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.