Math is forever

Mathematician Eduardo Sáenz de Cabezón answers a question that’s wracked the brains of bored students the world over: What is math for? With humor and charm, he shows the beauty of math as the backbone of science — and shows that theorems, not diamonds, are forever.

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

and you start talking to a girl,

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

And since 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)

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

And there is 1 %
that actually follows the conversation.

When that conversation happens,

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

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

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

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

(Laughter)

I'll deal with case B.

(Laughter)

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

about the application
of mathematical science.

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 actually asking.

So when mathematicians
are asked what math is for,

they tend to split into two groups.

54.51 % of mathematicians
will take an attacking posture

and 44.77 % of mathematicians
will take a defensive posture.

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

Who are the ones that attack?

The attacking ones are mathematicians
who would tell you:

"This question makes no sense,

because mathematics
have a meaning on their own--

a beautiful edifice with its own logic--

and that there's no use

in constantly searching
for 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 instance, is a prime example
for this type of attack.

And those who stand in defense tell you:

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

(Laughter)

They always--

always name bridges and computers.

"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
would give you if you asked him--

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?

Actually, both are right.

But remember I told you

I belong to that strange 0.8 %
claiming something else.

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

Audience: What is math for?

Okay, so 76.34 % of you
asked the question,

23.41 % didn't say anything,

and 0.8 %--

not sure what those guys were 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,

probably one
of the greatest collective effort

the human race
has ever achieved in history.

But it's also true that there,

where scientists and technicians
are looking for mathematical theories,

models that allow them to advance,

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

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

to see what's behind science.

Science is based on intuition, creativity.

Math dominates intuition
and tames 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.