Translator: Dreamscribe
Seo-ha was in trouble.
‘What happened?’
Beep, beep.
Mechanical sounds could be heard.
He glanced sideways and saw his mother sitting there. It was hard to tell whether she was happy that he had woken up or if she was angry.
“Oppa, you’re awake!”
Seo-eun, her eyes swollen, was holding his hand.
Only then did he realize.
‘Ah! I’ve done it.’
His memory of completing the proof was clear.
After that, there was a blank.
Judging by the situation, he must have collapsed.
Looking around the room, it was surprisingly neat and spacious.
The walls finished with wood looked luxurious. Next to the bed, there was a small sofa and even a bed for a guardian.
‘This looks like an expensive hospital room....’
As he turned his gaze, Woo-hyun was standing by the door with his back against the wall.
‘Ah, teacher.... Still, I should get out quickly.’
When Seo-ha tried to sit up, Woo-hyun approached and stopped him.
“Let’s rest for a few days. Fortunately, they said there’s nothing seriously wrong. If you eat and rest well, you’ll recover.”
“Yes....”
Seo-ha lowered his head as if he knew the sin he had committed.
If everything had gone according to plan, he would have finished the proof on Sunday and erased all traces of it before Monday. But he failed to do so.
He blamed himself for setting such a tight schedule. Because of it, he ended up worrying many people.
He got scolded a lot over the next few days, but life in the hospital wasn’t so bad.
When classmates said they wanted to visit, Seo-ha begged them not to, trying to dissuade them. It wasn’t like he was seriously ill, he had just collapsed from dehydration. He thought everyone was overreacting.
He shared hospital meals with his younger sister, and in the evening, they secretly ordered snacks.
The two of them had a wonderful time playing all the games they had not been able to play.
‘My head doesn’t hurt anymore. I feel strong again.’
Just when he was about to bring up the topic of being discharged, Woo-hyun came to visit. His expression was scarier than usual.
“Seo-ha.”
“Yes?”
“Have you been working on the Four Color Theorem since back then?”
Even on the day they first met, Seo-ha’s research had already been quite advanced.
That meant at least seven years.
“Yes.”
Woo-hyun was angry.
Self-blame for perhaps having unnecessarily led a child who had been living happily into the path of mathematics, and self-reproach for not having stopped Seo-ha who had been grappling with a difficult problem for years, both rushed over him simultaneously.
At Woo-hyun’s serious expression, Seo-ha’s face also stiffened.
“Why did you want to solve it so badly?”
It had been seven whole years.
Woo-hyun couldn’t understand Seo-ha’s obsession with the Four Color Theorem. It was already a proven problem, was there really a need to go that far?
Seo-ha stared at Woo-hyun intently.
“Teacher.”
“Yes.”
“Even if it took me my whole life, I was going to solve the Four Color Theorem.”
Seo-ha had this side to him.
Once he set a goal, no matter how reckless it seemed, he never backed down.
“So why exactly?”
“If I couldn’t solve it, then I wouldn’t be able to accomplish anything at all anyway.”
“What?”
The unexpected answer gave Woo-hyun an odd sense of unease.
“Newton, at twenty-three, laid the foundations for calculus, optics, and universal gravitation. Pascal proved the conic section theorem at sixteen and invented a calculator at nineteen.
Gauss, at twenty, had already proved the fundamental theorem of algebra. Galois founded group theory in his teens, and Abel died at twenty-six, but even now, every mathematician remembers his name.”
Woo-hyun shook his head.
It was a different era.
No matter how he thought about it, Seo-ha’s words weren’t rational.
“You can’t compare now with back then directly. Wiles solved Fermat’s Last Theorem, but that doesn’t make him a better mathematician than Euler.”
Euler had also attempted Fermat’s Last Theorem but never succeeded.
However, it wasn’t because Euler lacked something, it was simply a problem that couldn’t be solved until new mathematical theories emerged.
Woo-hyun took a breath and looked into Seo-ha’s eyes.
“Mathematics is a marathon, not a sprint. Some problems don’t get solved even if you spend your whole life on them. Because there are achievements that suit each era.
You were too reckless. Not only clinging to the Four Color Theorem for seven years, but also trying to finish it in just a few days like a 100-meter dash.”
Woo-hyun was inwardly concerned about Seo-ha’s mathematical tendencies.
It is no longer the era where, like in the past, one could sit alone at a desk with just paper and a pen and achieve feats that shook the world.
The most essential ability required of modern mathematicians is collaboration. It has now become the norm for dozens of people to form a team and approach a single problem from multiple angles.
If that weren’t the case, why would Elijah Cronen, known as the greatest mind of humanity, bother to assemble a team?
But this child had dug into a difficult problem alone for years, and in the end, had succeeded.
Yet, would he be so lucky next time as well? Woo-hyun was skeptical.
“Of course, all those people achieved what was fitting for their era. So what I meant was, I also want to do something that fits my time.”
Woo-hyun raised his voice in frustration.
“Why are you being so stubborn! Clinging to a difficult problem alone is something only fools do. Promise me you won’t do that again. That’s just a waste of your precious time.”
Woo-hyun could see it.
The future of Seo-ha achieving great accomplishments.
But modern mathematics was too complex and subdivided to be tackled alone.
At this rate, his brilliant talent might disappear without ever reaching its full potential.
“Teacher.”
“I’m listening.”
“If I really am the kind of genius you said I might be, the kind of person who comes along once in a century.”
Seo-ha looked straight at Woo-hyun.
“Then there’s no way I’d fail to solve something like the Four Color Theorem, right?”
Woo-hyun was speechless.
It was an incredibly arrogant statement, but coming from Seo-ha, it strangely had persuasive power.
That was how Seo-ha saw it.
He hadn’t uncovered the laws of the universe like Newton or laid the foundations of mathematics like Gauss. This was a far simpler problem.
“So the Four Color Theorem was a problem I used to test whether I truly deserved to stand alongside the great figures of history. If I couldn’t do it, I was ready to give up the expectations I had for myself.
Because Newton or Gauss would have definitely solved it.”
“Th-then...”
Woo-hyun’s face was full of confusion.
“You’re misunderstanding, teacher.
I don’t intend to stick to a medieval style of mathematics. I’ll accept all the help I need. If I need technology, I’ll use it. If I need a team, I’ll collaborate with others.”
“Huh?”
“It’s a waste, isn’t it? Why should I do everything by myself? There’s only one case where research should be done alone. When that’s the most efficient way.”
Woo-hyun’s face turned red.
He was embarrassed about having spoken so passionately just moments ago.
“Forget everything I said today.”
Woo-hyun ran his palm down his face.
“Yes!”
Seo-ha replied with a playful smile. Feeling embarrassed for no reason, Woo-hyun quickly changed the subject.
“Ah! The Korean Mathematical Society is planning to verify the proof you worked on. Won’t you consider helping out? If you go and explain it yourself, the process will go much faster.”
The solution to a difficult problem must undergo multiple rounds of verification. What was happening now was just the first stage, meant to weed out absurd errors.
Woo-hyun thought it was a good proposal, but Seo-ha’s response was lukewarm.
“They’re verifying it? I don’t think that’s necessary for me....”
“Huh? Why not?”
“I know I solved it perfectly. I’ve written down every necessary step. So if there’s any doubt, isn’t it up to them to resolve it?”
There was no malice in his face, but it somehow felt irritating.
Woo-hyun closed the hospital room door and stepped into the hallway.
Thud, thud.
The moment he felt he had gotten far enough away from Seo-ha, he burst into laughter he had been holding back.
“Hahaha!”
It was a laugh of disbelief.
Seo-ha didn’t harbor even a shred of doubt about his proof.
Most researchers would be anxious, wondering if their results would be accepted. But that child had pushed aside the entire verification process as if it had nothing to do with him and calmly left it to others.
Even recognition from the academic community likely meant little to him.
Just like how Newton didn’t publish his work on calculus for over thirty years.
“I can’t understand him, not as a mere mortal like me.”
Woo-hyun shook his head and muttered to himself.
***
Korean Mathematical Society conference room,
The professors who had conducted the first round of verification were organizing the meeting minutes.
“It was unexpected. The logic was more solid than I thought.”
One professor spoke in admiration.
“I actually debated whether we even needed to take this seriously, considering he’s only thirteen. But I’m glad I went.”
At first, they were skeptical.
A new proof of the Four Color Theorem written by a high school student?
They expected piles of simple mistakes and immature development.
But they were wrong.
The flow of logic was astonishingly meticulous, and the symbols defined with new concepts blended in naturally, as if they had always been a part of the established framework.
There were hardly any flaws or logical leaps that a mathematician would immediately notice.
They were both impressed and unsettled.
The network of logic intertwined across combinatorics, graph theory, and computation theory could not be assessed using the standards of any single field.
At some point, the professors began exchanging glances and shaking their heads.
“We can’t reach a final conclusion at our level.”
Someone finally spoke.
Despite being skilled researchers, none of them could fully grasp Seo-ha’s proof or confidently say whether it was correct or incorrect.
That was how vast and unfamiliar the approach was.
This was the conclusion of their first investigation:
[No critical errors found. Recommendation to convene an international verification panel.]
“Very well. Let’s send out the emails immediately. We’ll need to request cooperation from overseas academic societies too. Since the proof spans multiple theories, we’ll need experts from various fields.”
Click.
[Summary: A draft of a new proof of the Four Color Theorem presented by a student from a Korean Gifted School. No evident errors found in the first verification. International cooperation recommended.]
The email quickly spread to mathematicians around the world.
***
2 a.m. Eastern Time, USA,
Elijah Cronen opened his laptop in a dark research lab.
“Four Color Theorem?”
It was a theory he hadn’t paid attention to in a long time. Since the proof was essentially completed, he had thought there was no reason to revisit it....
“A new approach? Without using computers?”
It had always been a proof that left a bitter aftertaste. If possible, he would have liked to overturn the whole thing.
But there were too many things he had to do.
Click.
He opened the email and slowly read through the attached summary.
‘Reduction of local rules through automata theory, boundary encoding?’
His eyebrow twitched.
With his extraordinary mathematical intuition, Cronen was able to visualize how this proof would unfold in his mind.
After thinking for a while, he stroked his chin.
“It might actually be possible.”
Elijah turned his chair and looked at the world map hanging on the wall.
It was already late, but his heart began to beat strangely.
He opened the email and began to write a reply.
[Please send the full materials. I will participate in this matter. I will personally contact experts from each relevant field.]
A few days later, emails under Cronen’s name were sent to leading authorities around the world.
A combinatorics expert at MIT in the U.S., 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 expressed interest in joining....
Those who saw Elijah Cronen’s name nodded gravely.
None of them could take his request lightly.