You can imagine: You're in a bar,
or, you know, a disco,

like that, and you start talking
to a girl, and after a while

this comes up in the conversation:
"and what do you do?"

And as you think your job is interesting
you say: "I'm a mathematician." (Laughter)

33.51 % of girls (Laughter)

in that moment pretend to get
an urgent call and leave. (Laughter)

And 64.69 % of girls desperately try
to change the topic and leave. (Laughter)

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

that knows you work in something weird but
don't remember what (Laughter)

and there's a 1 % that
follows the conversation.

When that conversation
follows, invariably

in some moment, one of these
two phrases shows up:

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

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

And B) "But that math thing,
what is it for?" (Laughter)

I'll deal with case B.
(Laughter)

When someone asks you what
math is for,

they're not asking you about the
applications of mathematical sciences.

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

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

That's what they're asking you really.

Given this, when they ask
a mathematician

what math is for, us
mathematicians split in two groups.

A 54.51 % of mathematicians
assumes an attacking posture,

and a 44.77 % of mathematicians
assumes a defensive posture.

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

Who are the ones who attack?

The attacking ones are mathematicians
that tell you the question

makes no sense, because mathematics
have their own sense by themselves,

they're a beautiful edification with
its own logic built by itself

and that there's no use in one always
looking after the possible applications.

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

What's the use of life itself? 
What kind of question is that? (Laughter)

Hardy, for example, is an
exponent of this attack.

And those who stand in 
defense tell you that

even if you can't notice, dear,
math is behind everything. (Laughter)

They always name bridges
and computers, always.

If you don't know math,
your bridge falls off. (Laughter)

In reality computers
are all about math.

Now these guys always happen
to tell you that behind

information security and credit
cards are prime numbers.

These are the answers your math teacher
will give you if you ask him.

Those are the defensive ones.

Okay, but, who's right then?

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

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

In reality both are right.

But I told you I'm of that strange 0.8 %
that says something else, right?

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

(Audience asks the question)

Okay! A 76.34 % of people
have asked, there's a 23.41 %

that shut up, and a 0.8 % that
I don't know what those guys are doing.

Well, dear 76.31 %, it's true
that math can be

useless, it's true that it's
a beautiful edification,

a logical one, one probably one of
the greatest collective efforts

the human being has ever made
along history.

But it's also true that there where
scientists, where technicians,

are looking for mathematical theories,
models that allow them to advance,

there they are, in the edification
of math, which permeate everything.

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

we're going to see what's
behind science.

Science works by intuition,
by creativity, and math

dominate intuition
and tame creativity.

Almost everyone who hasn't heard it before
is surprised by the fact that if one took

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

big enough, and that I
could fold 50 times,

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

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

That's what math is for.

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

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

And because it does, it helps us
avoid the traps

of this painful world
we're in.

There are sciences that grasp
this very application.

Oncological science, for example.

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

but knowing we are what supports them.

All the basic sciences
are the support of them,

and among these is math.

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

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

Probably you said before,
or you were told sometime,

that diamonds are 
forever, right?

It depends on what one
understands by forever!

A theorem, that really
is forever! (Laughter)

The Pythagorean theorem,
that is still true

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

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

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

the Pythagorean theorem works
to the max. (Applause)

Well, us mathematicians
devote ourselves to making theorems.

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

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

You need a demonstration.

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

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

I could use squares, right?

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

Which is the best piece I can use?

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

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

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

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

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

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

until 1700 years later,
1700 years later,

in 1999 Thomas Hales
demonstrated that Pappus

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

And that became a theorem,
the honeycomb theory,

that will be true forever
forever and ever,

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

But what happens if we go to 3 dimensions?

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

I can use cubes, right?

Not spheres, those leave little gaps.
(Laughter)

What is the best piece
I can use?

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

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

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

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

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

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

He stayed in a conjecture,
Kelvin's conjecture.

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

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

someone found a better structure.

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

(Laughter) this structure they put the
imaginative name of

the Weaire-Phelan structure. (Laughter)

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

it's also present in nature.

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

was used to build
the swimming building

in the Beijing Olympic Games.

There Michael Phelps won
8 gold medals, and became

the best swimmer of all times.

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

As it happens to the
Weaire-Phelan structure,

it's the best until something better
shows up.

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

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

someone demonstrates that this
is the best piece possible.

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

For longer than any diamond.

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

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

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

However, you'll have to demonstrate,

that your love doesn't stay a conjecture.

(Applause)

Thank you.