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.

Imagine you're in a bar, or a club,

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 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:

"Why did I have to study that bullshit
I never used in my life again?" (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 assume 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 point

in constantly searching
for all 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, buddy,
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

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 every person
who hasn't heard this before

is surprised when they hear

that a 0.1 mm thick sheet of paper--
one that we normally use--

is big enough, that if you fold 50 times,

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

Your intuition tells you it's impossible.

Do the math and you'll see it's right.

That's what math is for.

It's true that the main purpose
of science, of all types of science,

is to make us better understand
the beautiful world we live in.

And because it does so,

it can help us avoid the traps
of this painful world we live in.

There are sciences
that grasp this very application.

Oncological science, for example.

And there are others we look at from afar,
with 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, science,
is the rigor of math.

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

You probably said or were told
at some point,

that diamonds are forever, right?

It depends on
what you understand by "forever"!

A theorem-- that really is forever!

(Laughter)

The Pythagorean theorem is still true

even though 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 at its the max.

(Applause)

Well, us mathematicians devote ourselves
to come up with theorems.

Eternal truths.

But it isn't always easy to know
what an eternal truth, a theorem, is

compared to a mere conjecture.

You need 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?

One that covers the same surface,
but has the smallest border.

In the year 300, Pappus of Alexandria
said the best is to use hexagons,

just like bees do.

But he didn't demonstrate it.

The guy said, "Hexagons, great!
Let's go with hexagons!"

He didn't demonstrate it,
he stayed in a conjecture.

"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 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 that the best was to use
a truncated octahedron

(Laughter)

which 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, get 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
found this little thing over here,

(Laughter)

they gave this structure
the imaginative name

of the Weaire-Phelan structure.

(Laughter)

It looks like a strange object,
but it isn't so strange,

it also exists in nature.

It's very interesting that this structure,

because of its geometric properties,

was used to build the Aquatics Center
for the Beijing Olympic Games.

There, Michael Phelps
won eight gold medals,

and became the best swimmer of all times.

Well, until someone better
comes along, right?

As it may happen
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 in a hundred-and-something years
from when, even if it's in 1700 years,

someone demonstrates
that this is the best possible piece,

it will then become a theorem,
a truth, forever and ever.

For longer than any diamond.

So, if you want to tell someone

that you will 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)