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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,[br]I know that not everybody loves math.

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Honestly speaking, [br]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[br]who hate math believe

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that math is all about numbers[br]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:[br]in the 19th century,

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there was a famous mathematician[br]called Ernst Kummer.

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

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"the father of arithmetics,"[br]"the father of number theory."

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

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

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

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

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

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

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

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So not all mathematicians[br]are good at numbers.

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He is a famous number theorist.[br]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[br]without talking about numbers

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for like a day or a week if you wish.[br]

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Every day there's a new theory improved,[br]

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every day a new idea,[br]every day a new concept is created.

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

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It's a little bit like music.

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For example, what's cool[br]and what's not

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depends on which culture and[br]which area you live in mathematics.

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

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Well, maybe you don't know[br]Category Theory.

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Some people think Set Theory[br]is much more sexy.

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Yeah, wow.

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And in some countries,[br]

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some people are good[br]at handling concrete stuff,[br]

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and some countries[br]are good at handling very abstract stuff.

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So math is not as rigid[br]as you might imagine.

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But the biggest difference[br]between math and music

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

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who create music and make music,[br]but at the same time[br]

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there are wonderful players[br]who play music.

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So you have Bach, Beethoven, Mozart.

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All the great composers[br]make beautiful music,

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but we get access to this music[br]because great players,

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Glenn Gould and Yo-Yo Ma and[br]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,[br]

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there are great composers;[br]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[br]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,[br]I started doing math concerts.

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

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and non-mathematicians[br]come to listen to mathematics.

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

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

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

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Then what is it about? [br]

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Mathematics is called [br]"Sugaku" in Japanese.

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Su means "numbers";[br]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[br]this is a good translation,

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because it gives the impression

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that mathematics is [br]actually about numbers.

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But the word mathematics originally[br]comes from a Greek expression,

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"ta mathemata."

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Ta mathemata means[br]"things we gain by taking",

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but it's not the taking[br]in the ordinary sense.

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It's the taking[br]of what we already have.

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So we usually take something[br]that we don't have,

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but ta mathemata means[br]things we gain by taking

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but the taking is the taking[br]of what we already have.

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

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means the taking of what you already have[br]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[br]called Oka Kiyoshi.

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I hope everyone will remember his name[br]after this presentation.

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He used to be in Kyoto.[br]

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

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

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that Oka was the name of a group.

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

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

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Oka was not just a great mathematician;[br]

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but he was also a profound thinker,[br]and philosopher.

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He has left some great quotes[br]and beautiful essays

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on the nature of mathematics,[br][br]

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In particular, he repeatedly said[br]that mathematics can say nothing

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of the first number one.

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Well, obviously numbers[br]are the most simplest objects

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in mathematics.

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

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or what the first number one is[br]in the first place,

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no matter how hard you try[br]mathematically or logically,

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you'll never be able to explain[br]or never be able to prove[br]

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the existence of the number one,[br]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[br]with no grounds.

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Without this power of our mind,[br]of believing things,

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math will be totally groundless,[br]and meaningless.

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

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and logic and all that stuff,[br]but underlying calculation and logic,

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

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

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there's not logic,[br]there's not calculation,

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but there's a huge dimension[br]our inner universe,

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which Oka Kiyoshi called "Joocho."[br]

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Joocho is a difficult Japanese word.

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I was looking for [br]a good translation for it,

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a good English word[br]that corresponds to Joocho,

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but unfortunately[br]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,[br]math is not about numbers;

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math is not about calculation;[br]math is not about logic;[br]

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math is about joocho.

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

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well, encountering with your own self,

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encountering with your own[br]rich inner universe, your Joocho.

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

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It doesn't have to be a difficult one.[br]

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

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

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and concentrate on it;[br]try to solve it yourself.

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Don't look at the answers.[br]Don't cheat.

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

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

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

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

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And if you are lucky enough,[br]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.[br]

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So this is a very short presentation[br]on mathematics.

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And basically I only have one message.[br]

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Math is not about numbers;[br]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[br]inside your mind,

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and encountering with your inner self[br]with your inner universe,[br]

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with your inner rich[br]whole dimension of Joocho.

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

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Thank you very much.

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(Applause)

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Thank you.