When he closed his eyes, the world changed.
A space where noise was cut off, scents grew faint, and only formulas remained. Seoha had long been familiar with this state. As if sinking into deep water, his consciousness quietly deepened.
Levin’s note slowly unfolded in his mind.
‘Try every possible method at the same time.’
A sentence that seemed simple.
But Seoha read the meaning it implied. Levin had not been talking about parallelizing an algorithm or increasing speed. He had been talking about structure.
Levin had also attached one more clue.
‘If more resources are allocated to what is fast.’
The “simultaneous” Levin spoke of likely did not mean increasing the number of physical operations. What was slow would not receive an allocation of resources. Thus, it would naturally disappear.
‘A structure where wrong answers destroy themselves?’
There was a problem. How could one know what was fast when one did not know the answer?
He had fallen back into circular logic.
But Ducky did not stop thinking. Seoha continued his thoughts from a distance away from the problem. His brain spun furiously.
In Seoha’s mind, formulas began to rearrange themselves.
Countless paths and candidate groups. Each flowed along a different computational route. It was a task requiring tremendous computational power and thinking ability, but to Ducky, it was closer to play.
“Not knowing the answer doesn’t mean there’s no method.”
Seoha grinned.
He only needed to define speed as a different concept. Not a consequential number, but acceleration granted by logical consistency. A path with a logical flaw was bound to get caught somewhere.
Click. Click-click.
His thought was correct. The formulas that had been repeating contradictions while trapped in circular logic began to fit together.
Some candidates connected smoothly.
They moved naturally to the next stage without unnecessary branching.
On the other hand, some candidates demanded many assumptions to survive after only a few steps.
“Ducky, this is…”
Seoha realized it.
Ducky nodded as if in agreement.
‘Yes, that’s right. Being slow doesn’t refer to time.’
“It meant the cost of survival was high.”
After two hours, Seoha opened his eyes. Then he approached the board and began frantically writing formulas.
Time into space.
Sequence into distribution.
In Yu-Riemann geometry, a space encompassing all of this could be unfolded.
Scribble, scribble.
His intuition was telling him that something incredible would come out at the end of this.
Seoha could not stop trembling.
* * *
“Seoha.”
Miyeong carefully knocked on his door.
“…”
There was no answer.
When she opened the door, Seoha was asleep, sprawled over his desk. A pencil was still clutched in his hand. What met her eyes were a board and papers densely packed with formulas.
In the middle of the night, Seoha had failed to replenish his lacking sugar and had finally fallen asleep as if he had passed out.
Rustle.
She brought over a folded blanket from one side of the room and draped it over Seoha’s shoulders.
“Is Oppa sleeping?”
Seoeun had woken up at some point and come outside.
“Looks like he was doing something all night, doesn’t it?”
“Yeah.”
Seoeun looked around the room.
Though she was outstanding, Seoeun only possessed knowledge at the level of an undergraduate, so she could not understand most of what was written on the board. She bit her lip, then quietly returned to her room.
Slide.
She opened the drawer of her desk.
A photo they had taken together by the Charles River, a bundle of cards her brother had made for her himself, a letter he had written before going to the training camp, and an introductory book on Yu-Riemann geometry she had painstakingly obtained without her brother knowing.
Seoeun had known from early on that she was different from her brother.
Not only in ability, but in temperament as well. However, though she herself had not realized it, there was a reason Seoeun had become someone who grew bored easily and gave up.
The existence of a brother who was far too smart.
‘If there’s something I don’t know, I can just ask Oppa.’
A habit that had become familiar from the moment she was born had inhibited Seoeun’s growth. She had never experienced the thrill of arriving at an answer herself after fierce contemplation.
At some point, Seoeun began to feel an inexplicable frustration. Even just now, the fact that she could not understand the formulas her brother had written had come to her as unbearable stress.
“Let’s try doing this alone.”
She opened the book.
On the inside of the cover was her brother’s face, looking somewhat nervous. On the facing page, the preface caught her eye.
「…The most beautiful moment in mathematics is not when one writes down the answer. It is the moment when someone who has long been blocked by a wall suddenly understands with their entire body why it must be so. And that moment belongs solely to oneself, something no one else can interfere with.
In the hope that this book may become a small stepping stone for you as you head toward that place.」
Seoeun read that section over and over for a long while.
For the first time in her life, the desire to understand something swirled violently within her heart.
Seoeun wiped the corner of her eye once with the back of her hand. Then she turned to the first page and began to read.
* * *
After two weeks of meticulous review, NIST officially declared Utopia the standard. The research institute was in a festive mood over the selection of the next-generation cryptographic standard—something they had hoped for, but had hardly dared to believe would happen.
As it was an issue that had drawn the attention of the entire world, the amount of coverage from Korean media was enormous.
[A Korean Cryptographic Algorithm Adopted as the Global Standard]
[Why Did NIST Choose Yu Seoha’s Encryption?]
[The Key to Online Security Is Now in Korea’s Hands. Praise Pours in for Apex Lab Korea]
The response from the public and experts was heated as well.
In particular, reporter Nam Gisun’s in-depth article was like a moving film.
The fear that a digital apocalypse was approaching, financial markets collapsing in real time—citizens had witnessed all of it with their own eyes. And at the most decisive moment, as if by a lie, a hero had appeared. Of course, the ending was a happy one accompanied by extreme dopamine and catharsis.
└This… means he saved the world, right? How are movie directors supposed to make a living? Reality is this insane.
└Probably? Didn’t you see the White House put up a message of thanks? lol
└No, no, don’t exaggerate. Even without Utopia, they would’ve blocked it with another encryption. It just got picked because it had the best performance.
└I’m screwed. I bought gold at the peakㅠㅠ I converted it into physical gold and put it in my wardrobe, what do I do?
└Where do you live?
Researchers were gathered here and there in small groups, shaking hands.
On one side of the hallway, people who had only exchanged greetings before were now raising their hands high and high-fiving each other whenever their eyes met.
One researcher asked in an excited voice.
“Director, aren’t you happy?”
“We’re only just getting started.”
The researchers nodded with solemn expressions.
The adoption of a cryptographic standard was not a full stop. From now on, Utopia would be placed in endless real-world conditions.
Unending supplementation work and an update hell. Of course, that was not something he had to do himself. Seoha gave them a light nod, then headed to the conference room.
The team members had taken their seats in the conference room early.
[Monday, 9 a.m., small conference room. I have something I’d like to propose about the team’s next objective.]
A single text sent by Seoha.
Theo could barely suppress his heart, which was pounding as if it might burst. Creating an encryption algorithm had been fun, but it had not been a difficult problem that could draw out the team’s full capabilities.
The tremendous catharsis he had felt when solving the Riemann Hypothesis. The more painful the process, the sweeter it was. Before he and the team members knew it, they had become dopamine addicts.
“What could it be? It must be a Millennium Problem, right?”
Ben asked, swallowing hard.
“It could be the Collatz Conjecture or Goldbach’s Conjecture.”
A theory where number theory would be the main focus, no matter what.
Sujeong clenched her fist.
“I’m voting for the Navier-Stokes equations.”
“I hope it’s the P=NP problem. I’ve been studying information theory like crazy these days. What do you think, Theo?”
Sri asked, looking at Theo.
“Hmm… I’m not sure. I have a feeling it might be something completely different.”
Clack—
Seoha opened the door and came in. Both hands were full of printed materials. Perhaps he had been researching all night, because the blood vessels in his eyes had burst and they were red.
“Hello! First, could you all take a look at this?”
He smiled brightly and handed the materials out to everyone.
It was a summary in his own way of what he had organized over the past few days. The team members accepted it without a word and began to read.
“Yes! It was the P=NP problem after all!”
Sri cheered. But Cecilia threw cold water on him.
“I don’t think so? Read further.”
“Ah… This is…”
Rustle.
As the pages turned one by one, the conference room gradually grew quiet. Before long, it finally fell into complete silence.
Seoha opened his mouth with a calm expression.
“Every time I read about P=NP theory, I felt a sense of incongruity. P is definitely not NP, but it felt like that wasn’t all there was to it.”
Seoha had created an energy called logical consistency from the note.
It was fresh. An idea no one had ever tried before. Theo glanced at Seoha’s face.
‘It’s like cellular activity in living organisms.’
In the structure Seoha had designed, each computational path functioned like a cell. The reason the P=NP problem had not been solved for decades was simple. Problems that multiplied infinitely had exhausted the system’s resources.
‘Are those things cancer cells, then?’
Seoha had arranged it so that only cells with traits suited to the objective would receive resources and differentiate into the next stage. It was an approach made possible because of Yu-Riemann geometry.
Rustle.
Every single team member read the notes and fell into deep thought.
Cecilia broke the silence.
“Seoha.”
“Yes.”
She asked with a grave face.
“You know your hypothesis directly clashes with the mainstream opinion of academia, right?”
“Yes. I know very well.”
In modern computer science and mathematics, the influence of the Turing machine was absolute.
The so-called deterministic worldview.
“This won’t just be ordinary criticism. Your hypothesis denies computational complexity theory itself, the foundation of computer science. The side that venerates Turing will go wild as if they’ve been blasphemed against. You’d be overturning the foundation built over the past seventy years.”
Ben quietly raised his hand.
“My mother is a biologist, so I know a little, but this hypothesis has a much deeper connection to biology. If this is proven, it’ll create breakthroughs in all kinds of research currently underway in that field. In my opinion, they’ll welcome it with open arms.”
Sujeong shook her head.
“I’m worried about the mathematics side. There are an enormous number of papers related to P=NP. But right now, you’re basically saying all of them have been barking up the wrong tree.”
P=NP was the holy grail of computer science. Thousands of papers on it poured out each year alone.
That was because this problem was directly connected to the entire direction of computer science. The fields were varied as well. Artificial intelligence, cryptography, philosophy touching on Gödel’s incompleteness theorems, and on top of that, Seoha had even brought in biology, including evolutionary theory.
Theo said, clutching his throbbing head.
“Looks like we might end up making a lot of enemies this time.”
He lifted the materials and read them again.
Was he excited? His hands were trembling.
To think they would challenge Turing—it was absurd.
The axioms he had established were so absolute that no one would even have thought to do so. But Theo had faith that Seoha’s intuition was never wrong.
“Ah, prophets are always persecuted, after all.”
Ben’s voice sounded playful.
“Like Copernicus?”
“There’s also Galileo and Cantor. In their own eras, all of them were probably treated like madmen, every last one.”
Theo smiled fiercely and said,
“Fine. If we make enemies, then we make enemies. But let’s win the war.”
Nod.
As if they all felt the same, everyone was wearing an expression that was exactly to his liking.