WEBVTT

00:00:20.352 --> 00:00:23.215
Ok, let me talk about mathematics.

00:00:23.760 --> 00:00:26.026
I am sure all of you love math, yeah?

00:00:27.028 --> 00:00:32.157
Not so much? Well,
I know that not everybody loves math.

00:00:32.909 --> 00:00:36.767
Honestly speaking, 
how many of you guys hate math?

00:00:37.993 --> 00:00:40.227
Not so many. That's good!

00:00:40.227 --> 00:00:42.868
Actually I think that some people
who hate math believe

00:00:42.868 --> 00:00:46.600
that math is all about numbers
and calculation and formulas

00:00:46.600 --> 00:00:48.374
and other boring stuff.

00:00:49.004 --> 00:00:51.176
Let me tell you. That's not true.

00:00:51.456 --> 00:00:54.587
Here's this famous joke:
in the 19th century,

00:00:54.587 --> 00:00:57.643
there was a famous mathematician
called Ernst Kummer.

00:00:58.234 --> 00:01:01.331
He is a very famous mathematician,
and actually he's called

00:01:01.331 --> 00:01:04.620
"the father of arithmetics,"
"the father of number theory."

00:01:05.680 --> 00:01:09.119
But actually, he wasn't so good
at handling simple numbers.

00:01:09.939 --> 00:01:16.413
Once in a lecture, he was giving a class, 
he got stuck trying to calculate 7 x 9.

00:01:17.083 --> 00:01:24.362
So he was writing on the blackboard
and said, "What is 7 x 9?"

00:01:24.362 --> 00:01:28.542
One of his students said, "it's 61, sir,"
and another said, "it's 69".

00:01:29.142 --> 00:01:32.259
And then Kummer said, "Come on!
Calm down, gentlemen.

00:01:32.259 --> 00:01:36.201
It can't be both 61 and 69.
It has to be one of them."

00:01:37.231 --> 00:01:41.725
This is supposed to be funny.
Yes, it was a famous joke.

00:01:41.725 --> 00:01:44.121
So not all mathematicians
are good at numbers.

00:01:46.711 --> 00:01:49.764
He is a famous number theorist.
Ok, thank you.

00:01:49.764 --> 00:01:54.367
Anyway, math is not just about numbers.

00:01:54.367 --> 00:01:58.130
And I can keep on talking about math
without talking about numbers

00:01:58.130 --> 00:02:00.949
for like a day or a week if you wish.


00:02:00.949 --> 00:02:03.274
Every day there's a new theory improved,


00:02:03.274 --> 00:02:07.399
every day a new idea,
every day a new concept is created.

00:02:07.669 --> 00:02:11.586
Math is a totally endless,
open-ended, creative act.

00:02:12.296 --> 00:02:14.768
It's a little bit like music.

00:02:14.808 --> 00:02:17.520
For example, what's cool
and what's not

00:02:17.520 --> 00:02:21.200
depends on which culture and
which area you live in mathematics.

00:02:21.200 --> 00:02:25.333
For example, some people think
Category Theory is really cool.

00:02:25.933 --> 00:02:27.966
Well, maybe you don't know
Category Theory.

00:02:27.966 --> 00:02:31.825
Some people think Set Theory
is much more sexy.

00:02:32.825 --> 00:02:33.994
Yeah, wow.

00:02:35.684 --> 00:02:38.023
And in some countries,


00:02:38.023 --> 00:02:40.865
some people are good
at handling concrete stuff,


00:02:40.865 --> 00:02:44.168
and some countries
are good at handling very abstract stuff.

00:02:45.218 --> 00:02:47.888
So math is not as rigid
as you might imagine.

00:02:49.038 --> 00:02:52.170
But the biggest difference
between math and music

00:02:52.170 --> 00:02:55.933
is that in the world of music,
there are wonderful composers

00:02:55.933 --> 00:02:59.809
who create music and make music,
but at the same time


00:02:59.809 --> 00:03:02.671
there are wonderful players
who play music.

00:03:03.071 --> 00:03:06.266
So you have Bach, Beethoven, Mozart.

00:03:06.266 --> 00:03:08.514
All the great composers
make beautiful music,

00:03:08.514 --> 00:03:11.892
but we get access to this music
because great players,

00:03:11.892 --> 00:03:15.306
Glenn Gould and Yo-Yo Ma and
all the other players play the music,

00:03:15.306 --> 00:03:18.796
so we can get access to beautiful music.

00:03:18.796 --> 00:03:22.158
But in the world of math, unfortunately,


00:03:22.158 --> 00:03:26.154
there are great composers;
every day a lot of math is created,

00:03:26.154 --> 00:03:28.590
but no one plays math.

00:03:30.090 --> 00:03:34.218
So, the world, the beauty of mathematics
is only accessible

00:03:34.218 --> 00:03:36.515
to professional mathematicians.

00:03:36.515 --> 00:03:39.359
I want to change this a little bit.

00:03:39.359 --> 00:03:42.375
Actually, three years ago,
I started doing math concerts.

00:03:42.375 --> 00:03:48.128
At places like this hall, restaurants
even at temples, I talk about mathematics,

00:03:48.128 --> 00:03:52.110
and non-mathematicians
come to listen to mathematics.

00:03:52.110 --> 00:03:57.984
And I wish that not only me
but more people start doing math concerts,

00:03:57.984 --> 00:04:03.632
so that the beautiful world of mathematics
will be accessible to non-mathematicians.

00:04:05.062 --> 00:04:10.388
Anyway, let's get back to the subject.
I said math is not just about numbers.

00:04:10.388 --> 00:04:11.875
Then what is it about? 


00:04:12.725 --> 00:04:15.802
Mathematics is called 
"Sugaku" in Japanese.

00:04:16.102 --> 00:04:19.341
Su means "numbers";
gaku means "study "of something.

00:04:19.341 --> 00:04:21.865
So sugaku means "the study of numbers."

00:04:21.865 --> 00:04:25.195
And I don't think
this is a good translation,

00:04:25.285 --> 00:04:27.497
because it gives the impression

00:04:27.497 --> 00:04:30.359
that mathematics is 
actually about numbers.

00:04:31.079 --> 00:04:34.941
But the word mathematics originally
comes from a Greek expression,

00:04:35.911 --> 00:04:38.191
"ta mathemata."

00:04:38.511 --> 00:04:41.922
Ta mathemata means
"things we gain by taking",

00:04:42.212 --> 00:04:45.519
but it's not the taking
in the ordinary sense.

00:04:45.519 --> 00:04:48.644
It's the taking
of what we already have.

00:04:48.644 --> 00:04:51.660
So we usually take something
that we don't have,

00:04:51.660 --> 00:04:55.118
but ta mathemata means
things we gain by taking

00:04:55.118 --> 00:04:58.421
but the taking is the taking
of what we already have.

00:04:58.421 --> 00:05:03.120
This is difficult. In other words,
mathematics in its original sense

00:05:03.120 --> 00:05:08.589
means the taking of what you already have
and the knowing what you already know.

00:05:08.589 --> 00:05:10.838
So what does that mean?

00:05:11.868 --> 00:05:15.021
There is a Japanese mathematician
called Oka Kiyoshi.

00:05:15.421 --> 00:05:19.603
I hope everyone will remember his name
after this presentation.

00:05:19.603 --> 00:05:21.808
He used to be in Kyoto.


00:05:21.808 --> 00:05:27.985
He is one of the world's most known
Japanese mathematicians.

00:05:27.985 --> 00:05:31.941
And Oka was actually so great
that some people in Europe thought


00:05:31.941 --> 00:05:34.295
that Oka was the name of a group.

00:05:34.295 --> 00:05:37.544
They couldn't believe that
he did all this job by himself.

00:05:37.544 --> 00:05:41.301
Just one single person did all this job.
They couldn't believe it.

00:05:42.611 --> 00:05:45.266
Oka was not just a great mathematician;


00:05:45.266 --> 00:05:49.362
but he was also a profound thinker,
and philosopher.

00:05:49.362 --> 00:05:52.655
He has left some great quotes
and beautiful essays

00:05:52.655 --> 00:05:55.351
on the nature of mathematics,



00:05:55.351 --> 00:06:02.406
In particular, he repeatedly said
that mathematics can say nothing

00:06:02.406 --> 00:06:05.889
of the first number one.

00:06:05.889 --> 00:06:09.586
Well, obviously numbers
are the most simplest objects

00:06:09.586 --> 00:06:11.135
in mathematics.

00:06:11.135 --> 00:06:16.109
But if you try to explain
why the first number one has to exist

00:06:16.109 --> 00:06:18.941
or what the first number one is
in the first place,

00:06:18.941 --> 00:06:21.998
no matter how hard you try
mathematically or logically,

00:06:21.998 --> 00:06:26.060
you'll never be able to explain
or never be able to prove


00:06:26.060 --> 00:06:29.839
the existence of the number one,
or what the first number one is.

00:06:29.839 --> 00:06:31.672
We simply believe it.

00:06:32.932 --> 00:06:36.178
It's the believing of something
with no grounds.

00:06:37.156 --> 00:06:40.900
Without this power of our mind,
of believing things,

00:06:40.900 --> 00:06:43.767
math will be totally groundless,
and meaningless.

00:06:45.317 --> 00:06:50.270
So at first sight, math seems
to be about numbers and calculation,

00:06:50.270 --> 00:06:54.644
and logic and all that stuff,
but underlying calculation and logic,

00:06:54.644 --> 00:07:00.798
there's a huge dimension in our minds
that underlies all calculation and logic.

00:07:00.798 --> 00:07:03.935
So at the heart of mathematics,
there's not numbers,

00:07:03.935 --> 00:07:06.832
there's not logic,
there's not calculation,

00:07:06.832 --> 00:07:10.781
but there's a huge dimension
our inner universe,

00:07:11.591 --> 00:07:16.123
which Oka Kiyoshi called "Joocho."


00:07:17.503 --> 00:07:20.402
Joocho is a difficult Japanese word.

00:07:20.402 --> 00:07:22.694
I was looking for 
a good translation for it,

00:07:22.694 --> 00:07:25.720
a good English word
that corresponds to Joocho,

00:07:25.720 --> 00:07:28.295
but unfortunately
I was not able to find one.

00:07:28.295 --> 00:07:30.934
So let's just call this Joocho.

00:07:30.934 --> 00:07:33.353
(Laughter)

00:07:33.353 --> 00:07:37.166
So in Oka's terms,
math is not about numbers;

00:07:37.166 --> 00:07:39.850
math is not about calculation;
math is not about logic;


00:07:39.850 --> 00:07:42.294
math is about joocho.

00:07:42.294 --> 00:07:45.218
It's the very act of looking
inside your mind, and,

00:07:47.278 --> 00:07:49.981
well, encountering with your own self,

00:07:49.981 --> 00:07:55.026
encountering with your own
rich inner universe, your Joocho.

00:07:55.026 --> 00:07:58.489
So if you want to do mathematics,
pick up a problem.

00:07:58.489 --> 00:08:00.451
It doesn't have to be a difficult one.


00:08:00.451 --> 00:08:03.524
You don't even have to prove
a theory no one has proved yet.

00:08:03.524 --> 00:08:06.252
Just pick up a problem;
it can be an easy one,

00:08:06.252 --> 00:08:09.688
and concentrate on it;
try to solve it yourself.

00:08:09.688 --> 00:08:11.643
Don't look at the answers.
Don't cheat.

00:08:11.643 --> 00:08:16.400
Keep on thinking about the problem
until you figure your way out by yourself.

00:08:17.090 --> 00:08:21.550
Then you have to be patient;
you have to keep on paying attention.

00:08:21.990 --> 00:08:26.879
Being patient and keeping attention
on one subject is very important.

00:08:27.169 --> 00:08:33.006
During this mindfulness, you find yourself
encountering with your own mind.

00:08:33.006 --> 00:08:37.930
And if you are lucky enough,
you find yourself swimming around

00:08:37.930 --> 00:08:41.024
in the sea of Joocho inside your mind.

00:08:41.024 --> 00:08:43.908
Well, try this if you have time.


00:08:43.928 --> 00:08:48.103
So this is a very short presentation
on mathematics.

00:08:48.103 --> 00:08:51.051
And basically I only have one message.


00:08:51.051 --> 00:08:55.164
Math is not about numbers;
math is not just for calculation;

00:08:55.524 --> 00:08:57.834
math is not just about logic;

00:08:57.834 --> 00:09:00.883
math is the very act of looking
inside your mind,

00:09:00.883 --> 00:09:04.138
and encountering with your inner self
with your inner universe,


00:09:04.138 --> 00:09:09.660
with your inner rich
whole dimension of Joocho.

00:09:09.660 --> 00:09:14.582
So in this sense everybody, including you,
can be a mathematician.

00:09:14.582 --> 00:09:16.125
Thank you very much.

00:09:16.125 --> 00:09:17.986
(Applause)

00:09:17.986 --> 00:09:18.846
Thank you.