Ok, let me talk about mathematics.

I am sure all of you love math, yeah?

Not so much? Well,
I know that not everybody loves math.

Honestly speaking, 
how many of you guys hate math?

Not so many. That's good!

Actually I think that some people
who hate math believe

that math is all about numbers
and calculation and formulas

and other boring stuff.

Let me tell you. That's not true.

Here's this famous joke:
in the 19th century,

there was a famous mathematician
called Ernst Kummer.

He is a very famous mathematician,
and actually he's called

"the father of arithmetics,"
"the father of number theory."

But actually, he wasn't so good
at handling simple numbers.

Once in a lecture, he was giving a class, 
he got stuck trying to calculate 7 x 9.

So he was writing on the blackboard
and said, "What is 7 x 9?"

One of his students said, "it's 61, sir,"
and another said, "it's 69".

And then Kummer said, "Come on!
Calm down, gentlemen.

It can't be both 61 and 69.
It has to be one of them."

This is supposed to be funny.
Yes, it was a famous joke.

So not all mathematicians
are good at numbers.

He is a famous number theorist.
Ok, thank you.

Anyway, math is not just about numbers.

And I can keep on talking about math
without talking about numbers

for like a day or a week if you wish.

Every day there's a new theory improved,

every day a new idea,
every day a new concept is created.

Math is a totally endless,
open-ended, creative act.

It's a little bit like music.

For example, what's cool
and what's not

depends on which culture and
which area you live in mathematics.

For example, some people think
Category Theory is really cool.

Well, maybe you don't know
Category Theory.

Some people think Set Theory
is much more sexy.

Yeah, wow.

And in some countries,

some people are good
at handling concrete stuff,

and some countries
are good at handling very abstract stuff.

So math is not as rigid
as you might imagine.

But the biggest difference
between math and music

is that in the world of music,
there are wonderful composers

who create music and make music,
but at the same time

there are wonderful players
who play music.

So you have Bach, Beethoven, Mozart.

All the great composers
make beautiful music,

but we get access to this music
because great players,

Glenn Gould and Yo-Yo Ma and
all the other players play the music,

so we can get access to beautiful music.

But in the world of math, unfortunately,

there are great composers;
every day a lot of math is created,

but no one plays math.

So, the world, the beauty of mathematics
is only accessible

to professional mathematicians.

I want to change this a little bit.

Actually, three years ago,
I started doing math concerts.

At places like this hall, restaurants
even at temples, I talk about mathematics,

and non-mathematicians
come to listen to mathematics.

And I wish that not only me
but more people start doing math concerts,

so that the beautiful world of mathematics
will be accessible to non-mathematicians.

Anyway, let's get back to the subject.
I said math is not just about numbers.

Then what is it about?

Mathematics is called 
"Sugaku" in Japanese.

Su means "numbers";
gaku means "study "of something.

So sugaku means "the study of numbers."

And I don't think
this is a good translation,

because it gives the impression

that mathematics is 
actually about numbers.

But the word mathematics originally
comes from a Greek expression,

"ta mathemata."

Ta mathemata means
"things we gain by taking",

but it's not the taking
in the ordinary sense.

It's the taking
of what we already have.

So we usually take something
that we don't have,

but ta mathemata means
things we gain by taking

but the taking is the taking
of what we already have.

This is difficult. In other words,
mathematics in its original sense

means the taking of what you already have
and the knowing what you already know.

So what does that mean?

There is a Japanese mathematician
called Oka Kiyoshi.

I hope everyone will remember his name
after this presentation.

He used to be in Kyoto.

He is one of the world's most known
Japanese mathematicians.

And Oka was actually so great
that some people in Europe thought

that Oka was the name of a group.

They couldn't believe that
he did all this job by himself.

Just one single person did all this job.
They couldn't believe it.

Oka was not just a great mathematician;

but he was also a profound thinker,
and philosopher.

He has left some great quotes
and beautiful essays

on the nature of mathematics,

In particular, he repeatedly said
that mathematics can say nothing

of the first number one.

Well, obviously numbers
are the most simplest objects

in mathematics.

But if you try to explain
why the first number one has to exist

or what the first number one is
in the first place,

no matter how hard you try
mathematically or logically,

you'll never be able to explain
or never be able to prove

the existence of the number one,
or what the first number one is.

We simply believe it.

It's the believing of something
with no grounds.

Without this power of our mind,
of believing things,

math will be totally groundless,
and meaningless.

So at first sight, math seems
to be about numbers and calculation,

and logic and all that stuff,
but underlying calculation and logic,

there's a huge dimension in our minds
that underlies all calculation and logic.

So at the heart of mathematics,
there's not numbers,

there's not logic,
there's not calculation,

but there's a huge dimension
our inner universe,

which Oka Kiyoshi called "Joocho."

Joocho is a difficult Japanese word.

I was looking for 
a good translation for it,

a good English word
that corresponds to Joocho,

but unfortunately
I was not able to find one.

So let's just call this Joocho.

(Laughter)

So in Oka's terms,
math is not about numbers;

math is not about calculation;
math is not about logic;

math is about joocho.

It's the very act of looking
inside your mind, and,

well, encountering with your own self,

encountering with your own
rich inner universe, your Joocho.

So if you want to do mathematics,
pick up a problem.

It doesn't have to be a difficult one.

You don't even have to prove
a theory no one has proved yet.

Just pick up a problem;
it can be an easy one,

and concentrate on it;
try to solve it yourself.

Don't look at the answers.
Don't cheat.

Keep on thinking about the problem
until you figure your way out by yourself.

Then you have to be patient;
you have to keep on paying attention.

Being patient and keeping attention
on one subject is very important.

During this mindfulness, you find yourself
encountering with your own mind.

And if you are lucky enough,
you find yourself swimming around

in the sea of Joocho inside your mind.

Well, try this if you have time.

So this is a very short presentation
on mathematics.

And basically I only have one message.

Math is not about numbers;
math is not just for calculation;

math is not just about logic;

math is the very act of looking
inside your mind,

and encountering with your inner self
with your inner universe,

with your inner rich
whole dimension of Joocho.

So in this sense everybody, including you,
can be a mathematician.

Thank you very much.

(Applause)

Thank you.