-You mean competitions by “achievements”?
“Of course.”
-Isn’t a competition a little too much for a first grader? I wouldn’t even know where to send her.
“I can answer that only after accurately gauging the child’s abilities.”
-Hmm···.
“Why? You’re not keen on it?”
-Seoha—ah! That child’s name is Seoha. Her family seemed incredibly happy. I started wondering if I’d be bringing trouble into a home that was already doing well. If I just leave her alone, won’t she continue living happily, just as she does now?
“Maybe she will. The price of that decision would be losing the possibility of a future Fields Medalist or Nobel Prize winner appearing. To be honest, I don’t think your idea that she’d be happier if left alone is wrong at all. Even if she stands out now, there’s no guarantee she’ll succeed in the future, is there?”
Woohyun could not even imagine how difficult and painful the life of a mathematician without talent might be. Though he hardly had the right to say such a thing, having fled from that very threshold himself.
-But why achievements? Wouldn’t it be better for her to skip grades and follow the regular education system? She’ll have to go to college anyway···.
“Like I did? That would be a fallback at best.”
-You said things were difficult for you when you were young, too, right?
“When rumors spread that there’s an exceptional child somewhere, people who want to take hold of them and shake them around inevitably appear. Sometimes it’s pure interest, but most of the time there’s a filthy calculation behind it—the desire to use the child for their own achievements. Suspicious eyes never stop watching, and the parents end up under tremendous pressure. In the meantime, the child herself begins to wonder, ‘Am I really that exceptional? Couldn’t I be overrated, just as everyone says?’”
-Ah···. I think I know what you mean.
“But if there are overwhelming achievements, the story changes. Whether it’s a competition or a paper, if there’s an achievement that could only have come from someone at that level, everyone has no choice but to fall silent.
Objective indicators help you avoid unnecessary depletion. And they’ll give her confidence in herself, too.”
For a mathematician setting out on a long and distant road, self-confidence was more important than anything else.
-Then you’ll come, right?
“To Okcheon?”
-Yes.
“Are you crazy? Do you know how much my time is worth for a day?”
-That money, money, money! You used to be pretty cool, you know. You’re not at all anymore.
A self-deprecating shadow fell across Woohyun’s face. Something heavy sank on one side of his chest. It felt as though shame were spreading through his veins and throughout his entire body.
The young mathematician who once shone with eagerness before a blackboard until dawn, determined to solve an unsolved problem, no longer existed.
‘What was I like back then?’
When he lifted his head, equations had burst like fireworks inside his mind. And he had believed those sparks would eventually change the world. But now, the number that occupied him most was written not on a blackboard, but on a contract.
It felt as though the remnants of the dream he had abandoned himself were tearing him apart with their sharp edges. It had been a dream that had gone out right there, without even traveling very far—so why did it still hurt so much?
Woohyun wondered if the time had come to put everything in order, arriving through Yoonmi’s words.
Perhaps unaware of what he was thinking, Yoonmi continued speaking.
-I honestly didn’t want to say this, but at my level, I can’t tell where Seoha’s limits are. I can’t even figure out what she can do or where she’s getting stuck. It feels incredibly miserable. You don’t know what this feels like, do you, Oppa?
How could he not know? He knew it far too well.
“All right. I’ll make time for one day. Find some good restaurants.”
-Hehe, thank you. I’ll give you the full Okcheon treatment.
His head was already aching at the thought of how he would get out of his classes, but the prospect of meeting Yoonmi after such a long time left him in a surprisingly good mood.
* * *
One afternoon on the weekend, at a hanok in Okcheon.
While Miyeong cooked, Seoha stared intently at her younger sibling, who was absorbed in the mobile hanging above her.
‘Is she different from me?’
He thought he had roughly understood what people were saying around this age, but judging by her reaction, Seoeun did not seem to be the same. Seoeun looked at him and opened and closed her mouth as though trying to say something.
“Do you have something you want to say to your big brother? Me too. I hope Seoeun learns to talk soon.”
Seoeun smiled brightly. She was so adorable that Seoha unconsciously reached out a finger toward her plump cheek.
Press.
The cheek yielded softly beneath his fingertip, then, when he pulled his hand away, returned to its original shape with a little pop.
“Oh!”
Seoha’s eyes grew round, and he pressed it once more.
This time, both cheeks at once.
The soft, jelly-like texture was addictive.
‘This is fun.’
While Seoha played with his younger sister, a guest arrived at the house.
“Hello. This is Seoha’s house, right?”
“Oh my! Teacher!”
Recognizing Yoonmi, Miyeong stopped hanging laundry and ran out into the yard. Cheolho, who had been mixing formula, also slipped outside and put on his slippers.
“Hello, Mother! I’m Seoha’s homeroom teacher.”
“I heard you were coming, so I’ve been waiting. Please, come inside. But who is this gentleman?”
Miyeong asked while pointing to the man standing behind Yoonmi.
He was tall and slender. Though he wore an expensive-looking suit, he kept adjusting his tie, apparently uncomfortable in it. His expression looked somewhat irritable.
“My name is Shin Woohyun. Teacher Kim Yoonmi said she wanted to show me a student, so I came with her.”
At Woohyun’s stiff greeting, Yoonmi jabbed him in the side and quickly cut in.
“He may not look it, but he majored in mathematics at Princeton University. He’s a famous instructor now, too. I thought he’d be much more helpful than I would in understanding Seoha, so I brought him along.”
“What? When you say this is about Seoha, then···. Please, come inside first.”
Miyeong led the two of them into the house.
“I’d like to see the student’s room. Would that be all right?”
At Woohyun’s abrupt request, Yoonmi frowned and rubbed her temple. She realized anew just how completely ruined Woohyun’s social skills were.
“Pardon? Yes! Of course.”
Cheolho led Woohyun to Seoha’s room.
Creak.
The old wooden floorboards screamed with every step. Cheolho gave an awkward smile and carefully chose the sturdier spots to step on.
Creeeak—
“Here it is.”
Woohyun nodded his thanks and entered the room.
‘There are more books than I expected.’
He took out an encyclopedia. Every page showed signs of use, as though it had been read carefully. The children’s picture books had been pushed onto the lowest shelf, while most of the books within easy reach were related to mathematics.
“These are books mostly used by undergraduate students.”
Woohyun pulled out James Munkres’s *Topology*. He had studied from it himself.
“He started asking us to buy books like these about a year ago. I’m a civil servant working at the township office, so even if I look through them, I don’t understand a thing. But since my son says he studies from them, I just keep buying them for him.”
Even after visiting Yoonmi’s classroom and checking the test papers, Woohyun had not been certain until he came here. Had the boy really come this far through self-study? At such a young age?
A certain person came to Woohyun’s mind—the person who had supposedly nearly finished university-level mathematics on his own before turning eight.
‘Is he similar? No, that person’s parents were a doctor and a mathematics teacher. This child’s talent might be even greater.’
Sheets of colored paper he had been playing with lay scattered across the desk.
‘So he has a childlike side, too?’
Woohyun gave a faint smile as he picked up a sheet of colored paper. Beneath it was a sketchbook. He saw something resembling an unfinished map. Below that were symbols that looked like scribbles.
‘Hm?’
There were four colors in total on the colored paper.
Equations were scrawled messily across the sketchbook.
‘No way···.’
Woohyun read through the equations. He could not take them in at a glance.
“G is V, E···. A planar graph?”
He muttered under his breath.
“∀e ∈ E, c(u) ≠ c(v)—adjacent vertices must have different colors?”
His fingertips trembled faintly.
“min |C| ≤ 4? K5, K3, 3···. Even the conditions for planarity?”
The colored-paper scraps on the desk came back into view.
Red, blue, yellow, and green. Exactly four colors.
“Euler’s formula, V - E + F = 2.”
He swallowed.
“My God. Was he trying to work out the Four Color Theorem himself?”
Cheolho, who had been listening quietly, could not hold back any longer and interrupted.
“The Four Color Theorem? What is that?”
“It’s a theory proposed by Francis Guthrie in 1852. The basic idea is that no matter how complicated a map is, it can be colored using four colors so that every region is distinguishable.”
“Is it difficult?”
“Should I say it’s difficult? It’s beyond that. Countless mathematicians challenged it for a hundred years, but none of them could solve it. In the end, it wasn’t proven true until after computers appeared.
That isn’t a proof. It would be more accurate to call it computation, or programming. Many mathematicians found it hard to accept, but since there was no alternative, the academic world accepted it. These days, there probably aren’t any mathematicians who seriously pursue it.”
After touching the colored paper for a moment, Woohyun smiled as though he had realized something.
“Ah! So that’s why he studied topology. To convert maps into planar graphs and define the properties of their boundaries and faces!”
At that moment, the door opened, and Seoha peeked his head inside.
“Mister, did you touch my colored paper?”
Woohyun smiled awkwardly.
Mathematicians absolutely hated other people touching their research without permission. Judging by this prickly reaction, Seoha seemed to possess the makings of a mathematician despite his young age.
“Ah···. Sorry. I’ll put it back the way it was.”
“No, it’s fine. You can just leave it.”
The worst possible first impression.
He was clearly angry. Woohyun decided to start a conversation on a subject Seoha might like.
“Where did you get stuck? The coloring conditions?”
“Huh? How did you know? Do you know this game too, Mister?”
Seoha’s expression changed in an instant, and he began firing off questions excitedly.
A game?
Woohyun was at a loss for words. A problem that had frustrated countless mathematicians for a hundred years seemed to this child to be nothing more than a somewhat advanced coloring game. But Woohyun could not afford to concede from the very beginning.
“I could tell from the four colors of colored paper and the notes about the adjacent-vertex conditions. It looked like you’d already finished checking planarity.”
Seoha hesitated for a moment, then took out his sketchbook.
“I got stuck after that. Adjacent vertices have to be different colors, right? But when I actually try it, if I change the order, sometimes the colors don’t overlap, while in other cases it only works if I use a third or fourth color.
Then I get confused about whether four colors will actually be enough. No matter how much I change things around, sometimes the conditions break down at the third edge.”
Seoha pointed to a page in the sketchbook.
It was densely filled with the process of four colors gradually overlapping.
“Look here. If I start with blue, the last two vertices end up the same color, so it doesn’t work. So I started with red, but then I got stuck in the middle···.”
Woohyun spoke with a smile.
“That’s the trap of the coloring order. Even if planarity is guaranteed, choosing the wrong coloring order can make it seem as though more colors are necessary. To avoid that, you need techniques like ‘inductive coloring’ or ‘reduction.’”
“Reduction?”
“Yeah. You remove one vertex from the larger graph and color it first, then put it back in while satisfying the conditions. Using only the four colors.”
Seoha’s eyes shone.
“Ah···. Then even if I get stuck in the middle, I can go back and change the colors, right?”
“Exactly. But it’s more complicated than it sounds. If you do everything by hand like this, you’ll reach your limits quickly. To prove the Four Color Theorem, you have to check every single case. Thousands, tens of thousands of cases. You couldn’t call that a proof, could you?”
Only now realizing the reality of the situation, Seoha’s expression fell.
Woohyun, on the other hand, was feeling exhilarated.
Amazingly, this child was following precisely the same approach the outstanding mathematicians of the era had taken toward the Four Color Theorem.