Professor Abraham came out to the front gate to see Seoha off.
Seoha bowed his head several times to express his gratitude before blending into the crowd and fading into the distance. Abraham remained standing there until Seoha’s figure had completely disappeared.
“What is the God of Fate plotting now?”
He was a mathematician, but he was also a fatalist.
His colleagues would sometimes tease him. They found it absurd for someone who made his living with numbers to talk about fate. But Abraham paid them no mind and simply laughed it off.
He did not bother to explain. There were things one came to understand only after long dealings with numbers. The question of whether there was truly any room for coincidence in a world that operated with such high precision.
Probability was predicated on ignorance. Humans called something coincidence simply because they could not know every variable.
He thought about Seoha.
A young man who had appeared in the mathematical world at a tender age and was solving centuries-old unsolved problems one after another. Assuming it was a coincidence, what were the odds of that?
He shook his head and let out a short laugh.
“As if it could be coincidence.”
Seoha’s abilities had already transcended the realm of probability. Abraham felt a powerful pull of destiny.
The world was moving. In a direction no one could foresee.
Certain systems leap into an entirely different state the moment specific conditions are met. Water boils past 100 degrees Celsius, stars collapse, and civilizations reach turning points.
He reflected on what had transpired over the past century.
The long silence of the mathematical world.
Some attributed it to the difficulty of the problems; others spoke of the limitations of human intellect.
But the mathematical world had not been idle all that time. The language of computation had grown precise, topology and information theory had joined hands, and finally, analysis and number theory had fused to make infinity tractable.
A hundred years of preparation.
The system had been readying the conditions on its own.
And when all the conditions were met, Seoha appeared.
“My teacher and I were never variables either.”
So Abraham decided he might as well become an observer.
Suddenly, his teacher’s words came to mind.
“Some proofs, only after decades or centuries pass, do we learn why they were needed.”
He was certain.
That the reason he held his teacher’s records would prove to be the same.
* * *
Okcheon, Chungbuk.
Seoeun had been doing her homework but stopped to check the clock. It was already the third time in ten minutes.
“There’s still over an hour left?”
3:47.
Seoeun set down her pencil.
The homework Uhyeon had given her was of a different nature from the problems she had been solving until now. Seoeun had picked out only the interesting ones from among them and solved those.
She closed her textbook and paced around the yard. Various plants were visible in the vegetable garden.
Pumpkins, perilla, chili peppers, cherry tomatoes.
All of them had been planted after returning to Korea, together with her family.
On one side of the yard was a persimmon tree she and her brother had tended together since childhood. It was still unripe, but in a little while, the persimmons would hang heavy from every branch, filling the yard with a vivid orange hue.
“I’ll make dried persimmons with Mom.”
Seoeun clenched her small fist as if making a pledge.
Her gaze turned toward a corner.
*We used to play a lot over there too.*
Seoeun’s oldest memory was of running around wildly here with her brother.
Her brother had always followed one step behind so he could catch her if she fell. On snowy days, he always went outside with her to ride sleds and build snowmen.
*He was only my age back then.*
A sharp pang pierced one side of her chest.
It would have been a lie to say she hadn’t felt regret when they said they were returning to Korea. She hadn’t wanted to part with her close friends. But she had missed this place even more.
The days when she had a brother who cared only for her.
Now he had become a world-renowned mathematician who had to live up to everyone’s expectations. The world made a fuss, saying Seoha had achieved unbelievable feats, but Seoeun couldn’t quite understand what the big deal was.
“Idiots. I’ve known since I was five that my brother is the smartest person in the world.”
She felt a bit dejected that his attention seemed to have drifted slightly away from her.
But she couldn’t remain a child forever. Seoeun decided to follow the path her brother had walked. Starting with the Olympiad.
And this time, she would win the gold medal and give it to her brother as a gift.
“Huh?”
A small figure could be seen in the distance.
He had grown much taller, but the sight of him pulling his suitcase was no different from before. Seoeun felt the urge to run out to him but forced it down.
“I’ll wait! I’m in middle school now.”
Tick, tock.
Why was time moving so slowly?
Was it because they hadn’t seen each other in two weeks, or because she had been drowning in memories since returning to her hometown? The clattering sound of the suitcase wheels grew louder.
Screech—
“Seoeun, I’m back.”
Seoeun turned her head.
At the sound of the voice she had longed for, the dam she had held back collapsed all at once. Seoeun couldn’t contain herself any longer and jumped off the wooden porch. Wearing dusty sandals, she ran across the yard.
“You’re late! You said you’d come before five!”
Seoeun shouted sharply and wrapped her arms tightly around his waist.
A familiar, long-forgotten scent wafted from her brother’s clothes. Seoha flinched in surprise, but soon smiled brightly and carefully stroked Seoeun’s hair.
“Sorry. Traffic was bad.”
Seoeun grabbed her brother’s large hand and pulled.
“Hurry inside. Mom made food.”
Miyeong, who had been sitting at the edge of the wooden floor watching the two siblings, tidied her manuscript and stood up.
“Welcome back.”
“I’ve returned.”
“You’ve worked hard. Go wash up quickly. Seoeun helped prepare food all morning because she heard you were coming.”
“Mom!”
At Seoeun’s protest about why she would say such a thing, Miyeong let out a pleasant laugh.
The fragrant aroma filling the house.
Seoeun moved quickly, carrying plates to the table. Seoha picked up his chopsticks and spread a pumpkin leaf on his palm. On it, he placed freshly cooked rice and homemade soybean paste.
“I’ll eat well.”
A simple yet perfect taste spread throughout his mouth. His stiff, taut nerves relaxed. Seoeun stopped eating and stared intently at her brother’s face.
“Is it good?”
Seoha nodded at Seoeun, who asked with sparkling eyes.
“Yeah. Better than any feast in the world.”
Only then did Seoeun hum a tune in satisfaction and move her utensils busily.
* * *
He had returned to daily life.
He ate the food his mother made at home and looked over his sister’s homework.
Seoha changed the exam problems his sister disliked into fun ones. In his hands, complicated competition formulas transformed into geometric shapes.
Seoha continued drawing small squares. And finally, a massive pyramid was completed. Seoeun’s eyes sparkled as she derived the degree the problem asked for.
“Smart girl. Well done.”
“Ehehe!”
Pleased by Seoha’s praise, Seoeun grinned broadly.
His sister lacked the patience to become a mathematician. But that wasn’t something you could acquire through teaching. When she one day encountered a problem she desperately wanted to solve, then.
He had started exercising early on, determined not to die young like Ramanujan, but as time went by, physical activity was becoming bothersome.
Seoha steeled his mind and ran a lap around the neighborhood.
Swoosh.
He entered his room and sat at his desk.
He felt the cold touch of metal in his pocket. It could no longer be put off. Seoha had not yet opened it. He felt sorry about prying into the years of anguish his mentor had left behind.
He took out the memory stick and placed it on his palm.
A small, worn USB drive.
Tick.
After a brief hesitation, he plugged the USB into the laptop port.
With a light mechanical sound, several folders appeared on the screen. Inside, only dates had been recorded. Seoha double-clicked the oldest folder.
Scanned handwritten notes.
Formulas had been scribbled messily on the paper. But Seoha read them at a glance.
‘An abstract?’
It was a record from 1970.
A draft of the paper later known as the Cook-Levin Theorem. But it was one year earlier than the date Cook presented it.
Before leaving Texas, Abraham had told Seoha about his teacher. Levin had a habit of rarely publishing his ideas as formal papers, preferring to share them verbally. This was likely a memo someone had compiled.
The Western academic world had called it “Cook’s Theorem” for a long time, but it was only after Levin emigrated to America that his contribution was recognized and the name was changed to the Cook-Levin Theorem.
“Hahaha! My teacher never felt wronged about this at all.”
The corner of Seoha’s mouth rose.
It was because he had taken a liking to Levin.
Click.
The second folder.
This, too, was a slip of paper on which only an idea had been written.
[There is a magical algorithm that can solve every computable problem. Try every possible method simultaneously. If you allocate more resources to the faster ones, you can always obtain an algorithm that is slower than the optimal by a fixed ratio.]
“Huh?”
Seoha stared at the note and then began writing formulas like mad.
Scratch scratch.
At a glance, this problem seemed far too easy.
Perhaps even a first-year undergraduate could scoff and prove it.
“If you send people in every direction of a maze, someone will reach the exit eventually. But so what?”
One might ask such questions.
But Seoha could see it. This was merely the prelude. What Levin really wanted to say was about the ratio. If one could obtain an algorithm that was exactly k times slower than the optimal?
‘So this is why he called it riddled with traps.’
Abraham’s complaints now made sense.
Who, in an algorithm whose very purpose is to find the fastest route, would deliberately take a detour?
“Hahaha! Interesting! It’s so absurd.”
Seoha covered his mouth and laughed loudly without realizing it.
The ratio could be derived even now.
Provided, of course, that the optimal algorithm was already known for the problem. But why would anyone use a slower method when they already knew the optimal solution?
“Levin, did you really try to do this?”
No one who saw this could have grasped his true intention. But Seoha could.
Levin had tried to infer a constant (ratio) from the very structure of the problem. And this was a conclusion that could only hold when P equals NP.
‘This problem is unsolvable. But…’
Seoha had no intention of solving all the Millennium Problems. Some of them didn’t interest him at all.
However, having created a cipher that humanity would use for hundreds of years to come, he wanted to guarantee its stability theoretically.
Deoki opened its eyes in the darkness. It licked its lips as if hungry.
[So this is the next prey? I like it.]
Deoki might be satisfied for a moment, but its hunger was never sated. Seoha decided to accept that fact. And when he someday found a formula that explained all the principles of the world, then he would see what expression this wicked duck would make.
“I want to delve deep into this problem.”
He blinked his eyes greedily.
[As much as you like.]
This was the second time he was tackling a Millennium Problem. What kind of monster was waiting inside?
Seoha took a deep breath and closed his eyes.