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Can you imagine,
you're in a bar, or a disco,

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and you start talking to a girl,

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and after a while this question come up:
"So, what do you do for work?"

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And since you think
your job is interesting you say:

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"I'm a mathematician."

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(Laughter)

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33.51 % of girls,

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(Laughter)

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in that moment, pretend
to get an urgent call and leave.

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(Laughter)

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And 64.69 % of girls

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desperately try to change the topic and leave.

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(Laughter)

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There's a 0.8 % made up by your cousin,
your girlfriend and your mother,

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(Laughter)

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who know that you work in something weird
but don't remember what it is. (Laughter)

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And there is 1 %
that actually follows the conversation.

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When that conversation happens,

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at some point, invariably,
one of these two phrases come up:

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A: "I was terrible at math,
but it wasn't my fault,

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it's that the teacher
was horrendous." (Laughter)

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And B: "But what is math really for?"

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(Laughter)

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I'll deal with case B.

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(Laughter)

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When someone asks you what math is for,
they're not asking you

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about the application
of mathematical science.

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They're asking you:
"And why did I have to study

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that bullshit I never used
again in my life?" (Laughter)

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That's what they're actually asking.

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So when mathematicians
are asked what math is for,

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they tend to split into two groups.

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54.51 % of mathematicians
will take an attacking posture

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and 44.77 % of mathematicians
will take a defensive posture.

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There's a strange 0.8 %,
among which I include myself.

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Who are the ones that attack?

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The attacking ones are mathematicians
who would tell you:

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"This question makes no sense,

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because mathematics
have a meaning on their own--

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a beautiful edifice with its own logic--

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and that there's no use

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in constantly searching
for possible applications.

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What's the use of poetry?
What's the use of love?

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What's the use of life itself? 
What kind of question is that?"

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(Laughter)

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Hardy, for instance, is a prime example
for this type of attack.

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And those who stand in defense tell you:

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"Even if you don't notice it, dear,
math is behind everything."

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(Laughter)

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They always--

51
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always name bridges and computers.

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"If you don't know math,
your bridge falls off."

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(Laughter)

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In reality, computers are all about math.

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Now, these guys always happen to tell you

56
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that behind information security
and credit cards are prime numbers.

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These are the answers your math teacher
would give you if you asked him--

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the defensive ones.

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Okay, but, who's right then?

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Those who say math
doesn't need to be useful at all,

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or those who say
that it's really behind everything?

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Actually, both are right.

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But remember I told you

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I belong to that strange 0.8 %
claiming something else.

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So, go ahead, ask me what math is for.

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Audience: What is math for?

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Okay, so 76.34 % of you
asked the question,

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23.41 % didn't say anything,

69
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and 0.8 %--

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not sure what those guys were doing.

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Well, dear 76.31 %

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it's true that math can be useless,

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it's true that it's
a beautiful edification, a logical one,

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probably one
of the greatest collective effort

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the human race
has ever achieved in history.

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But it's also true that there,

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where scientists and technicians
are looking for mathematical theories,

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models that allow them to advance,

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they are in the edification of math,
which permeates everything.

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It's true that we have to go
somewhat deeper,

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to see what's behind science.

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Science is based on intuition, creativity.

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Math dominates intuition
and tames creativity.

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Almost everyone
who hasn't heard it before

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is surprised by the fact that if one took

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a sheet of paper 0.1 mm thick,
one of those we use normally,

87
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big enough, and that I
could fold 50 times,

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The thickness of that pile would take up
the distance from the Earth to the Sun.

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Your intuition tells you: "Impossible."
Do the math and you'll see it's right.

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That's what math is for.

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It true that science, all science,
not only has a purpose

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because it makes us understand better
the beautiful would we're in.

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And because it does, it helps us
avoid the traps

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of this painful world
we're in.

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There are sciences that grasp
this very application.

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Oncological science, for example.

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And there are others we look
from afar, with some jealousy sometimes,

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but knowing we are what supports them.

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All the basic sciences
are the support of them,

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and among these is math.

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All that makes science be science
is the rigor of math.

102
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And that rigor belongs to it
because its results are eternal.

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Probably you said before,
or you were told sometime,

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that diamonds are 
forever, right?

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It depends on what one
understands by forever!

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A theorem, that really
is forever! (Laughter)

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The Pythagorean theorem,
that is still true

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even if Pythagoras is dead,
I'm telling you. (Laughter)

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Even if the world collapsed the
Pythagorean theorem would still be true.

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Wherever any two sides and a
good hypotenuse get together (Laughter)

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the Pythagorean theorem works
to the max. (Applause)

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Well, us mathematicians
devote ourselves to making theorems.

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Eternal truths. But it isn't always
easy to know what is an

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eternal truth, a theorem, and
what is a mere conjecture.

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You need a demonstration.

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For example: imagine you have
a big, enormous, infinite field.

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I want to cover it with equal pieces,
without leaving any gaps.

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I could use squares, right?

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I could use triangles.
Not circles, those leave little gaps.

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Which is the best piece I can use?

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The one that to cover the same surface
has the smallest border.

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Pappus of Alexandria, in the year 300
said the best was to use hexagons,

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like bees do.
But he didn't demonstrate it!

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The guy said "hexagons, great,
come on, hexagons, let's go with it!"

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He didn't demonstrate it, he stayed
in a conjecture, he said "Hexagons!"

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And the world, as you know, split into
pappists and anti-pappists,

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until 1700 years later,
1700 years later,

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in 1999 Thomas Hales
demonstrated that Pappus

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and the bees were right,
the best was to use hexagons.

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And that became a theorem,
the honeycomb theory,

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that will be true forever
forever and ever,

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for longer than any diamond
you may have. (Laughter)

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But what happens if we go to 3 dimensions?

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If I want to fill the space, with equal
pieces, without leaving any gaps,

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I can use cubes, right?

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Not spheres, those leave little gaps.
(Laughter)

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What is the best piece
I can use?

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Lord Kelvin, the one of the Kelvin degrees
and all said, he said

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that the best was to use a
truncated octahedron (Laughter)

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that as you all know (Laughter)
is this thing over here! (Applause)

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Come on! Who doesn't have a truncated
octahedron at home? (Laughter)

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Even if it's plastic. Kid, bring
the truncated octahedron, we have guests.

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Everybody has one! (Laughter)
But Kelvin didn't demonstrate it.

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He stayed in a conjecture,
Kelvin's conjecture.

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The world, as you know, split between
kelvinists and anti-kelvinists (Laughter)

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until a hundred-and-something years later,
a hundred-and-something years later,

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someone found a better structure.

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Weaire and Phelan, Weaire and Phelan
found this little thing over here,

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(Laughter) this structure they put the
imaginative name of

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the Weaire-Phelan structure. (Laughter)

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It seems like a strange thing
but it isn't that strange,

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it's also present in nature.

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It's very curious that this structure,
because of its geometric properties,

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was used to build
the swimming building

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in the Beijing Olympic Games.

156
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There Michael Phelps won
8 gold medals, and became

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the best swimmer of all times.

158
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Well, of all times
until someone better comes along, no?

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As it happens to the
Weaire-Phelan structure,

160
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it's the best until something better
shows up.

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But be careful, because this one
really has the opportunity,

162
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that if a hundred-and-something years
pass, even if it's in 1700 years,

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someone demonstrates that this
is the best piece possible.

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And then it will be a theorem,
a truth forever, forever and ever.

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For longer than any diamond.

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So, well, if you want to tell someone
you'll love them forever (Laughter)

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you can give them a diamond,
but if you want to tell them

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that you'll love them forever and ever,
give them a theorem! (Laughter)

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However, you'll have to demonstrate,

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that your love doesn't stay a conjecture.

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(Applause)

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Thank you.