# Marguerite's Theorem (2023) Movie Script

1

How long will this take?

Not long.

It's just a quick profile of you.

It's for our newsletter, not the Times.

Can you introduce yourself?

I'm Marguerite Hoffmann, 25,

in my last year

of a math PhD at ENS.

You like life here at Normale Sup?

A lot. I'd like to be

a research professor here.

ENS is home away from home for you?

Which explains the slippers?

They're comfortable.

You're working on the Goldbach theorem,

is that right?

Goldbach's conjecture.

Not exactly but it's linked.

It's one of the most important

unresolved math problems.

Nobody's ever proved it.

You think you can?

Perhaps it won't be proved

in my lifetime.

Besides math, any other passions?

I like walking. It helps me think.

And playing yahtzee with my mother.

Why is the seminar

on March 7 so important?

It's my first time

presenting to specialists.

Their feedback is crucial.

It could result in publications.

What do you love about mathematics?

I couldn't live without it.

- That's it?

- I've got all I need.

Thanks.

Bye.

MARGUERITE'S THEOREM

So...

is every even number

the sum of two prime numbers?

For example, for 98,

what are the solutions?

Take your time!

Marguerite, since you popped in,

enlighten these young men

before I despair of them.

98 = 19 + 79,

31 + 67, 37 + 61.

That's it?

Yes, those are the only three solutions.

Nothing else to say?

You're sure?

Yes.

Indeed. That's correct.

But, and "but"

cancels everything said previously...

Finding three solutions

should surprise you.

It should lead you to other questions

on Goldbach's conjecture,

the number of solutions

and why all these solutions.

Research is not

about answering a question.

A computer could do that better.

It's about exploring, questioning,

finding links between phenomena.

To excel at mathematics,

to roll back the limits,

you must create.

Side step, change perspective,

invent new methods...

Or you don't evolve.

Okay, let's leave it there for today.

A reminder to the class

about the seminar next week,

once more featuring Marguerite Hoffmann,

who'll be presenting aspects

of her thesis on prime numbers.

I don't need to remind you,

your presence is required. Thank you.

- We said we'd rehearse the seminar?

- Yes.

I can't.

I'm welcoming a new postgrad.

You're supervising two of us?

Exceptionally, yes.

He was doing his PhD at Oxford.

It should interest you. Same subject.

The same subject?

Yes. To finish my Szemerdi proof

for the Lausanne conference,

3 brains are better than 2.

- You did the interview?

- This morning.

See, it's no big deal.

Elite female mathematicians are rare.

Grab the spotlight.

With regard to your seminar,

it's crucial to be as clear as possible.

Just facts,

your argument, the proof.

It'll be fine.

You won't disappoint me.

I'm not worried.

Lucas Savelli.

Marguerite Hoffmann, my other postgrad.

Nice to meet you.

You'll soon get a chance

to discuss your research.

- See you soon, I guess.

- See you.

Guys, it's Marguerite.

Marguerite, seminar star!

Marguerite, you're the best.

World champ!

All right, guys?

Tomorrow, what time?

2 pm. So you know,

we're not the Oxford brass band.

Lucky I'm not Fred Wesley.

See you later.

The mathematician in slippers.

Can I sit with you?

Yes.

A rattleback.

Spins normally one way.

The other way, it stops

and reverse-spins.

A buddy at Oxford did his thesis on it.

A real character, Werner.

A throwback mathematician.

What's a throwback mathematician?

Old-school.

He must like your work

to be your supervisor.

I'd hope so. He contacted me.

He contacted you?

I was with Frears at Oxford.

Werner saw

one of my articles on Szemerdi.

So you dumped Frears?

Yes.

Maybe we can compare results

to be more efficient.

Sorry, I don't work that way.

Great, tomorrow at 9 at the library?

Just kidding.

Enjoy your lunch.

Thanks.

Mom

All right?

Not too stressed, my little darling?

I'm re-reading.

I'd be in a real state.

I shouldn't say it,

but I'm nervous for you.

I'm not alone. I'm with Werner.

I know. I'm so proud of you.

You're sleeping well?

Sleeping well's important.

Yes.

Too bad I can't be there.

But I'd be super intimidated,

meeting Werner.

Anyway, get on with your work.

Lots of love.

Love you, my little darling.

Can you check

a set of lemmas in section 4.1?

Why?

To insure there's no flaw.

You've re-read it a hundred times.

You've no perspective.

It's best to let it settle.

I want your perspective.

I have no time.

If it reassures you,

ask Lucas to read it.

All right.

Good morning.

My work deals with arithmetic progressions

in finite sets of integers.

I'll start with the theorem

of Szemerdi.

Published in the 1970s.

Let

k

an integer

greater than 2

and delta

a real number

that is positive.

There exists

an integer N

depending on k and delta

such that each subset

of integers

smaller than

N

of cardinal

greater than delta N.

E contains a progression

of length k+1.

Please...

Introducing an expected value

into Szemerdi's theorem

is a highly original approach.

Can we take it further?

I considered that.

I'd like to find an upper bound

of the minimal size of N.

How do you find the constant C?

There's the initial combinatorial step

then we conclude

with Werner's hypergraphs.

C depends on what?

k and delta.

I deduce C from the regularity lemma.

How do you do that?

I apply it to Werner's hypergraphs.

So you need the multidimensional lemma.

You can't duck k, N and delta

simultaneously.

True. It's empty.

That invalidates your whole proof.

Excuse me...

Mom

So, how did it go?

It went well.

I'm so proud of you.

I can't really talk now.

Call you back?

Of course.

You'll call me, right?

Lots of love.

All my love, my little darling.

Come in.

It's catastrophic.

I should never have presented so early.

I told you

there was a lemma problem.

Don't start rewriting history.

I advised you to check with Lucas.

He's a student. You supervise my thesis.

By now, you should be autonomous.

Admit you should've heard me out.

Look, let's stop there.

It's going nowhere.

We both know this mistake

undermines 3 years' work.

Most likely, the research field

was too ambitious.

Now, it's essential you rest

and gather your wits,

to come up with another thesis.

With another supervisor.

You won't be my supervisor?

You can't do that to me. Not now.

Stop being so dramatic.

Know what you're missing

to be a great scientist?

Maturity.

You don't walk out on a proof

over one mistake.

You stay dignified, own your errors.

You don't flee.

Take it on the chin.

Mathematics and emotions do not mix.

You'll continue your research with Lucas?

Yes, of course.

Sorry, excuse me.

Checking account

Savings account

49 nights in a hotel

without other...

My little darling, it's mom.

I don't want to intrude,

I just wanted to...

hear how it went.

This is Laurent Werner.

I just found your letter.

I have to say I don't get it.

Your sudden departure

caused quite a sensation.

You certainly picked your moment.

The director called a crisis meeting

on Marguerite Hoffmann.

Everybody finds your leaving

most unfortunate.

The director and I

insist you take a new thesis.

With you?

Prof. Blanchard would be delighted

to supervise your thesis.

You'd be in good hands

with someone who has more time.

I don't think you understood me.

My decision is final.

You know, if you drop your thesis,

the School will demand

repayment of your scholarship.

Yes. 44,000 euros.

At minimum wage, 3 years' work.

2 years, 8 months exactly.

Twice that, to save it up.

I'm telling you,

there is no objective reason to stop.

On the contrary.

There's every reason.

I'll never do mathematics again.

Your teenage crisis

has come a little late.

What does your mother say?

She supports me.

The mission is simple.

It's about polling customers

making purchases in Minolga stores.

It's essential

to stay patient and friendly.

To them, you're staff.

So, even employed by us,

you represent the brand...

Minolga.

For example, to question 1,

would you answer,

1, yes, I prefer lipstick

of a more vivid color,

2, yes, lipstick

of a more subdued color,

3, no, lipstick

of the same color as it is now.

What did you say?

The survey doesn't work.

Really? Care to tell us why?

The survey favors the no's

since the yes's

are spread over two answers.

It skews the results.

You're not here

to criticize the survey, miss,

but to receive training and apply it.

We're not machines,

dumbly following

a protocol that's "skewed."

Your results won't be representative.

I told you,

your role is not to argue.

Just apply a dumb protocol?

If you're not happy, the door's...

there.

Good luck, girls!

Where was I?

The lipstick survey

just needs reformulating to work.

You, follow your friend out.

She's not a friend. We never met.

I don't give a shit!

Get out of my class.

You messed with the idiot's mind.

It was so illogical.

I don't get how pollsters

can manipulate results like that.

Welcome to the 21st century.

It's not coming. The subway?

All right.

I'd given up lame gigs

but my roommate bailed.

I'm in shit.

How much is the room?

500 cash in hand. Why?

Could I move in tonight?

Aren't we going too fast?

I know. You need guarantees.

I can pay six months upfront.

3,000 euros, if that's okay?

Stranger, you'd give me 3 grand in cash?

If it reassures you.

One payment or six, same deal.

You stuck up a bank?

A life doing math sounds like hell.

Just the idea, call an ambulance.

What do you do?

I'm a dancer.

I got it through my uncle,

a plumber who's here a lot.

Nothing's up to code.

Welcome!

Kitchen.

Living room.

What about the cleaning?

We take turns?

Yeah.

It was my roommate's turn.

She flaked on it before she bailed.

The room.

It's perfect.

I'll take it.

Great.

Can you spot me an advance

on the 3,000?

Yes.

Cool.

Marguerite, my new roommate.

In future, I want the rent on time.

- I informed your uncle.

- It's all new now.

New roommate, new deal.

No hassle, Mr. Kong.

Monsieur Kong, please.

What are they playing?

Mahjong.

It's like poker in Asia.

Right?

Not at all.

Far more complicated.

There's a lot less chance.

See you.

- See you.

- Goodbye.

Stock control is crucial.

Apply the method, or it's a mess.

We sort by size not model, okay?

I know it might seem...

But it's how we do it.

You'll see, we're not on your back.

We like our staff to be autonomous.

Do your job,

don't overdo the smoke breaks,

and we're cool.

Switch Block are high-end,

spring-summer sneakers,

strap closure and embroidered logo.

Suede and leather,

they boast a breathable insole

to prevent unpleasant odors.

You're learning it by heart?

Sure.

Can I come in?

I heard you have an orgasm last night.

The soundproofing's terrible.

It really feels so good?

Meaning?

Yes, it really feels so good.

Not for you?

I don't think I ever had an orgasm.

Seriously? Never?

No. At least, not like that.

You've already been with guys? Or girls?

Yes, two relationships.

Both short.

I'm heterosexual.

I always prioritized math.

Anyway...

I was never very attractive to men.

You're pretty, though.

I'm not feminine.

I bet some guys go for your type.

What's my type?

Your type? The class whiz.

Do you look at guys?

How else will you know

if they look at you?

- Can I be of assistance?

- Just looking, thanks.

Hi, Marguerite.

Lucas Savelli at ENS.

I heard you dropped out.

I hope you're okay.

Laurent Werner asked me to call.

We need your permission

to publish an article together.

Why would I sign?

I've nothing to do with Werner now.

Your lemma was irretrievable.

But your idea altered our perspective

on the problem.

We've developed a new method to prove

arithmetic progressions for prime numbers.

We'll submit it to Annals of Math.

Our pseudo random weight

is truncated von Mangoldt function.

You realize all that it opens up?

If we prove Szemerdi,

maybe we'll prove Goldbach.

She hung up?

Hey.

Enough of the post-its.

They're triggering.

Walls of your disapproval, no thanks.

A house-share is cohabitation.

Nobody's perfect.

Accept each other's flaws.

Or it won't work.

You're going out tonight?

With dancer buddies in a bar nearby.

Can I come?

Yeah, if you want.

Thanks.

Chris is there!

He's an insane dancer.

It's gonna be dope.

That was so cool.

- Yeah, awesome.

- So cool.

We're made to dance together.

Think I don't see what you're pulling?

You're shitting me?

Quit hitting on him.

You're wack.

Okay, take it easy, girls. Cool it.

It's cool.

Noa, keep strutting,

showboating in front of everyone,

soon you'll make hooker

in a rap video.

Who are you?

Have we met?

We were in the same nightclub.

- Le Nouveau Casino?

- Yes.

Come on!

All right.

I mean,

come on, you're following me.

It bothers you?

You often follow folks in the street?

No, it's the first time.

People don't usually

come onto me like that.

How do they come onto you?

They don't come onto me.

Let's say I did. What would you do?

I'd start by asking your name.

My name's Marguerite.

Yanis. Nice to meet you.

Want a drink?

I'm not thirsty, thanks.

I'm not your type?

Sure.

Sure, you're lovely.

It's just that...

Staring at me stresses me out.

Sorry.

Don't you want to talk first?

No, not specially.

That's hitting really hard.

We'll wake the neighbors.

With all the noise.

Marguerite, I'm not sure I understand.

Laurent Werner called

to say you left ENS.

Is that true?

You left ENS?

I'm talking to you. Is it true?

I apologize.

You had no right to drop out.

Wrecking everything. It's outrageous.

And what's going on

with this article you won't sign?

He shouldn't drag you into it.

You have a passion for math!

It's your whole life!

With your gift, you can't just quit.

Why did you call my mother?

Lucas, leave us alone, will you?

You had no right to involve her.

I just wanted her to convince you

to sign the article.

Why not call me in person?

You're far too emotional.

Going through

your mother seemed easier.

I thought she knew that you had left.

I truly regret

you giving up mathematics.

How can you say that

after shunting me aside?

I didn't. I was trying to help you

out of this deadlock.

Truth is, you used me for your research,

and when I didn't fulfill expectations,

you tossed me away like I'm worthless.

See, you take it far too personally.

Yeah, right,

mathematics and emotions don't mix.

You can release your publication.

It's the last time

our names will be associated.

Wait!

You owe me this month's rent.

You owe me this month's rent.

Sorry. I guess Noa forgot.

Yeah, sure.

By Friday evening, or you're out.

Got it.

Friday evening.

When I heard about Zadig N'Diaye

in Montpellier,

it's like a huge opportunity.

He auditions after the course.

It costs 2,500 euros

and you'd just given me it.

I cracked, couldn't resist.

I'll pay it back.

Promise.

For the rent, where will you get

1,000 euros by Saturday?

Monsieur Kong?

What now?

I'll pay the rent by playing mahjong

with the 350 euros I have left.

That's a new one on me.

If I lose, we leave tomorrow morning.

Or the end of the week, maybe.

Know what? You'll lose your 350.

And you'll be out tomorrow.

Good evening.

Mahjong.

Thank you.

Stopping already?

We can partner up.

I'll line up games, for a 20% cut.

You're unbelievable.

Thanks.

No problem.

What you doing?

Trying a new proof

of arithmetic progressions

in prime numbers.

And why not?

Mahjong has sets of 2, 3 and 4.

Like prime numbers smaller than N,

there's a finite number of tiles.

I'm looking for a link

as a path to proving Szemerdi.

Awesome.

I wanted to buy you a beer

but I'll leave you with math.

Thanks.

Nice neighborhood.

It's vibrant.

Quite a change for you.

When did you last come to Paris?

Back in your first year, I think.

What's the game in your room?

Mahjong.

You'll have to teach me.

Is it okay if I smoke at the window?

Something's different about your face.

Class 5B still stressing you out?

No, I managed to hook them on algebra.

I made it a game. It works great.

And you? How's work?

I was terminated.

Shoot.

How come?

I refused to obey an illogical order.

But I found

a far more lucrative occupation.

Doing what?

Playing mahjong, actually.

- How is that lucrative?

- You play for money.

I earn 2-6,000 euros a month.

Sorry, I...

I don't understand.

Where do you play?

Here, locally.

There are lots of gaming tables.

As an occupation, isn't it illegal?

Sure. But no more than poker.

You can't be serious.

You can't earn a living like that.

What does your friend Noa say?

She's delighted. I pay the rent.

It's crazy.

You understand I'm scared for you?

That I worry after all that's happened?

You always worried

and you'll always worry.

That's why it's easier to lie.

It's all going to be my fault now.

It's so much easier to blame me.

I'd better be going.

Having fun?

You've finished packing?

Not even.

I'll do it last-minute.

I can't wait but it stresses me out.

It's wack.

The audition at the end

freaks me out.

A real game-changer.

Noa, the first time I saw you dance,

it was like nothing else.

You're so sweet.

The wallpaper's looking pretty good.

I still don't get the point of it.

When they proved the earth was

round not flat,

it changed our way of seeing the world.

It allowed us

to draw a line

between what we know and what we don't.

That's the point of math.

Seeking the truth.

In the world of mathematics,

things are moving at ENS.

Prof. Laurent Werner

has just proved Szemerdi's theorem.

You might think

if it's a theorem, it must be true,

so it changes nothing.

In fact, it changes everything,

with a revolutionary new approach.

There are high hopes

the method may be applied

to other problems.

According to Laurent Werner,

why not the famous Goldbach conjecture?

He will present his work,

with assistant Lucas Savelli,

at a conference in Lausanne...

Sorry for the slap. It was insensitive.

You didn't come all this way to apologize?

It's unnecessary.

No, about your progress with Werner.

Right now? Let's talk another time.

No, it's urgent.

Can you come to my place?

Sorry?

What I need to show you

won't fit on a slate.

Come with me?

You're really funny.

Math is no laughing matter.

Nothing is to you.

That's why you're so funny.

It's in your interest to come.

You did all this alone?

How long did it take to prove Szemerdi?

Two months, ten days.

Unbelievable!

But you two proved it first.

I wanted to see you

about my new project.

It's a new method, never tried.

You have a shot at Goldbach?

I'd like to present some proofs

at Lausanne.

You're invited?

No, but you are.

We could work together.

I thought you hated it.

Goldbach, I can't crack it alone.

Why me?

With you, I can solve the problem.

You mean, only I can help you

solve the problem?

Why'd I accept?

I didn't think you'd risk missing out

on a major step forward.

And you think I'm funny.

So funny.

But no interference from Werner.

It's all our work and discoveries.

It's tricky with regard to Werner.

Lucas, yes or no?

We'll control the number of solutions

with the singular function.

So decompose minor and major arcs.

You have to make that noise?

Sorry, it helps me think.

- What helps you concentrate?

- Silence.

Received loud and clear.

Problem solved.

We need to isolate the factor

with the Euler function, actually.

You want veal or beef stew?

Veal.

Want a beer?

Sure, thanks.

Big place you have.

You live alone here?

My roommate's doing a dance course

in Montpellier.

Incoming text.

Who from?

All alone tonight?

I want you so bad...

From Yanis.

Sounds eager to see you.

What?

So Marguerite has a life

outside of math.

Boyfriend?

No, it's just recreational.

"Recreational"!

Why a passion for Goldbach at 11?

I always loved math.

From your father or mother?

You're always so inquisitive?

It's just normal, right?

You never ask questions?

It's no help with Goldbach.

So working relationships

are pointless?

For me, they're vital to progress.

- Good luck getting on with Werner.

- Precisely.

I'm hoping you're less rigid than him.

You'll do anything to succeed,

whoever you work with.

Back to work?

No, it's 2 am. I'm going home.

"Life outside of math"!

See you Wednesday.

Tomorrow, I'm with you-know-who.

Thanks for dinner.

See you Wednesday then.

Yup, Wednesday.

Can I help?

This isn't working for me.

How come?

Sometimes, you hit a wall.

Actually, you're the wall.

Your earplugs make me feel

like I'm sound pollution.

Problem solved.

No, Marguerite.

You're too cold and closed.

It won't work, we're too different.

You like Chinese?

Math comes from my mother.

She teaches in middle school.

I started helping grade tests

when I was little.

She wasn't well.

My father had just left her.

Back then, I suffered from insomnia.

Full of anxiety about infinity,

the idea that...

the universe had no end.

So, in the library,

I read all the math books I could find

to solve tangible problems

that have solutions.

And one day, I...

I came across Goldbach's pyramid.

A currently unsolved problem

with its infinity of prime numbers.

It was...

such a challenge.

A problem...

so complex and magnificent.

I knew I'd spend my life

trying to solve it.

Goldbach was a way

of putting order into infinity.

Your mother raised you?

Yes.

My father left when I was 9.

We lived in Berlin then.

When he left us,

my mother chose to move back to France.

You still see him?

No.

He lives in Canada. We're not in touch.

And you? From your father or mother?

Neither.

Dad's a financial advisor.

Mom's an antique dealer.

They never understood

why I chose research.

An occupation that pays so badly.

Evening, Marguerite.

Your boyfriend?

No, a colleague.

She's the best mahjong player

in the neighborhood.

Mahjong?

She's very good.

Enjoy your evening.

Yes, I came across it after ENS.

I play in illicit, local gaming rooms.

From mahjong.

So funny.

So, tomorrow, are we working together?

It's still early.

Back at it?

How about we try this?

Or else, like this.

Or this.

Then this.

And this.

Beautiful.

I hate being stuck like this.

A prof at Oxford,

working on the Riemann theorem...

When he got stuck,

he let off steam by pumping iron.

He never proved Riemann

but he's a bodybuilder now.

I like your hair.

You do?

It won't stay in place.

I like the disorder.

I have my mom's hair.

Straighter than straight.

It suits you combed back like that.

It's very...

Class whiz?

How about using distribution

of prime numbers to find a lower bound?

Yes, but for our method to work...

we need to maximize sieve functions.

Exactly.

Race you to the apartment.

Can I come in a minute?

I hope this isn't a bad time.

I came at your mother's request.

You may wonder

what it has to do with me...

but she was so worried

that I felt partly responsible

for what we might call your slide.

I know how mathematics

can make a person vulnerable.

We carry within us

an obsessive aspect,

which can be even more dangerous

mixed in with gambling.

You're not the first mathematician

it's happened to.

You're working on Goldbach.

It's none of your business.

I had a long rivalry

with an ENS colleague

who also worked on prime numbers.

We despised each other.

I was quite relieved

when he left to teach at Yale.

Five years later,

he won the Fields Medal

by proving what I was looking for.

So I moved onto

an even more ambitious goal.

Goldbach.

Since Szemerdi,

I know it will be proved one day.

By me...

or someone else.

You need to be solid

to work on Goldbach.

It's a labyrinthine problem

that you can wander around for ages

until it eats you up completely.

Be very careful, Marguerite.

You know, ultimately,

who gets there is irrelevant.

The main thing

is progressing mathematics.

The rest is pride

and it's equal to zero.

Seriously, he just rocks up here?

What did he want?

To see what I was working on.

We're running out of space.

It won't be dry before tomorrow.

Can I sleep here tonight?

Take Noa's room. The bed's made.

Goodnight.

Didn't we say 2 pm?

- You didn't get my email?

- No.

Ending our work sessions for Lausanne.

- We're sufficiently prepared.

- Fine.

As for your thesis,

it can wait till after Lausanne.

Sure, there's no hurry.

Hey Noa, this is Lucas,

who works with me.

Pinch me, this is getting stupid.

Ask me before you repaint!

I'm talking to you!

Sorry, I'm onto something

really important.

And you think I wasn't?

Sorry, I absolutely must finish.

You okay?

You'd know

if you listened to my messages.

Is she for real?

My fucking bedroom!

I'm gonna take off before I really flip.

I think I've got the last movement.

You check. I'll grab a shower.

You were right.

We're proving a swathe of Goldbach.

Something wrong?

It doesn't stand up.

Same old parity problem.

Looks good but it's an abyss.

How come?

It opens up way more boxes.

Checking the conditions is even harder

than the arithmetic progressions.

We find a new method or have

an exponential number of proofs to make.

Infinite.

Right, I see what you mean.

Anyway, we made a huge leap forward.

The conference is in two weeks.

We're screwed.

If it's not this year, then next.

This is Werner's year.

Look, I get it,

but this doesn't negate all we've done.

It'll just take a bit longer.

It's all good.

It might take months or years

to prove his movement.

Werner might get there first.

You want to prove Goldbach

for him or you?

You don't give a shit.

Your Szemerdi proof

gets you to Lausanne.

Afterwards, why'd you work with me,

when you'll have offers worldwide?

You'll go solve the problem

with someone else.

You're like every mathematician.

Be the best at all costs.

Right, like all the others,

I'll walk out on you.

Don't you see you have a problem?

Waiting for everyone to betray you.

Can't you imagine

you matter to someone?

I was wrong to ask you

to work with me.

I'm not cut out for it.

- You really believe that?

- Yes.

- What's that mean? We're done?

- Yes.

You're losing it...

I'd like you to leave now.

Now.

You know you said

I'd do anything to succeed?

You were right. I sacrificed my PhD

with Werner to work with you.

That's impossible.

I counted.

That's not possible.

He can't have that tile.

It's been played.

It's been played.

There's one extra. It's impossible.

He's cheating.

He cheated. Look, I'll show you.

He cheated!

It's impossible.

I counted the tiles.

He cheated, sir. He cheated!

Monsieur Kong called. What's going on?

What day is it?

For the train station. Take care of her.

Thanks for everything.

Don't bitch out on me. Keep in touch.

Have a good trip.

Mom...

I think I've met someone important.

It's strange.

I think about him more than math.

You're in love?

Perhaps.

You know, Marguerite...

Even if it ended badly with your dad...

I've never forgotten

how happy I was with him.

Lucas, it's Marguerite.

I wanted to tell you,

yesterday I...

I found a drawing

of Goldbach's pyramid in my room,

and I saw it upside down.

I must see you.

I'll take my mom's car

and I'm on my way.

Excuse me,

it's okay.

You can't just appear out of the blue.

I have the last movement.

It's all about perspective.

It's magnificent. I have to show you.

Coming?

A room with a board, this way.

Follow me.

We begin with a circle method

with decomposition in major and minor arcs

to control the number of solutions.

Apparently a girl in the auditorium

is doing a wild proof...

I heard it's a proof of Goldbach.

We introduce a sum weighted

by Selberg weights.

The Goldston-Pintz-Yildirim method.

Exactly.

That's it.

You've found a path.

She's my student.

I love you.

for my mother

How long will this take?

Not long.

It's just a quick profile of you.

It's for our newsletter, not the Times.

Can you introduce yourself?

I'm Marguerite Hoffmann, 25,

in my last year

of a math PhD at ENS.

You like life here at Normale Sup?

A lot. I'd like to be

a research professor here.

ENS is home away from home for you?

Which explains the slippers?

They're comfortable.

You're working on the Goldbach theorem,

is that right?

Goldbach's conjecture.

Not exactly but it's linked.

It's one of the most important

unresolved math problems.

Nobody's ever proved it.

You think you can?

Perhaps it won't be proved

in my lifetime.

Besides math, any other passions?

I like walking. It helps me think.

And playing yahtzee with my mother.

Why is the seminar

on March 7 so important?

It's my first time

presenting to specialists.

Their feedback is crucial.

It could result in publications.

What do you love about mathematics?

I couldn't live without it.

- That's it?

- I've got all I need.

Thanks.

Bye.

MARGUERITE'S THEOREM

So...

is every even number

the sum of two prime numbers?

For example, for 98,

what are the solutions?

Take your time!

Marguerite, since you popped in,

enlighten these young men

before I despair of them.

98 = 19 + 79,

31 + 67, 37 + 61.

That's it?

Yes, those are the only three solutions.

Nothing else to say?

You're sure?

Yes.

Indeed. That's correct.

But, and "but"

cancels everything said previously...

Finding three solutions

should surprise you.

It should lead you to other questions

on Goldbach's conjecture,

the number of solutions

and why all these solutions.

Research is not

about answering a question.

A computer could do that better.

It's about exploring, questioning,

finding links between phenomena.

To excel at mathematics,

to roll back the limits,

you must create.

Side step, change perspective,

invent new methods...

Or you don't evolve.

Okay, let's leave it there for today.

A reminder to the class

about the seminar next week,

once more featuring Marguerite Hoffmann,

who'll be presenting aspects

of her thesis on prime numbers.

I don't need to remind you,

your presence is required. Thank you.

- We said we'd rehearse the seminar?

- Yes.

I can't.

I'm welcoming a new postgrad.

You're supervising two of us?

Exceptionally, yes.

He was doing his PhD at Oxford.

It should interest you. Same subject.

The same subject?

Yes. To finish my Szemerdi proof

for the Lausanne conference,

3 brains are better than 2.

- You did the interview?

- This morning.

See, it's no big deal.

Elite female mathematicians are rare.

Grab the spotlight.

With regard to your seminar,

it's crucial to be as clear as possible.

Just facts,

your argument, the proof.

It'll be fine.

You won't disappoint me.

I'm not worried.

Lucas Savelli.

Marguerite Hoffmann, my other postgrad.

Nice to meet you.

You'll soon get a chance

to discuss your research.

- See you soon, I guess.

- See you.

Guys, it's Marguerite.

Marguerite, seminar star!

Marguerite, you're the best.

World champ!

All right, guys?

Tomorrow, what time?

2 pm. So you know,

we're not the Oxford brass band.

Lucky I'm not Fred Wesley.

See you later.

The mathematician in slippers.

Can I sit with you?

Yes.

A rattleback.

Spins normally one way.

The other way, it stops

and reverse-spins.

A buddy at Oxford did his thesis on it.

A real character, Werner.

A throwback mathematician.

What's a throwback mathematician?

Old-school.

He must like your work

to be your supervisor.

I'd hope so. He contacted me.

He contacted you?

I was with Frears at Oxford.

Werner saw

one of my articles on Szemerdi.

So you dumped Frears?

Yes.

Maybe we can compare results

to be more efficient.

Sorry, I don't work that way.

Great, tomorrow at 9 at the library?

Just kidding.

Enjoy your lunch.

Thanks.

Mom

All right?

Not too stressed, my little darling?

I'm re-reading.

I'd be in a real state.

I shouldn't say it,

but I'm nervous for you.

I'm not alone. I'm with Werner.

I know. I'm so proud of you.

You're sleeping well?

Sleeping well's important.

Yes.

Too bad I can't be there.

But I'd be super intimidated,

meeting Werner.

Anyway, get on with your work.

Lots of love.

Love you, my little darling.

Can you check

a set of lemmas in section 4.1?

Why?

To insure there's no flaw.

You've re-read it a hundred times.

You've no perspective.

It's best to let it settle.

I want your perspective.

I have no time.

If it reassures you,

ask Lucas to read it.

All right.

Good morning.

My work deals with arithmetic progressions

in finite sets of integers.

I'll start with the theorem

of Szemerdi.

Published in the 1970s.

Let

k

an integer

greater than 2

and delta

a real number

that is positive.

There exists

an integer N

depending on k and delta

such that each subset

of integers

smaller than

N

of cardinal

greater than delta N.

E contains a progression

of length k+1.

Please...

Introducing an expected value

into Szemerdi's theorem

is a highly original approach.

Can we take it further?

I considered that.

I'd like to find an upper bound

of the minimal size of N.

How do you find the constant C?

There's the initial combinatorial step

then we conclude

with Werner's hypergraphs.

C depends on what?

k and delta.

I deduce C from the regularity lemma.

How do you do that?

I apply it to Werner's hypergraphs.

So you need the multidimensional lemma.

You can't duck k, N and delta

simultaneously.

True. It's empty.

That invalidates your whole proof.

Excuse me...

Mom

So, how did it go?

It went well.

I'm so proud of you.

I can't really talk now.

Call you back?

Of course.

You'll call me, right?

Lots of love.

All my love, my little darling.

Come in.

It's catastrophic.

I should never have presented so early.

I told you

there was a lemma problem.

Don't start rewriting history.

I advised you to check with Lucas.

He's a student. You supervise my thesis.

By now, you should be autonomous.

Admit you should've heard me out.

Look, let's stop there.

It's going nowhere.

We both know this mistake

undermines 3 years' work.

Most likely, the research field

was too ambitious.

Now, it's essential you rest

and gather your wits,

to come up with another thesis.

With another supervisor.

You won't be my supervisor?

You can't do that to me. Not now.

Stop being so dramatic.

Know what you're missing

to be a great scientist?

Maturity.

You don't walk out on a proof

over one mistake.

You stay dignified, own your errors.

You don't flee.

Take it on the chin.

Mathematics and emotions do not mix.

You'll continue your research with Lucas?

Yes, of course.

Sorry, excuse me.

Checking account

Savings account

49 nights in a hotel

without other...

My little darling, it's mom.

I don't want to intrude,

I just wanted to...

hear how it went.

This is Laurent Werner.

I just found your letter.

I have to say I don't get it.

Your sudden departure

caused quite a sensation.

You certainly picked your moment.

The director called a crisis meeting

on Marguerite Hoffmann.

Everybody finds your leaving

most unfortunate.

The director and I

insist you take a new thesis.

With you?

Prof. Blanchard would be delighted

to supervise your thesis.

You'd be in good hands

with someone who has more time.

I don't think you understood me.

My decision is final.

You know, if you drop your thesis,

the School will demand

repayment of your scholarship.

Yes. 44,000 euros.

At minimum wage, 3 years' work.

2 years, 8 months exactly.

Twice that, to save it up.

I'm telling you,

there is no objective reason to stop.

On the contrary.

There's every reason.

I'll never do mathematics again.

Your teenage crisis

has come a little late.

What does your mother say?

She supports me.

The mission is simple.

It's about polling customers

making purchases in Minolga stores.

It's essential

to stay patient and friendly.

To them, you're staff.

So, even employed by us,

you represent the brand...

Minolga.

For example, to question 1,

would you answer,

1, yes, I prefer lipstick

of a more vivid color,

2, yes, lipstick

of a more subdued color,

3, no, lipstick

of the same color as it is now.

What did you say?

The survey doesn't work.

Really? Care to tell us why?

The survey favors the no's

since the yes's

are spread over two answers.

It skews the results.

You're not here

to criticize the survey, miss,

but to receive training and apply it.

We're not machines,

dumbly following

a protocol that's "skewed."

Your results won't be representative.

I told you,

your role is not to argue.

Just apply a dumb protocol?

If you're not happy, the door's...

there.

Good luck, girls!

Where was I?

The lipstick survey

just needs reformulating to work.

You, follow your friend out.

She's not a friend. We never met.

I don't give a shit!

Get out of my class.

You messed with the idiot's mind.

It was so illogical.

I don't get how pollsters

can manipulate results like that.

Welcome to the 21st century.

It's not coming. The subway?

All right.

I'd given up lame gigs

but my roommate bailed.

I'm in shit.

How much is the room?

500 cash in hand. Why?

Could I move in tonight?

Aren't we going too fast?

I know. You need guarantees.

I can pay six months upfront.

3,000 euros, if that's okay?

Stranger, you'd give me 3 grand in cash?

If it reassures you.

One payment or six, same deal.

You stuck up a bank?

A life doing math sounds like hell.

Just the idea, call an ambulance.

What do you do?

I'm a dancer.

I got it through my uncle,

a plumber who's here a lot.

Nothing's up to code.

Welcome!

Kitchen.

Living room.

What about the cleaning?

We take turns?

Yeah.

It was my roommate's turn.

She flaked on it before she bailed.

The room.

It's perfect.

I'll take it.

Great.

Can you spot me an advance

on the 3,000?

Yes.

Cool.

Marguerite, my new roommate.

In future, I want the rent on time.

- I informed your uncle.

- It's all new now.

New roommate, new deal.

No hassle, Mr. Kong.

Monsieur Kong, please.

What are they playing?

Mahjong.

It's like poker in Asia.

Right?

Not at all.

Far more complicated.

There's a lot less chance.

See you.

- See you.

- Goodbye.

Stock control is crucial.

Apply the method, or it's a mess.

We sort by size not model, okay?

I know it might seem...

But it's how we do it.

You'll see, we're not on your back.

We like our staff to be autonomous.

Do your job,

don't overdo the smoke breaks,

and we're cool.

Switch Block are high-end,

spring-summer sneakers,

strap closure and embroidered logo.

Suede and leather,

they boast a breathable insole

to prevent unpleasant odors.

You're learning it by heart?

Sure.

Can I come in?

I heard you have an orgasm last night.

The soundproofing's terrible.

It really feels so good?

Meaning?

Yes, it really feels so good.

Not for you?

I don't think I ever had an orgasm.

Seriously? Never?

No. At least, not like that.

You've already been with guys? Or girls?

Yes, two relationships.

Both short.

I'm heterosexual.

I always prioritized math.

Anyway...

I was never very attractive to men.

You're pretty, though.

I'm not feminine.

I bet some guys go for your type.

What's my type?

Your type? The class whiz.

Do you look at guys?

How else will you know

if they look at you?

- Can I be of assistance?

- Just looking, thanks.

Hi, Marguerite.

Lucas Savelli at ENS.

I heard you dropped out.

I hope you're okay.

Laurent Werner asked me to call.

We need your permission

to publish an article together.

Why would I sign?

I've nothing to do with Werner now.

Your lemma was irretrievable.

But your idea altered our perspective

on the problem.

We've developed a new method to prove

arithmetic progressions for prime numbers.

We'll submit it to Annals of Math.

Our pseudo random weight

is truncated von Mangoldt function.

You realize all that it opens up?

If we prove Szemerdi,

maybe we'll prove Goldbach.

She hung up?

Hey.

Enough of the post-its.

They're triggering.

Walls of your disapproval, no thanks.

A house-share is cohabitation.

Nobody's perfect.

Accept each other's flaws.

Or it won't work.

You're going out tonight?

With dancer buddies in a bar nearby.

Can I come?

Yeah, if you want.

Thanks.

Chris is there!

He's an insane dancer.

It's gonna be dope.

That was so cool.

- Yeah, awesome.

- So cool.

We're made to dance together.

Think I don't see what you're pulling?

You're shitting me?

Quit hitting on him.

You're wack.

Okay, take it easy, girls. Cool it.

It's cool.

Noa, keep strutting,

showboating in front of everyone,

soon you'll make hooker

in a rap video.

Who are you?

Have we met?

We were in the same nightclub.

- Le Nouveau Casino?

- Yes.

Come on!

All right.

I mean,

come on, you're following me.

It bothers you?

You often follow folks in the street?

No, it's the first time.

People don't usually

come onto me like that.

How do they come onto you?

They don't come onto me.

Let's say I did. What would you do?

I'd start by asking your name.

My name's Marguerite.

Yanis. Nice to meet you.

Want a drink?

I'm not thirsty, thanks.

I'm not your type?

Sure.

Sure, you're lovely.

It's just that...

Staring at me stresses me out.

Sorry.

Don't you want to talk first?

No, not specially.

That's hitting really hard.

We'll wake the neighbors.

With all the noise.

Marguerite, I'm not sure I understand.

Laurent Werner called

to say you left ENS.

Is that true?

You left ENS?

I'm talking to you. Is it true?

I apologize.

You had no right to drop out.

Wrecking everything. It's outrageous.

And what's going on

with this article you won't sign?

He shouldn't drag you into it.

You have a passion for math!

It's your whole life!

With your gift, you can't just quit.

Why did you call my mother?

Lucas, leave us alone, will you?

You had no right to involve her.

I just wanted her to convince you

to sign the article.

Why not call me in person?

You're far too emotional.

Going through

your mother seemed easier.

I thought she knew that you had left.

I truly regret

you giving up mathematics.

How can you say that

after shunting me aside?

I didn't. I was trying to help you

out of this deadlock.

Truth is, you used me for your research,

and when I didn't fulfill expectations,

you tossed me away like I'm worthless.

See, you take it far too personally.

Yeah, right,

mathematics and emotions don't mix.

You can release your publication.

It's the last time

our names will be associated.

Wait!

You owe me this month's rent.

You owe me this month's rent.

Sorry. I guess Noa forgot.

Yeah, sure.

By Friday evening, or you're out.

Got it.

Friday evening.

When I heard about Zadig N'Diaye

in Montpellier,

it's like a huge opportunity.

He auditions after the course.

It costs 2,500 euros

and you'd just given me it.

I cracked, couldn't resist.

I'll pay it back.

Promise.

For the rent, where will you get

1,000 euros by Saturday?

Monsieur Kong?

What now?

I'll pay the rent by playing mahjong

with the 350 euros I have left.

That's a new one on me.

If I lose, we leave tomorrow morning.

Or the end of the week, maybe.

Know what? You'll lose your 350.

And you'll be out tomorrow.

Good evening.

Mahjong.

Thank you.

Stopping already?

We can partner up.

I'll line up games, for a 20% cut.

You're unbelievable.

Thanks.

No problem.

What you doing?

Trying a new proof

of arithmetic progressions

in prime numbers.

And why not?

Mahjong has sets of 2, 3 and 4.

Like prime numbers smaller than N,

there's a finite number of tiles.

I'm looking for a link

as a path to proving Szemerdi.

Awesome.

I wanted to buy you a beer

but I'll leave you with math.

Thanks.

Nice neighborhood.

It's vibrant.

Quite a change for you.

When did you last come to Paris?

Back in your first year, I think.

What's the game in your room?

Mahjong.

You'll have to teach me.

Is it okay if I smoke at the window?

Something's different about your face.

Class 5B still stressing you out?

No, I managed to hook them on algebra.

I made it a game. It works great.

And you? How's work?

I was terminated.

Shoot.

How come?

I refused to obey an illogical order.

But I found

a far more lucrative occupation.

Doing what?

Playing mahjong, actually.

- How is that lucrative?

- You play for money.

I earn 2-6,000 euros a month.

Sorry, I...

I don't understand.

Where do you play?

Here, locally.

There are lots of gaming tables.

As an occupation, isn't it illegal?

Sure. But no more than poker.

You can't be serious.

You can't earn a living like that.

What does your friend Noa say?

She's delighted. I pay the rent.

It's crazy.

You understand I'm scared for you?

That I worry after all that's happened?

You always worried

and you'll always worry.

That's why it's easier to lie.

It's all going to be my fault now.

It's so much easier to blame me.

I'd better be going.

Having fun?

You've finished packing?

Not even.

I'll do it last-minute.

I can't wait but it stresses me out.

It's wack.

The audition at the end

freaks me out.

A real game-changer.

Noa, the first time I saw you dance,

it was like nothing else.

You're so sweet.

The wallpaper's looking pretty good.

I still don't get the point of it.

When they proved the earth was

round not flat,

it changed our way of seeing the world.

It allowed us

to draw a line

between what we know and what we don't.

That's the point of math.

Seeking the truth.

In the world of mathematics,

things are moving at ENS.

Prof. Laurent Werner

has just proved Szemerdi's theorem.

You might think

if it's a theorem, it must be true,

so it changes nothing.

In fact, it changes everything,

with a revolutionary new approach.

There are high hopes

the method may be applied

to other problems.

According to Laurent Werner,

why not the famous Goldbach conjecture?

He will present his work,

with assistant Lucas Savelli,

at a conference in Lausanne...

Sorry for the slap. It was insensitive.

You didn't come all this way to apologize?

It's unnecessary.

No, about your progress with Werner.

Right now? Let's talk another time.

No, it's urgent.

Can you come to my place?

Sorry?

What I need to show you

won't fit on a slate.

Come with me?

You're really funny.

Math is no laughing matter.

Nothing is to you.

That's why you're so funny.

It's in your interest to come.

You did all this alone?

How long did it take to prove Szemerdi?

Two months, ten days.

Unbelievable!

But you two proved it first.

I wanted to see you

about my new project.

It's a new method, never tried.

You have a shot at Goldbach?

I'd like to present some proofs

at Lausanne.

You're invited?

No, but you are.

We could work together.

I thought you hated it.

Goldbach, I can't crack it alone.

Why me?

With you, I can solve the problem.

You mean, only I can help you

solve the problem?

Why'd I accept?

I didn't think you'd risk missing out

on a major step forward.

And you think I'm funny.

So funny.

But no interference from Werner.

It's all our work and discoveries.

It's tricky with regard to Werner.

Lucas, yes or no?

We'll control the number of solutions

with the singular function.

So decompose minor and major arcs.

You have to make that noise?

Sorry, it helps me think.

- What helps you concentrate?

- Silence.

Received loud and clear.

Problem solved.

We need to isolate the factor

with the Euler function, actually.

You want veal or beef stew?

Veal.

Want a beer?

Sure, thanks.

Big place you have.

You live alone here?

My roommate's doing a dance course

in Montpellier.

Incoming text.

Who from?

All alone tonight?

I want you so bad...

From Yanis.

Sounds eager to see you.

What?

So Marguerite has a life

outside of math.

Boyfriend?

No, it's just recreational.

"Recreational"!

Why a passion for Goldbach at 11?

I always loved math.

From your father or mother?

You're always so inquisitive?

It's just normal, right?

You never ask questions?

It's no help with Goldbach.

So working relationships

are pointless?

For me, they're vital to progress.

- Good luck getting on with Werner.

- Precisely.

I'm hoping you're less rigid than him.

You'll do anything to succeed,

whoever you work with.

Back to work?

No, it's 2 am. I'm going home.

"Life outside of math"!

See you Wednesday.

Tomorrow, I'm with you-know-who.

Thanks for dinner.

See you Wednesday then.

Yup, Wednesday.

Can I help?

This isn't working for me.

How come?

Sometimes, you hit a wall.

Actually, you're the wall.

Your earplugs make me feel

like I'm sound pollution.

Problem solved.

No, Marguerite.

You're too cold and closed.

It won't work, we're too different.

You like Chinese?

Math comes from my mother.

She teaches in middle school.

I started helping grade tests

when I was little.

She wasn't well.

My father had just left her.

Back then, I suffered from insomnia.

Full of anxiety about infinity,

the idea that...

the universe had no end.

So, in the library,

I read all the math books I could find

to solve tangible problems

that have solutions.

And one day, I...

I came across Goldbach's pyramid.

A currently unsolved problem

with its infinity of prime numbers.

It was...

such a challenge.

A problem...

so complex and magnificent.

I knew I'd spend my life

trying to solve it.

Goldbach was a way

of putting order into infinity.

Your mother raised you?

Yes.

My father left when I was 9.

We lived in Berlin then.

When he left us,

my mother chose to move back to France.

You still see him?

No.

He lives in Canada. We're not in touch.

And you? From your father or mother?

Neither.

Dad's a financial advisor.

Mom's an antique dealer.

They never understood

why I chose research.

An occupation that pays so badly.

Evening, Marguerite.

Your boyfriend?

No, a colleague.

She's the best mahjong player

in the neighborhood.

Mahjong?

She's very good.

Enjoy your evening.

Yes, I came across it after ENS.

I play in illicit, local gaming rooms.

From mahjong.

So funny.

So, tomorrow, are we working together?

It's still early.

Back at it?

How about we try this?

Or else, like this.

Or this.

Then this.

And this.

Beautiful.

I hate being stuck like this.

A prof at Oxford,

working on the Riemann theorem...

When he got stuck,

he let off steam by pumping iron.

He never proved Riemann

but he's a bodybuilder now.

I like your hair.

You do?

It won't stay in place.

I like the disorder.

I have my mom's hair.

Straighter than straight.

It suits you combed back like that.

It's very...

Class whiz?

How about using distribution

of prime numbers to find a lower bound?

Yes, but for our method to work...

we need to maximize sieve functions.

Exactly.

Race you to the apartment.

Can I come in a minute?

I hope this isn't a bad time.

I came at your mother's request.

You may wonder

what it has to do with me...

but she was so worried

that I felt partly responsible

for what we might call your slide.

I know how mathematics

can make a person vulnerable.

We carry within us

an obsessive aspect,

which can be even more dangerous

mixed in with gambling.

You're not the first mathematician

it's happened to.

You're working on Goldbach.

It's none of your business.

I had a long rivalry

with an ENS colleague

who also worked on prime numbers.

We despised each other.

I was quite relieved

when he left to teach at Yale.

Five years later,

he won the Fields Medal

by proving what I was looking for.

So I moved onto

an even more ambitious goal.

Goldbach.

Since Szemerdi,

I know it will be proved one day.

By me...

or someone else.

You need to be solid

to work on Goldbach.

It's a labyrinthine problem

that you can wander around for ages

until it eats you up completely.

Be very careful, Marguerite.

You know, ultimately,

who gets there is irrelevant.

The main thing

is progressing mathematics.

The rest is pride

and it's equal to zero.

Seriously, he just rocks up here?

What did he want?

To see what I was working on.

We're running out of space.

It won't be dry before tomorrow.

Can I sleep here tonight?

Take Noa's room. The bed's made.

Goodnight.

Didn't we say 2 pm?

- You didn't get my email?

- No.

Ending our work sessions for Lausanne.

- We're sufficiently prepared.

- Fine.

As for your thesis,

it can wait till after Lausanne.

Sure, there's no hurry.

Hey Noa, this is Lucas,

who works with me.

Pinch me, this is getting stupid.

Ask me before you repaint!

I'm talking to you!

Sorry, I'm onto something

really important.

And you think I wasn't?

Sorry, I absolutely must finish.

You okay?

You'd know

if you listened to my messages.

Is she for real?

My fucking bedroom!

I'm gonna take off before I really flip.

I think I've got the last movement.

You check. I'll grab a shower.

You were right.

We're proving a swathe of Goldbach.

Something wrong?

It doesn't stand up.

Same old parity problem.

Looks good but it's an abyss.

How come?

It opens up way more boxes.

Checking the conditions is even harder

than the arithmetic progressions.

We find a new method or have

an exponential number of proofs to make.

Infinite.

Right, I see what you mean.

Anyway, we made a huge leap forward.

The conference is in two weeks.

We're screwed.

If it's not this year, then next.

This is Werner's year.

Look, I get it,

but this doesn't negate all we've done.

It'll just take a bit longer.

It's all good.

It might take months or years

to prove his movement.

Werner might get there first.

You want to prove Goldbach

for him or you?

You don't give a shit.

Your Szemerdi proof

gets you to Lausanne.

Afterwards, why'd you work with me,

when you'll have offers worldwide?

You'll go solve the problem

with someone else.

You're like every mathematician.

Be the best at all costs.

Right, like all the others,

I'll walk out on you.

Don't you see you have a problem?

Waiting for everyone to betray you.

Can't you imagine

you matter to someone?

I was wrong to ask you

to work with me.

I'm not cut out for it.

- You really believe that?

- Yes.

- What's that mean? We're done?

- Yes.

You're losing it...

I'd like you to leave now.

Now.

You know you said

I'd do anything to succeed?

You were right. I sacrificed my PhD

with Werner to work with you.

That's impossible.

I counted.

That's not possible.

He can't have that tile.

It's been played.

It's been played.

There's one extra. It's impossible.

He's cheating.

He cheated. Look, I'll show you.

He cheated!

It's impossible.

I counted the tiles.

He cheated, sir. He cheated!

Monsieur Kong called. What's going on?

What day is it?

For the train station. Take care of her.

Thanks for everything.

Don't bitch out on me. Keep in touch.

Have a good trip.

Mom...

I think I've met someone important.

It's strange.

I think about him more than math.

You're in love?

Perhaps.

You know, Marguerite...

Even if it ended badly with your dad...

I've never forgotten

how happy I was with him.

Lucas, it's Marguerite.

I wanted to tell you,

yesterday I...

I found a drawing

of Goldbach's pyramid in my room,

and I saw it upside down.

I must see you.

I'll take my mom's car

and I'm on my way.

Excuse me,

it's okay.

You can't just appear out of the blue.

I have the last movement.

It's all about perspective.

It's magnificent. I have to show you.

Coming?

A room with a board, this way.

Follow me.

We begin with a circle method

with decomposition in major and minor arcs

to control the number of solutions.

Apparently a girl in the auditorium

is doing a wild proof...

I heard it's a proof of Goldbach.

We introduce a sum weighted

by Selberg weights.

The Goldston-Pintz-Yildirim method.

Exactly.

That's it.

You've found a path.

She's my student.

I love you.

for my mother