Chapter 203
Translator: Dreamscribe
Professor Abraham walked all the way out to the school gate to see Seo-ha off.
Seo-ha bowed his head several times in gratitude before slipping into the crowd and drifting away. Abraham remained standing there until Seo-ha's retreating figure had vanished completely.
"What is the god of fate scheming this time, I wonder?"
He was a mathematician, but he was also a fatalist.
His colleagues teased him about it now and then. They found it absurd that a man who made his living off numbers would go on about fate. But Abraham paid them no mind and simply laughed it off.
He never bothered to explain. When one works with numbers long enough, one comes to understand certain things instead. The question of whether chance truly has any place at all in a world that runs with such exquisite precision.
Probability presupposes ignorance. It is only because humans cannot know every variable that they attach the name "chance" to things.
He thought about Seo-ha.
A young man who had appeared in the world of mathematics at a tender age and was solving problems centuries old one after another. If one assumed it was mere coincidence, what on earth were the odds of that?
He shook his head and let out a soft chuckle.
'As if it could be coincidence.'
Seo-ha's ability had already left the realm of probability behind. Abraham felt the strong pull of fate.
The world was moving. In a direction no one could foresee.
Certain systems, the moment they satisfy a particular condition, leap into an entirely different state. Water boils past one hundred degrees Celsius, stars collapse, and civilizations reach their turning points.
He reflected on what had happened over the past century.
The long silence of the mathematical world.
Some blamed it on the difficulty of the problems; others spoke of the limits of human intellect.
But the field had not been idle all that while. The language of computation had grown more precise, topology and information theory had joined hands, and at last analysis and number theory had fused together, making it possible to handle infinity.
A hundred years of preparation.
The system had been assembling its own conditions all along.
And when every condition was met, Seo-ha appeared.
"Even my master and I were never the variables."
If that was the case, then Abraham decided he would rather become an observer.
Suddenly the words his master had once spoken came back to him.
"With some proofs, it's only decades, or even centuries, later that we come to understand why they were ever needed."
He was certain.
That the reason he had come to possess his master's records was surely the same.
* * *
Okcheon, North Chungcheong Province.
Seo-eun looked up from her homework at the clock. In the space of ten minutes, it was already the third time.
"There's still more than an hour to go?"
Three forty-seven.
Seo-eun set down her pencil.
The homework Woo-hyun had assigned was different in character from the problems she had been solving up until now. Seo-eun had gone ahead and picked out only the interesting ones to solve.
She closed her textbook and paced around the yard. The various plants growing in the vegetable patch.
Pumpkins, perilla, chili peppers, cherry tomatoes.
All of them planted together with her family after they returned to Korea.
In one corner of the yard stood a persimmon tree that she and her oppa had tended together since they were little. It was still unripe, but before long the branches would hang heavy with persimmons, filling the yard with their vivid orange.
"I should make dried persimmons with Mom."
Seo-eun clenched a small fist as if making up her mind.
Her gaze drifted toward the corner.
'I used to play over there a lot too.'
Seo-eun's oldest memory was of running around this place with her rambunctious oppa.
Her oppa had always followed one step behind her, so that he could catch her if she fell. On snowy days he would always go outside with her, pulling her on a sled and building snowmen.
'Back then oppa must have been only as old as I am now.'
A pang shot through one side of her chest.
It would be a lie to say she had felt no reluctance when they told her they were returning to Korea. She hadn't wanted to part from the friends she'd grown close to. But more than that, she had missed this place.
The days when she'd had an oppa who cared for her and her alone.
Now he had become a world-class mathematician who had to live up to everyone's expectations. The world was making a great fuss about how Seo-ha had achieved something unbelievable, but Seo-eun couldn't quite understand what all the noise was about.
"Fools. I've known my oppa was the smartest person in the world since before I turned five."
It stung a little, the sense that his gaze had drifted slightly away from her.
But she couldn't stay a child forever. Seo-eun had decided to follow the path her oppa had walked. Starting with the Olympiad.
And this time she would be the one to win the gold medal and give it to her oppa as a gift.
"Huh?"
A small figure appeared in the distance.
He had grown much taller, but the way he came along pulling a suitcase hadn't changed in the slightest from the old days. Seo-eun felt the urge to run out to him, but she pressed it down hard.
"Let's wait! I'm a middle schooler now."
Tick, tick.
Why was time crawling by so slowly?
Was it because they hadn't seen each other for two whole weeks, or because she'd come home and gotten lost in her memories? The rattle of the suitcase wheels was growing louder and louder.
Creak-
"Seo-eun, your oppa's home."
Seo-eun's head turned.
The moment that beloved voice reached her, the dam she'd been holding back collapsed all at once. Seo-eun couldn't hold it in any longer and leapt down from the wooden platform. She dashed across the yard in her dusty sandals.
"You're late! You said you'd be here before five!"
Seo-eun shrieked and threw her arms tightly around his waist.
His clothes carried a dear, familiar scent she had long forgotten. Seo-ha seemed startled for a moment, but then he broke into a bright smile and carefully smoothed down Seo-eun's hair.
"Sorry. Traffic was a little bad."
Seo-eun tugged at her oppa's big hand.
"Come inside, quick. Mom made food, you know."
"Welcome home."
"I'm home."
"You must be worn out. Go wash up and come back out. Seo-eun helped prepare the food all morning because her oppa was coming."
"Mom!"
At Seo-eun's protest of why she would say such a thing, Mi-young let out a pleased little laugh.
A fragrant smell spread through the whole house.
Seo-eun moved quickly, carrying plates over to the table. Seo-ha picked up his chopsticks and spread a single pumpkin leaf across his palm. On top of it he laid freshly cooked rice and the gangdoenjang they had made themselves.
"Thank you for the meal."
A humble but perfect taste spread through his mouth.
The nerves that had been stiff and taut relaxed. Seo-eun had stopped eating and was staring intently at her oppa's face.
"Is it good?"
To Seo-eun, who asked with sparkling eyes, Seo-ha nodded.
"Yeah. Better than any feast in the world."
Only then, looking satisfied, did Seo-eun hum a little tune and busily go back to work with her spoon.
* * *
He had returned to everyday life.
Eating the food his mother made at home, and helping his little sister with her homework.
Seo-ha reworked the exam problems his sister hated solving into something fun. In his hands, competition equations that were nothing but complicated turned into figures.
Seo-ha kept drawing small squares one after another. And at last, a giant pyramid was complete. With sparkling eyes, Seo-eun derived the degree the problem was asking for.
"Clever. Well done."
"Ehehe!"
At Seo-ha's praise, Seo-eun grinned wide, her mouth spreading open with delight.
His sister lacked the patience to become a mathematician. But that wasn't something one could gain by being taught. Someday, if she ran into a problem she desperately wanted to solve, then.
He had started exercising early on, resolved not to die young the way Ramanujan had, and yet lately moving his body was becoming more and more of a chore.
Seo-ha steeled himself and ran a lap around the neighborhood.
Swish.
He came back into his room and sat down at his desk.
He felt the cold touch of metal in his pocket. He could no longer put it off. Seo-ha still hadn't opened it. Peering into the years of anguish his late mentor had left behind felt like an intrusion.
He took out the memory stick and set it on his palm.
A small, worn USB.
Tick-
After a moment's hesitation, he plugged the USB into the laptop's port.
With a faint mechanical hum, several folders appeared on the screen. Inside, there were only dates recorded, nothing more. Seo-ha double-clicked the oldest folder.
Scanned handwritten notes.
Equations had been scrawled messily across the paper. But Seo-ha read through them in a single glance.
'An abstract (a short piece summarizing the core content of a paper)?'
A record from 1970.
A draft of the paper known as the Cook-Levin Theorem. And yet it was dated a full year before the day Cook had published his.
Before he left Texas, Abraham had told Seo-ha the story of his master. Levin had a habit of rarely publishing his ideas as formal papers, sharing them only by word of mouth. This was likely a note someone had jotted down of one such idea.
For a long time Western academia had called it "Cook's Theorem", and only after Levin immigrated to the United States was his contribution recognized and the name changed to the Cook-Levin Theorem, or so the story went.
"Hahaha! My master never felt the least bit wronged about it."
The corner of Seo-ha's mouth lifted.
It was because he had taken a liking to Levin.
Click.
The second folder.
This one too was just a scrap of paper describing an idea.
[There exists a magical algorithm that can solve every computable problem. Try every possible method at the same time. If you give more resources to the faster ones, you can always obtain an algorithm that is slower than the optimal solution by a fixed ratio.]
"Huh?"
Seo-ha peered at the note and then began writing out equations like a man possessed.
Scribble.
At first glance the problem looked far too easy.
Maybe even a first-year undergraduate would scoff and prove it.
"Send people off in every direction of a maze and sure, someone will reach the exit. But so what?"
Posing a question like that.
But Seo-ha could tell. This was merely the preface. What Levin really wanted to talk about was the ratio. What if one could obtain an algorithm exactly k times slower than the optimal solution?
'So this is why he said it was full of traps.'
Abraham's complaint made sense now.
In an algorithm whose whole reason for being was to find the fast path, who would deliberately take the long way around?
"Hahaha! Isn't it fun! It's so completely absurd."
Before he knew it, Seo-ha had clapped a hand over his mouth and burst out laughing.
The ratio could be found even now.
But only for problems where the optimal algorithm was already known. And yet if one already knew the optimal solution, what reason would there be to use a slower method?
"Levin, did you really mean to try this?"
No one who saw this could have grasped his true intent. But Seo-ha could.
Levin had been trying to deduce the constant (the ratio) from the very structure of the problem itself. And this was a conclusion that could only hold if P equaled NP.
'This problem can't be solved. But....'
Seo-ha had no intention of solving all of the Millennium Prize Problems. A few of them held no interest for him whatsoever.
But as the one who had created the cipher that humanity would use for centuries to come, he wanted to guarantee its security theoretically.
In the darkness, Ducky opened his eyes. He smacked his lips as if hungry.
'So this is the next meal? I like it.'
Ducky's hunger, satisfied though it might be for a moment, could never truly be filled. Seo-ha had decided to accept that fact. And someday, once he had found the equation that explained every principle in the world, Seo-ha intended to see just what sort of face this nasty duck would make.
"I want to dive deep into this problem."
His eyes gleamed greedily.
'As deep as you like.'
This was the second time he was taking on a Millennium Prize Problem. What kind of monster lay in wait inside this one?
Seo-ha took a deep breath and closed his eyes.
*****
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