FADE IN:

EXT. MOUNTAINS - DAY

A forest of pine trees covered in snow, a mountain range in the horizon. The voice of a man:

   VOICE OVER:
     A scholar will spend his whole life trying to solve a problem they've invented. But what to do they do when they've solved it? Some publish, others think it unimportant and tuck it into a forgotten notebook. Others are too scared of being proven wrong, and don't tell a soul.

EXT. SNOWY FOREST - DAY

The ground is thick with a carpet of snow, a dirt path winds along the ground.

   VOICE OVER:
     I wasn't scared to publish, no. I was scared to begin.

A horse-drawn carriage bumps along the path.

Text: Carpathian Mountains, 1838.

Inside the carriage is the man whose voice we've been hearing, Dr. Alistair Baines, a mathematician and British scholar of middle age, bringing sheets of old paper with scribbled notes and graphs. He's bundled up in navy blue, clearly not used to the cold, and in ill-health. He's adjusting his coat repeatedly, unable to get it to lay right and block the cold.

A manor appears at the end of the path. The grounds are ill-kept, as if abandoned, or meant to ward off visitors. Smoke is coming from the chimney.

The carriage pulls to a stop in front of the main door, and the carriage driver jumps from his seat and pulls the carriage door open. Dr. Baines steps out. He struggles to pay the driver in foreign currency.

   DR. BAINES
     Tell me, sir, what hour will you arrive for my return to the village?

   DRIVER
     By eight o'clock, sir. Sharp.

   DR. BAINES
     I have much to discuss with the Professor, surely you can extend our return?

   DRIVER
     I wouldn't dare, sir. I don't travel at night. There are wolves, and the cold and wind is dreadful.

Dr. Baines approaches the door of the house while the driver watches. A silhouette of a face appears in the windows of the house, watching Dr. Baines.

   DRIVER
    (Calling out)
     Tell me, what could possibly be this important?

   DR. BAINES
     Pardon?

   DRIVER
     To visit the professor, I mean. Haven't you heard the talk? They're old wives' tales and a proper man shouldn't indulge, but... They say the Professor is a recluse, a loony. He sits in silence, year-long, and a man can only go so long like that before his mind begins to crack.

   DR. BAINES
     You're quite right, a proper man shouldn't listen to such things.

The driver jumps atop the carriage and pulls away, leaving Dr. Baines alone in front of the massive house. Before using the knocker he doubles over in a fit of coughs into a handkerchief. He stows it in his pocket, noting specks of blood.

Dr. Baines uses the knocker and the door opens. Standing in the foyer is Professor Andrei Tudose, an older man dressed in warm and comfortable clothing, all in brown.

   DR. BAINES
     Dr. Tudose, I can't express my gratitude for your seeing me. I've heard much talk.
     I’m Dr. Baines.

He offers his hand to Prof. Tudose, who shakes it.

   PROF. TUDOSE
     Likewise. Pray, come in.

INT. TUDOSES' SITTING ROOM

The sitting room is well-lit by oil lamps hung on the walls between windows, and a roaring fire in the hearth. The two men sit opposite in arm chairs, a large coffee table between them. Dr. Baines has removed his outerwear, and in a navy blue shirt. Prof. Tudose is sitting next to the fire. He's poking at it with an iron poker as they talk.

   DR. BAINES
     I have a problem, and no one I've talked to has been able to help me. But I've been told that you may be unique.

Dr. Baines passes his notes to Prof. Tudose, who puts down the poker and studies them.

   PROF. TUDOSE
     Partitions, that's what this is about?

   DR. BAINES
     Similar, but not quite. They're called colourings.

Dr. Baines sits forward and points at a drawing on his notes.

   DR. BAINES
     Think of drawing a map. No two touching countries may share a colour. How many colours are required to guarantee a proper colouring for any given map?

   PROF. TUDOSE
     You've travelled from England to my land to ask of this?

   DR. BAINES
     I first proved that one can colour any map with six colours, and then later dropped the limit to five, but I have tried hundreds of maps and yet to find a single one that requires more than four colours. I posit that four is the true limit, yet the proof escapes me.

   PROF. TUDOSE
     Your methods don't work for the four case?

   DR. BAINES
     Nothing does, it's unsolved. I've talked to the best professors, and none can find a solution. I've been pursuing this problem for quite some time. If you can help me solve this, I can return to England a content man.

Prof. Tudose studies Dr. Baines, who's fixing the collar of his shirt. Prof. Tudose's eyes glint with recognition.

   PROF. TUDOSE
     I'll see what I can do.

   DR. BAINES
    (Relief)
     Thank you, sir. I swear, this will be worth it.

INT. TUDOSES' SITTING ROOM - LATER, ALMOST EVENING

The day's dying light is coming in through the window, and snow is falling. Dr. Baines's notes are sprawled over the table.

The two men are deep in concentration, each at the end of glasses of dark red wine. A half full bottle lies on the table next to Prof. Tudose. There is no drinks cart, nor food, as Prof. Tudose is not used to hosting.

   PROF. TUDOSE
     I suppose you've tried expanding from a base case.

   DR. BAINES
     That worked with the five case, but breaks at four. The pattern escapes my insight.

Prof. Tudose puts down the notes as Dr. Baines rubs his hands to keep them warm.

   PROF. TUDOSE
     I've looked, as promised, so answer me this. Why such a trifling problem? Surely a man with your renown has bigger puzzles at hand?

   DR. BAINES
     In my years of mathematics, dare not surpassing your own, I've found the most curious solutions in the simplest of questions, and this, sir, is the simplest.

   PROF. TUDOSE
     Conjectures have killed men. Simple statements that prove un-provable. A battle you can never win.

   DR. BAINES
     You, of all men, I wouldn't think an adversary of discovery.

Prof. Tudose moves a log with the poker, making the fire jump and illuminate his face.

   PROF. TUDOSE
     An adversary of discovery I may not be, yet I find myself growing ever familiar with the dangers of obsession.

   DR. BAINES
     It's obsession that drives brilliant minds, Professor. Who would Newton have been without his pages of scrawling computations? Or Euler and his volumes of writings?

   PROF. TUDOSE
     I thought similarly, when I was younger.

   DR. BAINES
     It's my ultimate problem. I'd do anything to solve it. That, I cannot concede.

Prof. Tudose refills both their glasses with more red wine.

   PROF. TUDOSE
     You're not the first, you know. Others have come to ask for my advice, since my retirement.

   DR. BAINES
    (Hesitant)
     What of them?

   PROF. TUDOSE
     I didn't let them in.

Wind screeches outside. Snow has begun to fall more heavily.

   PROF. TUDOSE
     Curious, I was not expecting a flurry.

Dr. Baines rushes to the window, where a storm rages outside.

   DR. BAINES
     The carriage, will it still come in this weather?

   PROF. TUDOSE
     I fear not. With these slopes, snowfall could beget a slide. The whole path could be swept from underneath you. Do not fret, for you may stay with me for the night.

   DR. BAINES
     I appreciate the sentiment, Professor, but I must be going. I haven't eaten, and I shan't impose-

   PROF. TUDOSE
     Unthinkable. No one is coming, Doctor. You must stay, I insist. We've yet to solve your problem.

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