Snow began to fall.
Uhyeon looked up at the sky and guided Seoha to a nearby cafe. Since it was near the school, there was nothing but a study cafe with an atmosphere like a library.
The exam was three hours.
Even if you finished early, you couldn't leave in the middle.
"Coffee?"
"Yes."
Seoha nodded.
He thought about how she used to give him juice or milk when he was young, and realized how much time had passed.
"Are you worried about your younger sibling?"
"Seoeun is stronger than me. Whether it's jealousy or expectations, she's someone who knows how to turn anything into her own energy."
Uhyeon laughed loudly.
"Hahaha! Right, that's why she has such quirky sides."
"She's the type of child who finds a way to enjoy even the things she hates when she has to do them."
"It's surely thanks to growing up in an excellent family."
"Our parents are incredible. Looking back now, I don't know how they even thought of going to America for their children. Neither of them could speak a word of English."
"That's true, but."
You learn this when you're in the private education industry.
Parents who can take risks for smart children aren't rare if you look for them. But children don't grow up to be like this brother and sister just from that.
Natural brains and upright character.
The perseverance to endure tedious processes to achieve what you want and the mental backbone to not be swayed by others' gazes aren't things obtained through teaching.
Especially for a child with rich emotions like Seoeun, the influence of the environment must have been absolute.
When she opens her eyes, she sees her older brother; the person she has spent the longest time with in her life is also Seoha. Parents who didn't force achievement and simply gave abundant love.
The more he looked, the more ideal the environment seemed. Seoha's success felt like a predetermined sequence, but it wasn't easy to picture what Seoeun would become in the future.
Seoha smiled gently and said.
"I was lucky. Because I was able to meet you early, Teacher. Even if the current me taught the younger me, I don't think I could have done any better."
Uhyeon shook his head with an awkward expression and said.
"No, you would have reached that point somehow. Regardless of time."
Seoha tried to answer that it was absolutely not so, then flinched.
The question he had been pondering lately.
'Regardless of time.'
"J-just a moment."
Seoha quickly raised his hand to ask for his understanding. Uhyeon looked puzzled but didn't mind much. It wasn't as if he hadn't seen Seoha's strange behavior once or twice before.
As if a switch had been flipped, the Deoki in his head suddenly opened its eyes.
'I think I've found the way.'
Seoha nodded as if in agreement.
Defining and measuring logical consistency as energy had been more arduous than he thought. Whenever he tried to calculate the survival cost, he inevitably ended up circling back to time.
Seoha admitted that he had been too bound by the engineering proposition that "it must be applicable in reality."
Deoki twisted his lips and said.
'That's only important to engineers. It has nothing to do with us.'
That was it.
The position and responsibility of being a research institute director had been constraining his thoughts.
It had to be implementable.
That premise had bound the theory's feet.
'Time itself was Turing's language.'
The words Uhyeon had tossed out without much thought removed the shackles that had been binding his ankles.
Riemannian geometry dealing with spacetime and dimensions. Seoha boldly decided to exclude time from it.
Then how?
You could judge by curvature. If you calculated the critical point of curvature, you could find the energy required for a path to close itself.
Fireworks exploded in his head.
If he didn't pour it out right now, this realization felt like it would escape.
Seoha hurriedly took out a notebook and pen from his bag.
Scritch scratch.
The sight of him writing formulas without minding the gazes around him.
He had known for a long time that when Seoha fell into that state, he forgot who was beside him.
Sip.
Uhyeon said nothing and took a sip of coffee. Then he got up and walked to the counter.
With his tall height and slender frame, as Uhyeon approached, the employee unknowingly stared at his face.
'His face looks familiar; where did I see him?'
"Are you perhaps the owner?"
"Yes! I am indeed the owner."
"Can I rent this entire place for the day?"
"What?"
"I'll calculate a week's worth of revenue right now. I think that should be enough compensation...."
His gaze alternated between Uhyeon and Seoha, who was wearing a pulled-down hat. As if a calculation had been made, he smiled brightly and said.
"Of course! A week is too much; you only need to calculate three days' worth!"
"You must be losing quite a bit by not taking customers, so I can't do that. Please feel free to charge accordingly."
The owner bent at the waist and took the card Uhyeon held out.
"Thank you. Then I'll ask the customers inside for their understanding."
The owner hurriedly came out from behind the counter.
Looking around the cafe, there were slightly more than ten students with laptops or books open on their tables. Though he worked in private education, he himself was just a teacher; kicking out students who were studying wasn't something he felt right about.
"The students who are already inside are fine."
"Is that okay? I'm grateful, but."
"Yes, please politely decline new customers. And please provide free service to those students today. I'll pay for the costs."
"There's no need to go that far...."
"Shh!"
Uhyeon raised his index finger to his lips.
"There's a reason for it, so please don't ask further."
The owner carefully went around explaining the situation to the students.
The quiet cafe began to buzz. The students, who had ended up drinking free coffee without knowing why, naturally directed their gazes toward the two people sitting in the corner.
Complex tensor formulas were spread out chaotically on the notebook. Instead of the finite tape of a Turing machine, Seoha tried to gauge the survival possibility of a path through the transformation of a Riemannian curvature tensor.
When time disappeared from the variables, the scenery beyond the world that Turing had seen was revealed.
At the point exceeding the critical curvature, nodes close themselves and perish. Just as a living being ends its life when its energy is depleted, the path of computation also collapses geometrically the moment its efficiency drops.
"I found it. This direction is right!"
He muttered softly and wrote down formulas. Uhyeon looked at them closely.
'Riemannian geometry? But something is different....'
The time axis is cut off.
Riemannian geometry and topology don't deal with time either, but this was something else entirely. They cannot explain the discontinuity where paths are severed.
'Dynamics, Ricci flow, calculus of variations, topology, bifurcation theory, computation theory.'
Numerous fields crossover within the space of Riemannian geometry.
It definitely wasn't a theory currently being researched. He must be taking concepts needed for logical development as he went, weaving them into a single system on the spot.
'A new theory of computation?'
"Just what are you...."
The notebook was now nearing its last page.
He had an instinctive feeling. He couldn't let the flow be broken. Turning his head, he saw students gathered a few meters away. Their eyes sparkled as if they recognized Seoha, whispering to the person next to them.
A scene from the past suddenly came to mind.
Uhyeon approached them and asked in a gentle voice.
"Students, would you like to do some part-time work?"
The students' eyes went wide at the sudden offer.
It was amazing enough to see Sin Uhyeon, but to have Yu Seoha together too. They had already posted on social media and communities: 'Yu Seoha spotted at a study cafe!'
"Su-sure!"
One student in the group shouted, raising his hand.
The students next to him also nodded vigorously in agreement. Instead of answering, Uhyeon took out a card from his wallet.
"I'd like you to cover all the walls of this cafe with paper from now on. Without gaps. I'll pay you handsomely for the part-time work, so don't worry."
"The walls... with paper?"
"Yes. We're making a giant whiteboard. Owner! Is that okay? We'll restore it to its original state when we leave."
Uhyeon asked, looking at the owner who was listening from behind.
He had already grasped who they were. The owner intuitively felt that a once-in-a-lifetime opportunity had come to his business.
"O-of course! As much as you want!"
The boy who had raised his hand first, Yi Juhan, was a student from the gifted high school.
He had only come to cheer on a friend who went to the KMO and stepped in here to do some homework. Yet before his eyes were the legendary senior and Sin Uhyeon.
"Hey, hurry up and move! You come with me to buy paper and tape."
They were meeting for the first time. But he unhesitatingly gave them instructions on what to do.
Juhan understood at once what Uhyeon was trying to do.
A chill-
ran down his spine.
The miraculous scene where Seoha-senior had covered the entire wall with formulas while proving the Four Color Theorem. Sin Uhyeon was trying to recreate that in this study cafe.
Thump, thump.
His heart pounded as if it would burst.
As students from the gifted high school, they all felt infinite pride at being direct juniors of Yu Seoha. His entrance exam results were also the undisputed number one in the nation.
The students who had gone to buy paper returned in less than ten minutes. It seemed they had swept through a nearby stationery store. Uhyeon smiled slightly at the sight of them rushing in with armfuls of paper bundles.
"That was fast?"
"Because your flow mustn't be broken."
Juhan said, panting. He took out his gifted high school student ID and showed it to Uhyeon. Uhyeon made a briefly surprised expression, then nodded.
The students began moving in unison. They must have heard something from Juhan, as they worked as quietly as possible, lowering their voices.
Seoha didn't notice.
Information was entering through his eyes, but everything unrelated to the proof was being automatically filtered by his brain.
His hand moved again.
Scritch scratch.
The last page of the notebook was filled.
When Uhyeon held out a marker, Seoha naturally accepted it. Then he walked over and began continuing his thoughts on the wall.
"Gasp!"
"For real?"
Seoha was writing formulas on the canvas they had laid out.
The students quietly held their breaths. The process of clearing desks and covering the walls with paper was as solemn as a sacred ritual.
Juhan carefully pressed the paper down firmly to avoid any air bubbles.
Though he couldn't understand the formulas his senior was writing, this role was enough for him.
Before long, all the cafe walls were covered with paper.
"I didn't know you'd do this well."
Uhyeon admired them and held out an envelope, but the students refused with waves of their hands.
"Huh? Why?"
"It's okay."
"Really? You worked hard, so shouldn't you receive your pay?"
"We're really okay!"
Juhan stepped forward as their representative and said.
He didn't know the reason. But he had a premonition that he would regret taking the money. Uhyeon looked at them with deep eyes and put the envelope away.
"I've been rude."
The feeling of not wanting to remain as a laborer who had received wages at the scene of history.
He wouldn't be so different from them himself. Uhyeon spoke as if encouraging them.
"We may have contributed to something incredibly important."
Juhan clenched his fist in his pocket. He had never been as proud of himself as he was today.
Ding.
Ding.
Contacts from friends who had seen his SNS posts were pouring in. But he didn't take out his phone.
The walls were being covered with formulas.
To the point that it naturally brought to mind the seminar room that was now under strict management.
The snowfall was growing heavier.
But time inside the cafe seemed to flow separately, as if isolated from the world.