Seoha was at a loss.
'What happened?'
Beep— Beep—
The sound of machines reached his ears.
When he glanced to the side, his mother was sitting there. It was difficult to tell whether she was happy he had woken up or angry.
"Brother, you're awake!"
Seoeun, her eyes swollen, was holding his hand.
Only then did he realize.
'Ah! I've really gone and done it now.'
He distinctly remembered finishing the proof.
After that, blank.
Given the situation, there was no doubt he had collapsed.
Looking around the room, it was so clean and spacious that it felt unfamiliar.
The walls finished with solid wood looked luxurious. Next to the bed, there was even a small sofa and a guardian's bed.
'This seems like an awfully expensive hospital room...'
Turning his head, he saw Woohyun leaning against the door.
'Ah, the teacher... Still, I should get out of here quickly.'
As Seoha tried to sit up, Woohyun approached and stopped him.
"Let's rest for a few days. Fortunately, they say there's nothing seriously wrong, so if you eat well and rest well, you'll get better."
"Yes..."
Seoha lowered his head as if acknowledging the wrong he had done.
If things had gone according to plan, he would have finished the proof on Sunday and erased all traces before Monday. But he hadn't been able to.
He blamed himself for setting such a tight schedule. Thanks to that, he had caused worry to many people.
He had gotten an earful for several days, but hospital life wasn't so bad.
When his classmates said they would visit him in the hospital, Seoha pleaded with them not to. It wasn't like he was seriously ill anywhere; he had simply collapsed from dehydration, so he thought everyone was overreacting.
He shared hospital meals with his younger sister, and in the evenings, they secretly ordered snacks.
The two spent a joyful time playing to their hearts' content, doing all the things they hadn't been able to do before.
'My head doesn't hurt anymore? I have enough strength in my body too.'
Just as he was about to bring up the subject of discharge, Woohyun came to see him. His face was frighteningly different from usual.
"Seoha."
"Yes?"
"The Four Color Theorem—have you been working on it ever since then?"
Even on the day they first met, Seoha's research was already in a fairly advanced state.
If so, at least seven years.
"Yes."
Woohyun was angry.
The guilt of having unnecessarily drawn a child who was living happily into the path of mathematics, and the self-loathing of having failed to stop Seoha from clinging to a difficult problem for all those years, washed over him simultaneously.
Seoha's face hardened at Woohyun's serious expression.
"Why did you want to solve it so badly?"
It had been a full seven years.
Woohyun couldn't understand Seoha's obsession with the Four Color Theorem. It was already a proven difficult problem—was there any reason to go that far?
Seoha stared straight at Woohyun.
"Teacher."
"Yes."
"I intended to solve the Four Color Theorem even if it took my whole life."
This was the kind of person Seoha was.
Once he set a goal, no matter how reckless it seemed, he never backed down.
"So why on earth?"
"Because if I couldn't solve it, I wouldn't be able to accomplish anything anyway."
"What?"
Woohyun felt a strange unease at the unexpected answer.
"Newton laid the foundations of calculus, optics, and universal gravitation at twenty-three. Pascal proved the theorem on conic sections at sixteen and built a calculator at nineteen.
Gauss had already proved the Fundamental Theorem of Algebra at twenty. Galois founded group theory in his teens, and though Abel died at twenty-six, every mathematician still remembers his name."
Woohyun shook his head.
It was a different era.
No matter how much he thought about it, Seoha's words weren't rational.
"You can't directly compare then and now. Wiles solved Fermat's Last Theorem, but that doesn't mean he's a greater mathematician than Euler."
Euler also challenged Fermat's Last Theorem but ultimately failed to solve it.
But that wasn't because Euler was lacking—it was because it was an impossible problem to solve before new mathematical theories emerged.
Woohyun took a breath, meeting Seoha's eyes.
"Mathematics is a marathon, not a sprint. Some problems won't be solved even if you spend your entire life on them. That's because there are achievements suited to one's own era.
You were too reckless. Holding on to the Four Color Theorem for seven years, and trying to finish it in just a few days as if running a hundred-meter dash."
Woohyun was inwardly worried about Seoha's mathematical tendencies.
This was no longer an era where one shook the world with achievements sitting alone at a desk with only paper and pen.
The most required ability for modern mathematicians is collaboration. It had become standard for dozens to form teams and tackle one problem from multiple angles.
Otherwise, why would Eliya Kronen, called the greatest mind of humanity, bother forming a team?
But this child had delved into a difficult problem alone for years and finally accomplished it.
But would he be so lucky next time? Woohyun was skeptical.
"Of course, they all achieved what suited their times. So I meant that I want to do what suits my time too."
Woohyun raised his voice as if frustrated.
"Why are you so stubborn! Clinging to a difficult problem alone is something only fools do. Promise you won't do this next time. It's a waste of your precious time."
Woohyun could see it.
Seoha's future achieving great things.
But modern mathematics was too complex and specialized; one could never walk this path alone.
If this continued, his shining talent might disappear worthlessly.
"Teacher."
"I'm listening."
"If I were truly the genius you spoke of, someone with the qualities that appear once in a century."
Seoha looked straight at Woohyun.
"There's no way I couldn't solve something like the mere Four Color Theorem, right?"
Woohyun was speechless.
It was an incredibly arrogant statement, but coming from Seoha's mouth, it was strangely persuasive.
That was how Seoha thought.
It wasn't like illuminating the laws of the universe like Newton, or laying the foundations of mathematics like Gauss. This was a far simpler problem.
"So the Four Color Theorem was a problem to test whether I truly had the qualifications to stand shoulder to shoulder with the great figures of history. If I couldn't accomplish it, I intended to give up my expectations of myself.
Because if it were Newton or Gauss, they would have certainly solved it."
"Th-then."
Confusion filled Woohyun's face.
"You're misunderstanding me, Teacher.
I have no intention of insisting on medieval-style mathematics. I'll accept all the help I need. I'll use technology if I need it, and I'll collaborate with others if I need a team."
"Huh?"
"It's a waste, isn't it? Why should I do everything alone? There's only one case where I should research alone: when it's the most efficient way."
Woohyun's face turned red.
He was ashamed of the passionate speech he had just delivered.
"Please forget what I said today."
Woohyun ran his hand down his face.
"Yes!"
Seoha answered with a playful smile. Woohyun, suddenly embarrassed for no reason, quickly changed the subject.
"Ah! The Korean Mathematical Society is planning to verify the proof you did. Don't you want to help? If you go and explain it directly, it would be much faster."
Solving a difficult problem required going through several verification procedures. What was being conducted this time was the primary verification to filter out absurdly wrong answers.
Woohyun thought it was a good suggestion, but Seoha's reaction was lukewarm.
"They're going to verify that? I don't think I need that..."
"Huh? Why?"
"I know that I solved it perfectly. I've written down all the necessary steps too. So if they have doubts, isn't resolving that their responsibility?"
His face held no malice, but it was strangely annoying.
Woohyun closed the hospital room door and stepped into the hallway.
Thud, thud.
The moment he felt he was sufficiently far from Seoha, the laughter he had been holding burst out.
"Hahaha!"
It was a hollow laugh.
Seoha didn't harbor even a shred of doubt about his own proof.
An ordinary researcher would be anxious about whether their results would be accepted, but that child calmly pushed verification aside as someone else's business, as if it had nothing to do with him.
Even academic recognition probably held little meaning for him.
Just as Newton completed calculus but didn't publish it to the academic community for over thirty years.
"A mediocre person like me can't understand."
Woohyun muttered to himself, shaking his head.
* * *
Korean Mathematical Society conference room.
The professors in charge of the primary verification were organizing the meeting minutes.
"It was unexpected. The logic was more solid than I thought."
A professor said, as if in admiration.
"I was actually worried whether I should seriously verify this since he's thirteen years old, but I'm glad I did."
At first, they had been skeptical.
A new proof of the Four Color Theorem written by a high school student?
They had thought simple errors and immature derivations would pour out like a mountain.
But they were wrong.
The flow of logic was astonishingly dense, and the symbols newly defined as concepts in between connected as naturally as if they were part of an established system.
Flaws or leaps in logic that any mathematician could spot were nowhere to be found.
They felt admiration and bewilderment simultaneously.
The web of logic intertwining across the boundaries of combinatorics, graph theory, and computation theory could not be judged by the standards of a single field.
At some point, the professors looked at each other and shook their heads.
"We won't be able to reach a final conclusion at our level."
Someone spoke up.
Despite being capable researchers, none of them could fully understand Seoha's proof and definitively declare it 'correct or incorrect.'
It was that vast and unfamiliar a method.
The result of their primary investigation was as follows:
[No fatal errors found. Recommendation to convene an international verification team.]
"Very well. Let's send out emails immediately. We'll need to request cooperation from overseas academic societies as well. Since the proof crosses multiple theories, we'll need specialists from each field."
Click.
[Summary: Draft of a new proof of the Four Color Theorem presented by a student at a Korean gifted school. No clear errors found in primary verification. International verification cooperation needed.]
The email spread instantly to mathematicians around the world.
* * *
Two in the morning, Eastern US time.
Eliya Kronen turned on his laptop in a dark research lab.
"The Four Color Theorem?"
It was a theorem he hadn't paid attention to in a long time. He had thought there was no reason to touch it again since the proof was practically finished, but...
"A new approach? Does it say no computers were used?"
It had been a proof with a bad aftertaste. One that made him want to overturn it entirely if possible.
But he had too many things to do.
Click.
He opened the email and slowly read through the attached summary.
'Reduction of local rules through automata theory, boundary encoding?'
His eyebrows twitched.
With his astonishing mathematical intuition, Kronen could visualize in his head how this proof would flow.
He pondered for a while, then stroked his chin.
"Could it actually be possible?"
Eliya turned his chair and looked at the world map hanging on the wall.
It was already late, yet his heart began to beat strangely.
He opened an email and began to write a reply.
[Please send the full materials. I will participate in this matter. I will contact the field specialists myself.]
A few days later, emails in Kronen's name flew to authorities around the world.
A combinatorics authority from MIT in the United States, a topologist from ENS in France, a computational complexity theorist from the University of Tokyo in Japan, a graph theory specialist from the University of Bonn in Germany.
And dozens of other researchers who wished to participate...
Having confirmed Eliya Kronen's name, they nodded heavily.
No one could take his request lightly.