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

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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 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:

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

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in constantly searching
for all 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, buddy,
math is behind everything."

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(Laughter)

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They always--

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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

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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,

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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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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 every person
who hasn't heard this before

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is surprised when they hear

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

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is big enough, that if you 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 it's impossible.

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

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

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And because it does so,

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it can help us avoid the traps
of this painful world we live 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 at from afar,
with 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, science,
is the rigor of math.

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

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You probably said or were told
at some point,

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that diamonds are forever, right?

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It depends on
what you understand by "forever"!

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A theorem-- that really is forever!

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(Laughter)

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The Pythagorean theorem is still true

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

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Even if the world collapsed

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the Pythagorean theorem
would still be true.

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Wherever any two sides
and a good hypotenuse get together

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(Laughter)

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the Pythagorean theorem
works at its the max.

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(Applause)

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

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Eternal truths.

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

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compared to a mere conjecture.

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You need demonstration.

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For example,

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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 covers the same surface
has the smallest border.

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

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just like bees do.

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But he didn't demonstrate it.

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

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

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"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--

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1700 years later--

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in 1999 Thomas Hales demonstrated

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that Pappus 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.

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There Michael Phelps won
8 gold medals, and became

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the best swimmer of all times.

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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,

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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,

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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.