Pi equals 3.141592653.
What a pain. Why don't they just make it 3?
If you made it 3, you'd get a hexagon, not a circle.
Hey, Root's here!
Rise.
Bow.
Sit.
I'll be your math teacher for the next year.
You already know...
I'm Root.
As you see, I'm having a bad-hair day.
Today, I want you to learn a little about me.
This isn't a lesson, so you don't have to take notes.
They've been calling me "Root,"
for 19 years now.
The way I came by the name Root, fell in love with math,
and ended up in front of you...
The Professor and His Beloved Equation
My mother loved someone she couldn't marry
and raised me on her own.
Uneducated and lonely, my mother became a housekeeper
because it was the only option available
for a person of her talents.
Your new clients may be a bit of a handful.
They've gone through 9 housekeepers in the past few years.
Though the youngest housekeeper at the agency,
she already had 10 years experience.
My spirited mother
pursued her profession with a fierce pride.
Excuse me.
I would like you to look after my brother-in-law.
Brother-in-law...
Your husband's brother?
No one lasts long.
Every time we get someone new, we have to start all over again.
It's such a bother.
I'm not asking for anything complicated.
Just feed and look after him
from 11AM to 7PM.
Where is your brother?
Don't come and go between the annex and the main house.
You work in my brother-in-law's house.
And it's up to you to solve
any problems with him yourself.
You must promise me that.
I will.
Shall I meet your brother?
There's no need.
Even if he meets you today, he won't remember you tomorrow.
What do you mean?
In other words, frankly, his memory is impeded.
He hit his head in a traffic accident.
The same accident left me lame.
My brother's memories
stop with the night we saw
a Noh play by bonfire at Kohfukuji Temple,
in the Spring of 1975.
It's been 10 years since the accident, but in his mind,
we've always just seen the Noh play yesterday...
In other words, it always just happened last night.
Ten years in a single day?
He doesn't even realize that I age with each day's passing.
The way I was 10 years ago,
is all he can see...
All he will ever see.
In any event, his memory lasts 80 minutes.
That's exactly an hour and 20 minutes.
Over and over again.
So...
I'll see you at 11am, Monday morning?
Yes.
And so my mother came to work as a housekeeper in the professor's house.
The professor had been able to pursue his study of mathematics
all the way to Cambridge University in England,
thanks to his older brother's success in an inherited textile business
which financed the much younger man's education.
After he earned his Ph.D.
and found a position in mathematics research,
his older brother passed away
and his widow closed the factory,
built apartments on the property moved out to the country,
and lived on income from the apartments.
But their comfortable lives
were shattered by the accident.
The professor lost his position,
and became dependent on his sister-in-law’s charity.
Hello! I'm the housekeeper.
Hello!
Hello. I'm your new housekeeper.
Hello.
What's your shoe size?
24 centimeters.
My, what a noble number...
It's the factorial of 4.
What is a factorial?
If you multiply all the whole numbers from 1 to 4,
you get 24.
What's your telephone number?
576-1455.
Did you say 5,761,455?
Why, that's wonderful.
That's equivalent to the prime numbers up to one billion.
In any event, come in.
I'm busy working, so you're on your own.
Go ahead and suit yourself.
As of that day,
my mother and the professor repeated this mathematical greeting every morning.
For the professor, whose memory spanned 80 minutes,
my mother was always the new housekeeper.
For the professor, bringing up math
was a communication strategy.
When he was confused about what to say,
numbers could always take the place of words.
This character in the word "factorial"
is the character for staircase.
The other character means multiply.
Whole numbers,
refer to the integers which start 1, 2, 3, 4 and extend infinitely.
Multiply these and you get 24.
So 24 is the factorial of 4.
Now, who knows what the factorial of 5 is?
Yes! 120.
Correct.
How about the factorial of 7?
5,040.
Correct.
You're fast.
This character in "prime number"
means genuine.
Like something genuine without embellishment.
In other words, a number which is only divisible by 1 or itself.
For instance...
2, 3, 5, 7,
11, 13, 17,
19, 23, 29...
These prime numbers
are as infinite as the stars in the night sky.
No known rules govern them.
I am here, utterly self-sustaining.
In other words, just like all of you, each one is unique.
Utterly noble and unbending,
these numbers remain aloof.
"Aloof."
What the professor cherished most in this world,
were these prime numbers.
Did he really love numbers?
Sure, the object of his affections may have been eccentric, but not his love.
He cherished them, served them without compensation,
respected them, always,
never straying from them for even a moment.
I'm sorry to bother you.
What would you like for lunch?
Any preferences, dislikes or allergies?
It would help to know.
What do you think?
I can go ahead and just fix something, but what do you think?
I'd welcome your opinion.
I have nothing to say.
I'm thinking now.
You come barging in and interrupt my love for my numbers.
It's as rude as peeping into a toilet.
I'm terribly sorry. Excuse me.
My memory lasts only 80 minutes.
The new housekeeper.
Would you care for more? I made plenty.
April 7th.
Every day adds to the others.
We should be grateful spring has finally come.
Hello!
Hello.
I'm your new housekeeper.
What's your shoe size?
24,
the factorial of 4.
That's wonderful.
What a noble number...
Excuse me.
Yes.
Please send this to The Journal of Mathematics,
at this address.
Sure, no problem.
By regular mail?
Yes.
That'll be 170 yen.
Thank you.
I'm home.
Welcome home, thanks for your work.
Not at all.
Do you often submit your papers to magazines?
Right...
I sent my proof to The Journal of Mathematics, Vol. 37 today...
That's good.
Oh, no!
I should've sent it express. Only First Place takes a cash prize.
No, there's no need to send it express.
It's important to arrive at the truth before anyone else,
but it's more important that the proof be beautiful.
There are such things as beautiful or ugly proofs?
Of course.
In a truly correct proof,
air-tight and compelling reasoning coexists without contradiction,
with supple logic.
Just as no one can prove why stars are beautiful,
it's difficult to express the beauty of mathematics.
What's your birthday?
February 20th.
What a charming number.
Take a look at this.
Back in college,
I won the President's award for my paper on Transcendental Number theory.
What a great honor.
No, that doesn't matter.
Can you read the number?
"President's Award No. 284."
Does that mean you're the 284th person to receive the honor?
I suppose.
The question is 284 and 220.
This is no time to be washing dishes. Come with me.
What do you think?
Well, I...
Both have 3 digits...
How can I phrase this?
At the meat counter at the supermarket,
if there are two packets of ground beef, one 220 grams the other 284,
they seem the same to me.
One quick glance and they look similar.
They're both in the 200 range and all the numbers are even.
That's a keen insight.
Intuition is important.
Grasp the numbers intuitively, from your heart.
You know what a divisor is?
Yes, I think so. I remember studying them...
Let's write out all the divisors for 220 and 284,
excepting themselves.
1, 2, 4, 5, 10,
11, 20, 22,
44, 55, 110,
1, 2, 4,
71, 142.
You can calculate all those divisors in your head?
I'm just using the same intuition you did.
Onto the next step.
Add it up.
Take your time.
I'm done.
Correct.
Will you behold,
this beautiful chain of numbers.
Add all the divisors for 284 and you get 220.
Add all the divisors for 220 and you get 284.
They're amicable numbers.
Amicable numbers?
Amicable Numbers.
Such pairs are very rare.
Even Fermat and Descartes only discovered one pair each.
They're numbers bound to each other by God's design.
God's design...
Isn't it beautiful?
Your birthday and the number engraved on my wristwatch
are so perfectly intertwined.
The first person to discover amicable numbers was Pythagoras.
Pythagoras made his famous statement,
"Number is the within of all things."
In the 6th century B.C.
Have numbers been around that long?
Of course. Numbers existed before humans,
no, even much, much longer.
They existed even before this world was born.
But humans invented numbers, right?
Not at all. No human being witnessed the birth of numbers.
They have always just been there, all along.
All humans can do is express with words,
what numbers provide for us.
What do you think?
Care to discover some more amicable numbers?
By the way, the next smallest amicable numbers are.
1184 and.
Four digits!
No way!
This pair...
In 1866...
Paganini, an Italian,
Nicolo Paganini, discovered this pair.
Can you believe it, at the time, Paganini was 16 years old.
In high school!
What matters is to think it through without giving up.
I'm so glad you're not a Giants fan.
Always been a Tigers fan.
My son and I are huge Tigers fans, too.
You have a son?
Yes.
How old is he?
Ten years old.
Ten?
Why, he's just a boy.
And where is your son now? What's he doing?
Oh, I'm not sure.
Probably playing ball with his friends.
"Oh, I'm not sure."
You should be more concerned.
It's going to get dark, soon.
Don't worry, he has a daily routine.
Routine?
You routinely abandon your son
to make hamburgers here?
I don't abandon him.
It's just that this is my job...
Who looks after him while you're away?
Your husband comes home early?
Oh...
I get it.
He has a grandmother.
No, unfortunately,
he has no father or grandmother.
My son and I live alone together.
Does your son wait for you alone?
He waits for you with an empty stomach?
While his mother cooks supper for a stranger...
My supper...
This is awful.
This can't be, it can't.
You don't need to worry.
It's always been just the two of us.
He's 10 now. He's fine on his own.
He knows the phone number here.
Our landlord can always help.
No, no, no.
You can't leave a child alone.
What if the stove falls over and there's a fire?
Who will save him if a candy gets stuck in throat?
It's terrifying to consider.
I can't bear it.
You must go home, now.
Right now, go home.
I won't be much longer. I just have to cook the burgers.
Forget about that.
What if your son dies in a fire while you're cooking the burgers!
Just let me...
Now, listen.
Starting tomorrow, just bring your son with you.
Just have him come here, right after school.
You'll cook supper here and the three of us will eat together.
But that's...
How dare a grown man
stuff his face in front a hungry child.
But my contract...
But if you don't cook him supper until you get home from work,
your son can't eat until after 8PM.
That's not right.
Don't underestimate me, assuming
I'll have forgotten by tomorrow.
I'll have none of that.
I won't forget.
Her son.
10 years old.
If you break our promise, I won't forgive you.
Hello!
You've come a long way. Good boy, good boy.
Thank you, thank you.
I can tell you've got a wise heart in there.
All right, you're a Root.
You accept any number that comes your way, rejecting none.
A truly generous symbol, Root.
Come on in.
Ever since that day, I've been called Root.
My head...
was as flat as this root symbol.
I remember well the day the professor and I tried to find out
what kind of magic happens
when you put numbers inside this root symbol.
The square root of 1.
The root of 1...
There's +1 and -1, two of them.
The square root of -1.
The square root of -1...
Is this +1 or -1?
Impossible.
Why?
Because the square roots of +1 and -1
are both +1.
Exactly.
All right, so the square root of -1,
what exactly is it?
There is no such number.
No, it's right here.
To answer this,
the Italian mathematician, Rafael Bombelli...
Rafael Bombelli,
invented a new number, "i."
This was in the 16th century, "i."
"i" is an imaginary number.
Because it's a very modest number...
It's written with the character for "candor,"
and...
the character for humility.
It never appears in the visible world,
but it's always inside our hearts,
using its short little arms
to support its whole world.
What do you imagine from this "i"?
Just try to imagine.
The "I" in "I love you!"
That's right, that "I."
But that "I" naturally
leads to "love."
Excuse me... May I help you?
I like watching you cook.
Why do you have to...
keep moving the meat around?
The temperature varies from the center to the sides of the pan.
To cook things evenly, you have to shift them around.
I see.
They all share every spot, so that one can't
monopolize the best spot.
What is... so fascinating?
I'm just cooking.
Oh, it's so peaceful.
Root will be back, soon.
Root?
He's my 10 year old son.
He has a flat head, so he's Root.
Oh, I see, you have a son?
Yes.
I'm home!
See, here's Root.
What's more heartwarming than a child calling, "I'm home."
That's a good boy.
I can tell you've got a wise heart in there.
Wash your hands, and let's eat.
You've got to eat all you can. A child's job is to grow.
And don't leave anything just because you don't like it.
And if you're still hungry,
just help yourself to some of mine.
Sure, thanks!
Every time I see children happily playing,
an old poem comes to mind.
"To see others' children frolic
"brings ceaseless tears for my own, now lost."
My heart is....
e^(Pi x i)'=-1.
Just as this equation will forever yield -1,
the new life we made is now lost forever.
To us, having stepped off course,
none will offer a friendly hand.
To share in your misfortune.
That is my only wish.
To my beloved N.
Can I ask you a favor?
If I can be of help, sure.
Try me out.
Can you fix the radio?
Fix the radio?
Yeah.
When I come here, I can't follow the baseball games.
There's no TV. The radio's busted.
Oh... professional baseball.
Which team are you for?
Can't you see from my cap? The Tigers.
Oh, right, the Tigers.
I'm an Enatsu fan.
The Tiger's ace pitcher, Enatsu.
Really! Oh, great.
Then you have to fix the radio.
What's Enatsu's Earned Run Average now?
How about his Strikeouts?
They traded Enatsu away.
Besides, he's already retired.
Retired?
Good night.
Are the Tigers playing tonight?
I hope they're winning.
I should've kept my mouth shut.
I had no idea the professor was such an Enatsu fan.
No matter the reason, we don't want him to suffer.
Of course not.
The professor repeats himself constantly.
Let's promise.
We'll never say, "You already told me that."
Sure, I promise.
Don't worry, tomorrow he'll be back the way he was.
In the professor's mind, Enatsu will be the Tiger's ace all over again.
It's such a glorious day out.
Would you like to take a stroll in the park?
What would be the point?
Walking improves your circulation,
so you might get some good math ideas.
Blood circulates differently
to the legs and the brain.
Now listen, I'm with you here.
Don't you just go home alone.
Sure, don't worry.
Farming is the work most similar to mathematics.
Farming?
That's right.
You select and plough the land,
plant and grow your seeds.
Mathematicians choose their field,
plant their seeds and work hard cultivating them.
The seeds themselves do all the growing.
Anything's edible.
Do you see?
Vegetables aren't just things you buy in a store.
Why, that's a weed.
It's scent of the earth, good smell.
Toss it with some mustard sauce for strength.
I say it's time to head back. Time for Root to come home.
Root?
Root is my son.
You have a son?
Yes!
Let's hurry home then, hardly the time for picking weeds.
Listen, now.
Every problem has its rhythm.
If you say the problem out loud and grasp its rhythm,
you can contemplate it in its entirety,
and you'll begin to surmise the suspicious areas where traps lurk.
"I bought 2 handkerchiefs and 2 pairs of socks for 380 yen.
"The same 2 handkerchiefs and 5 pairs of socks
"cost 710 yen.
"How much did each item cost?"
It's true, this may be
your toughest problem today.
But you read it out loud so beautifully.
Handkerchiefs, socks, cost.
You had the rhythm down perfectly.
A boring assignment,
read like a complete verse.
All right, let's try making a drawing of it.
Come over here.
Ready?
First the 2 handkerchiefs.
Then the 2 pairs of socks.
Those don't look like socks, they look like fat caterpillars.
I'll draw them for you.
In every situation,
the professor wasn't just after the right answer.
The professor preferred....
the bizarre mistakes born of trying too hard, to my falling silent,
for lack of an answer.
No matter what stupid dead end I wound up in,
the professor always found something positive for me to be proud of.
You're right, right!
Teach me baseball, OK?
Baseball...
You played baseball in high school, right?
Yes, I loved baseball.
In our junior year, we lost the Prefecturals in the semi-finals.
Will you coach our practices? Please.
Sure, all right.
All right.
Baseball...
Practice.
Excuse me...
May I tell you what I discovered?
If you add up 28's divisors,
you get 28.
Hmm...
That's a perfect number.
A perfect number...
The smallest perfect number...
is 6.
You're right, it's no big deal.
Oh, yes it is.
They're precious numbers which embody the meaning of perfection.
Descartes said,
"just as perfect humans are rare,
"so are perfect numbers."
Over the past several thousand years,
barely 30 have been found.
Only 30 of them?
Yes, the perfect number 28
is also Enatsu's number, the Tiger's ace pitcher.
Inside my head,
I can recall every detail of his games,
from his first professional win with the Carps in 1967,
with 10 Strikeouts, to a game on August 30th, 1973,
when he hit that game-ending home run
in a no-hit, no-run, extra-innings game.
Let me show you one more feature of perfect numbers.
Perfect numbers
can be expressed as a sum of consecutive whole numbers.
Here goes 1 plus 2 plus.
3 plus 4 plus.
5 plus 6 plus.
Wow, 28.
Right! 28.
See, 28.
To this day, perfect numbers are shrouded in mystery.
No one has ever proven
that an infinite number of perfect numbers exists.
Teacher, did he also teach you baseball?
Of course.
The professor had tried to pursue baseball
as a college math major, but he injured his shoulder.
He gave it up.
He injured his shoulder,
but his experience and the practice
he'd put in as a young man were the real thing.
Shortstop.
Second base.
That's right.
Right, here goes.
As fast as you can.
That's the Cycloid Curve.
Right.
The professor repeated the basics over and over again,
teaching us baseball with a great deal of love.
My teammates and I promised that no matter how many times
he taught us the same thing, we'd never say, "You already taught us that."
"To my eternally beloved N...
"From the one you must never forget."
That's a high fly, call the ball.
You didn't call the ball. Get up!
Are you OK? Don't move.
An ambulance!
Ambulance? He'll be fine if he doesn't move.
Call an ambulance now.
If I hadn't hit that fly ball.
It's my fault.
It happens all the time.
Here.
Try drawing a straight line here.
It'll calm you down.
Go ahead.
That's right, that's a line.
But think about it.
The line you drew has a beginning and an end.
Which means,
you've drawn a line segment linking the shortest distance
between two points.
The definition of a line doesn't include ends.
It's supposed to continue indefinitely.
But there are limits to a piece of paper
as there are to your strength.
So we agree to call what's
really a line segment, a line.
Where can a true line be found?
Only...
in here.
The eternal truth is invisible and unswayed by matter,
natural phenomenon or emotions.
The invisible world
supports the visible world.
The important things, we have to see with our hearts.
You don't have to worry.
The root symbol is sturdy.
It protects every number.
Hey! How are you?
How irresponsible.
How could you leave him in the professor's care!
Is he really all right?
Yes, he treated him appropriately.
He did nothing wrong?
A little more than necessary...
Look.
There's the first star, up there.
I'm sorry. What I said at the hospital was wrong.
I won't...
ever forget the professor's sad face...
Ever.
That I doubted the professor, even for a moment,
is something I'm ashamed of.
I apologize.
OK, I accept.
Let's make-up.
He said he'd come to our next game.
You know the professor can't make promises, don't you?
I'll ask him.
If only he could get to know
each of my teammates...
What about uniform numbers...
I know... numbers!
Leave everything to me.
Sure!
So this leaf is 1, too.
Right.
That's one leaf.
And that cedar tree with so many leaves
is one tree, too.
It's funny each only counts as one.
It truly is.
Defining "one" is quite a challenge.
Even for you?
So many things I don't know.
Let me see.
Ready?
Tell me,
what do you call this now?
It's like dust, it's not a leaf anymore.
That's right.
It's only a leaf when it's whole.
It's true of you, Root.
The harmony of the whole in an individual is beautiful.
That's what it means to be good.
Listen.
The walk-off victory. The no-hit, no-run game....
714 was.
Babe Ruth's 1935 career home run record.
Hank Aaron hit his career total of 715 home runs
on a pitch from the Dodger's Al Downing on April 8th, 1974.
Here goes!
Retired number 11
is Murayama with the Zatopek pitch.
Number 23 is Yoshida.
Number 10 is Fujimura.
There's Tabuchi, Miyake and...
Their coach and I did it for you.
What's the root symbol?
That's my son.
You have a son?
Yes!
A root symbol will share his friendship fairly with any player.
I don't see #28, ace pitcher Enatsu's number.
We've saved the perfect number, 28, for you.
Play ball!
Go!
Root!
Go! Go! Tigers!
Go, go, Root!
Hold this.
How are you? How are you feeling?
Tell me if you're thirsty.
I shouldn't have insisted...
It's all my fault.
Don't worry, it's not serious.
You go to bed, now.
Good night.
You shouldn't be up. You've still got a f ever.
You have to rest.
Get out of your clothes, let's change your underwear.
You were drenched in sweat last night.
I'll change the sheets and you'll feel refreshed.
Cheering at the ballgame must have exhausted you.
I'm sorry we insisted on inviting you.
If you keep warm and eat well, you'll recover.
Root's that way, too.
We've got to get something into your stomach.
Shall I bring some apple juice?
"My memory...
"lasts only 80 minutes."
I am your housekeeper.
I'm the housekeeper, hired to help you.
I am...
useless...
You helped my son,
and taught me something precious.
The eternal truth is invisible...
You must see it with your heart.
At dusk, my son will join us.
We call him Root, for his flat head.
You named him.
What is your birthday?
February 20th.
220, eternally bound to.
I thought...
women's hands were cold.
Are they warm?
If only this warmth...
Sorry.
This is no good.
A complaint.
What kind?
Don't pretend you don't know.
You've made a terrible mistake.
I hear you stayed over at the math professor's house.
I've made no mistake.
I'm offended by your vulgar insinuation.
You know the rules of your job.
Yes, very well.
I was wrong to ignore them.
You break the rules, spend 3 nights in a man's house,
and are offended by insinuations?
But I couldn't abandon an invalid.
I believed I was only fulfilling my obvious duties.
I feel I've been especially accommodating about your son.
It's a special arrangement.
I'm grateful about my son.
I can't thank you enough for your consideration.
I was careless in my actions.
I apologize.
So... we'll reassign you.
What? Please, wait a minute.
Is that the professor's wish?
His sister's.
I never troubled his sister.
I followed her orders and kept the professor's troubles to myself.
She's not involved with how I do my job.
So, how can she fire me?
She knew that you'd been staying over.
Then surely she knew he was ill.
And that he required more care than most invalids.
If I don't go today, the professor will be very...
He's probably getting out of bed,
reading the note on his jacket all alone...
I can't imagine anyone who can replace you...
But I have no choice.
That's all. It's final.
No room for discussion.
1... 2...
The factorial of 4 is 24.
My, what a noble number.
Please, come on in.
Now and then, I remember the professor's words.
The laws of mathematics are exquisite,
precisely because they are useless in everyday life.
Even if the characteristics of prime numbers were determined,
life wouldn't improve and no one would get rich.
Of course, no matter how you turn your back on the world,
many mathematical discoveries have found practical applications.
Even prime numbers collude in warfare, in the form of secret codes.
It's an ugly fact.
But that is not the purpose of mathematics.
Its only purpose is to ascertain truth.
Open your wise eyes with courage.
I'm sorry I'm late.
Welcome.
Coffee, please.
Why don't we visit the professor anymore?
Things changed.
What things?
Complicated things.
They say looking after someone makes them your responsibility.
You!
I'm not worried, because you're beautiful.
Is that so? Mom's beautiful?
That's right, didn't you realize?
That's why it's fine. Because you're beautiful.
Done.
Serial number 2311... I pronounce you a prime number.
Housekeeper, a call for you.
Yes.
I'm sorry to trouble you. I know you're busy.
Please, sit down.
Some tea for our guest.
Yes.
What exactly are you thinking?
Has my son done something wrong?
That's not the issue.
What do you mean by sending
your son to my brother-in-law's,
even after I fired you?
What do I mean?
He's a 10 year old child.
He came to play because he wanted to. Isn't that good enough?
Yes, I'm sure the child is innocent.
I'm asking about your reasons.
All I...
All I want is for my son to be happy.
Taking him out with your son, staying over to nurse him...
I don't recall telling you to do such things.
I acknowledge that I overstepped my duties.
But it was not intentional or calculating.
It was simpler.
Is it money?
Money?
How... can you say that?
You're no longer involved with us.
My time's up, I'm going home.
It's because we're friends.
What's wrong with coming to play with a friend?
My brother-in-law has no friends.
No friend has ever visited him.
Then Root and I are his first friends.
My brother doesn't remember you for even a single day.
Although he'll remember me his whole life.
For Root and me,
the time we spent with the professor
was really precious.
Even if his 80 minute memory
were none at all.
A line...
Just like a line.
An invisible eternal truth.
That's right.
If you see things with your heart, time doesn't matter.
What matters is right now.
I just wanted to express Root's real feelings...
No.
You can't torment a child.
Children struggle
with much larger problems than ours.
I, too...
have nothing...
left to lose.
I can only accept what is, as it is.
Leaving everything
up to nature,
living every moment as best I can.
Pi is the circle ratio, right?
"I" is the square root of -1 and an imaginary number.
Pi, a number that continues to the ends of the universe,
and the imaginary number "i" which never shows itself.
What's tricky is "e."
"e" is also called the "Napier number," after John Napier,
the British mathematician. The Napier number.
The Napier number is one of the constants, so critical to math.
For now, I'll just tell you the conclusion.
If you calculate this "e," its value is...
e = 2.7182818284...
This is just like Pi.
It goes on and on and on forever.
It's an irrational number.
From an infinite universe,
Pi...
drifts down to "e."
And shakes hands.
with bashful "i."
They come together,
and hold their breaths.
None of them are connected.
But, if a single human
adds just one thing,
the world is transformed.
The contradiction is resolved...
Zero,
in other words,
the realm of nothingness embraces them.
This formula was conceived by the greatest
18th century mathematician, Leonhard Euler.
Leonhard Euler.
This is Euler's Equation.
He found a natural relationship between apparently unrelated numbers.
This is like...
A star falling through the darkness.
This was the professor's beloved equation.
The beauty of a single star in the night sky,
the beauty of a single flower in a field.
Just as these elude description,
it's hard to explain the beauty of an equation.
There's so much I don't know.
But the professor taught me
how important it is to feel.
Polish your intuition
and nurture generous feelings.
I know you can experience this beauty.
So please love mathematics
and work together with me.
My mother went back to work for the professor.
Hello, I'm the housekeeper.
What's your shoe size?
24, the factorial of 4.
A truly noble number.
Please, come on in.
A letter from the Journal of Math. You won their competition.
It's the highest cash prize since they began publishing.
I'll always remember.
The day I first met you.
"You come barging in, interrupting my love for my numbers!"
You scolded me.
Let's celebrate.
There's no need to celebrate.
If we celebrate together, the joy will multiply.
I don't want to celebrate.
All I did was peep into God's notebook
and copy some ideas.
No, we're celebrating.
Root and I want to celebrate.
Root...
My son.
Oh, you have a son?
Yes.
I know, we'll celebrate Root's birthday, too.
It's May 18th.
He'll be thrilled if you're there.
How old will he be?
Eleven.
11?
Yes, he'll be 11.
A beautiful prime number.
An especially beautiful prime.
And it's Murayama's uniform number.
That's wonderful.
All right, let's celebrate. Children need celebrations.
May 18th.
Root's birthday.
Please have a seat.
Root, happy birthday.
Happy birthday.
Here, Root.
Here's your gift, Professor.
What? For me?
This is...
Thank you.
Kyoko san.
Yes.
My brother-in-law asked me to buy a baseball glove for his birthday.
Would you care to join us?
Not this evening.
I had invited my brother-in-law out when we had the accident,
and he lost his memory.
And the accident wasn't my only sin.
I cast aside my parents, relatives and friends...
If I had had the courage to bear that child...
Our path might have...
I am a sinful woman.
I leave everything to you.
I am so grateful to the professor.
From now on...
this door will always be open.
I can tell you've got a wise heart in there.
Like the root symbol, sharing your friendship fairly
with anyone.
Since that day, until I quit baseball
because of an elbow injury in college,
I cherished that baseball glove.
But what was far more valuable,
was the time I spent with the professor living only in the present.
Time doesn't matter.
I'm still pursuing the dreams I dreamed with him.
That's all for today's lesson.
Rise.
Bow.
Teacher.
Yes.
Thank you.
To see a world in a grain of sand,
And a heaven in a wild flower,
Hold infinity in the palm of your hand,
And eternity in an hour
- William Blake