)

0:09:48.683,0:09:50.883
However,

0:09:51.783,0:09:57.403
you'll have to prove it,[br]so your love doesn't remain a conjecture.

0:09:57.403,0:10:00.543
(Applause)