WEBVTT

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

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

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

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

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33.51 % of girls (Laughter)

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

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

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

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

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

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When that conversation
follows, invariably

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in some moment, one of these
two phrases shows 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 that math thing,
what is it for?" (Laughter)

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I'll deal with case B.
(Laughter)

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When someone asks you what
math is for,

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

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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 asking you really.

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Given this, when they ask
a mathematician

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

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A 54.51 % of mathematicians
assumes an attacking posture,

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and a 44.77 % of mathematicians
assumes 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 who attack?

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The attacking ones are mathematicians
that tell you the question

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

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

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and that there's no use in one always
looking after the 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? (Laughter)

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

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And those who stand in 
defense tell you that

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

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They always name bridges
and computers, always.

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

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In reality computers
are all about math.

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Now these guys always happen
to tell you that behind

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information security and credit
cards are prime numbers.

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

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Those are 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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In reality both are right.

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

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

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(Audience asks the question)

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

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

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

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

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

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the human being has ever made
along history.

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

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

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

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

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

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Science works by intuition,
by creativity, and math

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dominate intuition
and tame creativity.

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Almost everyone who hasn't heard it before
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,

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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.

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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.

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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.