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Ok, let me talk about mathematics.

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I am sure all of you love math, yeah?

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

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Honestly speaking, 
how many of you guys hate math?

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Not so many. That's good!

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Actually I think that some people
who hate math believe

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that math is all about numbers
and calculation and formulas

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and other boring stuff.

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Let me tell you. That's not true.

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

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there was a famous mathematician
called Ernst Kummer.

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

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

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

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

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

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

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

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

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

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So not all mathematicians
are good at numbers.

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

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Anyway, math is not just about numbers.

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

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for like a day or a week if you wish.


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Every day there's a new theory improved,


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

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

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It's a little bit like music.

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

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

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

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Well, maybe you don't know
Category Theory.

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Some people think Set Theory
is much more sexy.

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Yeah, wow.

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And in some countries,


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some people are good
at handling concrete stuff,


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and some countries
are good at handling very abstract stuff.

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So math is not as rigid
as you might imagine.

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But the biggest difference
between math and music

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

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


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there are wonderful players
who play music.

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So you have Bach, Beethoven, Mozart.

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All the great composers
make beautiful music,

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but we get access to this music
because great players,

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

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so we can get access to beautiful music.

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But in the world of math, unfortunately,


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

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but no one plays math.

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

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to professional mathematicians.

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I want to change this a little bit.

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

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

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and non-mathematicians
come to listen to mathematics.

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

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

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

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Then what is it about? 


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Mathematics is called 
"Sugaku" in Japanese.

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

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So sugaku means "the study of numbers."

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

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because it gives the impression

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that mathematics is 
actually about numbers.

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But the word mathematics originally
comes from a Greek expression,

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"ta mathemata."

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Ta mathemata means
"things we gain by taking",

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

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It's the taking
of what we already have.

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

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but ta mathemata means
things we gain by taking

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

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

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

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So what does that mean?

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There is a Japanese mathematician
called Oka Kiyoshi.

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I hope everyone will remember his name
after this presentation.

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He used to be in Kyoto.


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

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


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that Oka was the name of a group.

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

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

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Oka was not just a great mathematician;


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but he was also a profound thinker,
and philosopher.

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He has left some great quotes
and beautiful essays

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on the nature of mathematics,



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In particular, he repeatedly said
that mathematics can say nothing

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of the first number one.

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Well, obviously numbers
are the most simplest objects

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in mathematics.

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

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

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no matter how hard you try
mathematically or logically,

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


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

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We simply believe it.

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It's the believing of something
with no grounds.

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Without this power of our mind,
of believing things,

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math will be totally groundless,
and meaningless.

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

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

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

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

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

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but there's a huge dimension
our inner universe,

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which Oka Kiyoshi called "Joocho."


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Joocho is a difficult Japanese word.

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I was looking for 
a good translation for it,

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a good English word
that corresponds to Joocho,

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but unfortunately
I was not able to find one.

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So let's just call this Joocho.

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(Laughter)

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

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


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math is about joocho.

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

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well, encountering with your own self,

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encountering with your own
rich inner universe, your Joocho.

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

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It doesn't have to be a difficult one.


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

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

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and concentrate on it;
try to solve it yourself.

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

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

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

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

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

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

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in the sea of Joocho inside your mind.

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Well, try this if you have time.


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So this is a very short presentation
on mathematics.

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And basically I only have one message.


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

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math is not just about logic;

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math is the very act of looking
inside your mind,

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and encountering with your inner self
with your inner universe,


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with your inner rich
whole dimension of Joocho.

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

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Thank you very much.

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(Applause)

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Thank you.