I Got an Omnipotent Brain

-By achievements, do you mean competitions?

“Of course.”

-Isn’t it a bit too early for a first grader to enter competitions? I wouldn’t even know where to send him.

“I can only answer that if I know the child’s abilities accurately.”

-Hmm…

”Why, are you reluctant?”

-Seo-ha, ah! The kid’s name is Seo-ha. His family seemed really harmonious. I started to wonder if I’d be stirring up trouble in a well-functioning household. Don’t you think he’ll continue to live happily if we just leave him alone?

“Maybe. The price of that decision could be losing the potential of a future Fields Medal or Nobel Prize winner. Honestly, your thought that he might be happier just being left alone isn’t wrong at all. Even if he stands out now, there’s no guarantee he’ll succeed in the future, right?”

Woo-hyun couldn’t even begin to imagine how hard and painful life must be for a mathematician without talent. Though he was in no position to talk, having run away from that path himself.

-Then why focus on achievements? Wouldn’t it be better to just skip a grade and follow the regular education system? He’ll have to go to college anyway…

“Like me, you mean? That might be a decent fallback plan.”

-Oppa, didn’t you say you struggled when you were young too?

“Whenever rumors spread that there’s a gifted child somewhere, people always show up trying to manipulate them. Sometimes it’s out of pure interest, but most of the time it’s a dirty calculation to use the kid for their own achievements. The scrutiny never ends, and the parents face serious pressure. And during all that, the kid starts doubting themselves, thinking, ‘Am I really that good? Am I just overrated like people say?’”

-Ah.... I think I understand.

“But if there are overwhelming achievements, the story changes. Whether it’s competitions or research papers, if there are outcomes that can only come from that level, then everyone is forced to shut up.

Objective indicators help avoid unnecessary drain. And the child will also gain confidence.”

For a mathematician setting out on a long, distant path, self-confidence is more important than anything.

-Then you’ll come, right?

“To Okcheon?”

-Yeah.

“Are you crazy? Do you even know what my daily rate is?”

-Money, money, that’s all you talk about! You used to be pretty cool, you know. Not anymore, though.

A shadow of self-mockery passed over Woo-hyun’s face. A heavy weight sank in his chest. It felt like shame spreading through his veins and covering his whole body.

The young mathematician who used to light up in front of the blackboard until dawn, trying to solve unsolvable problems, no longer existed.

‘What was I like back then?’

When he lifted his head, formulas exploded like fireworks in his mind. And he believed those sparks would eventually change the world. But now, the numbers he cared about most were the ones written on contracts, not the blackboard.

The wreckage of dreams he had abandoned seemed to be cutting him up inside. It was a dream that had faded without even going far, so why did it still hurt this much?

Woo-hyun thought maybe it was time to sort everything out, and perhaps that time had come through Yoon-mi’s words.

Yoon-mi, unaware of what Woo-hyun was thinking, continued speaking.

-To be honest, I didn’t want to say this, but… I can’t figure out Seo-ha’s limits with my ability. I can’t even tell what he’s capable of or what his blocks are. It feels incredibly miserable. You don’t know what that’s like, do you?

How could he not know? He knew it all too well.

“Alright. I’ll make time for a day. Just find a good restaurant.”

-Hehe, thanks. I’ll treat you to a full-course Okcheon meal.

His head already started aching thinking about how to get out of classes, but thinking about meeting Yoon-mi after a long time didn’t feel so bad.

***

A weekend afternoon in a traditional Korean house in Okcheon.

While Mi-young was cooking, Seo-ha was staring intently at his younger sister, who was completely absorbed by a mobile.

‘Is she different from me?’

He thought he could roughly understand words at this age, but judging by her reactions, Seo-eun didn’t seem to. As he watched, Seo-eun moved her lips as if trying to say something to him.

“Do you want to say something to oppa? Me too. I hope you can start speaking soon, Seo-eun.”

Seo-eun smiled brightly. It was so adorable that Seo-ha couldn’t help but reach out a careful finger toward her chubby cheeks.

Poke-

The cheek that his fingertip touched softly indented and then, when he released his hand, it returned to its original shape with a ‘pop’.

“Oh!”

Seo-ha widened his eyes and pressed it again.

This time, both cheeks at once.

The squishy, jelly-like texture was addictively satisfying.

‘This is fun.’

While Seo-ha was playing with his little sister, a guest arrived at the house.

“Hello. Is this Seo-ha’s house?”

“Oh my! Teacher!”

Recognizing Yoon-mi, Mi-young left the laundry behind and ran out to the yard. Chul-ho, who had been mixing formula, also stepped out and slipped into his slippers.

“Hello, ma’am! I’m Seo-ha’s homeroom teacher.”

“I heard you were coming, so I’ve been waiting. Please come in. But who is this person?”

Mi-young asked, pointing to the man standing behind Yoon-mi.

Tall and lean. Though he wore an expensive-looking suit, he seemed uncomfortable and kept adjusting his tie. His expression gave off a slightly irritable vibe.

“My name is Shin Woo-hyun. Kim Yoon-mi teacher said there’s a student she wanted to show me, so I came along.”

At Woo-hyun’s stiff introduction, Yoon-mi poked him in the side and quickly jumped in.

“He may not look it, but he majored in mathematics at Princeton University. He’s a well-known lecturer now. I thought he’d be much more helpful in understanding Seo-ha than I would be, so I brought him along.”

“Huh? If this is about Seo-ha, then... Well, please come in first.”

Mi-young guided the two inside the house.

“I’d like to see the student’s room, if that’s alright?”

At Woo-hyun’s abrupt request, Yoon-mi frowned and rubbed her temples. She was reminded just how socially inept Woo-hyun really was.

“Uh? Oh! Yes, of course!”

Chul-ho led Woo-hyun to Seo-ha’s room.

Creak.

With every step, the old wooden floor creaked in protest. Chul-ho smiled awkwardly and stepped on the more solid spots.

Screeech-

“Here it is.”

Woo-hyun nodded to show his thanks and stepped into the room.

‘There are more books than I expected.’

He took out an encyclopedia. Every page showed signs of wear, as if it had been read thoroughly. Picture books for young children had been pushed to the bottom shelf, while most of the books within easy reach were about mathematics.

“These are the kinds of books typically read by undergraduate students.”

Woo-hyun pulled out ’Topology’ by James Munkres. It was a book he had studied himself.

“He started asking for these books about a year ago. I’m a civil servant working at the township office, so I don’t understand any of the content, but since my son said he wanted to study them, I’ve just been buying them for him.”

Even after checking the test paper in Yoon-mi’s classroom, Woo-hyun hadn’t been completely convinced before coming here. Had he really come this far through self-study? At this young age?

One person came to Woo-hyun’s mind. That person who had nearly finished college-level math before the age of eight.

‘Is it similar? No, that person’s parents were a doctor and a math teacher. The talent here might be superior.’

Color paper that had been used for play was scattered messily across the desk.

‘He’s still got a childlike side?’

Woo-hyun smiled slightly as he picked up a piece of colored paper. Beneath it was a sketchbook. What looked like a half-finished map was visible. Some doodle-like symbols were written beneath it.

‘Hmm?’

There were four colors of construction paper in total.

Mathematical formulas messily written across the sketchbook.

‘No way...’

Woo-hyun started reading the formulas. He couldn’t grasp them at a glance.

“G is V, E... A planar graph?”

He muttered under his breath.

“For all e ∈ E, c(u) ≠ c(v), adjacent vertices must be different colors?”

His fingertips trembled slightly.

“Minimum |C| ≤ 4? K5, K3,3... Even the planarity condition?”

The colored paper pieces on the desk came back into his vision.

Red, blue, yellow, green. Exactly four colors.

“Euler’s formula V - E + F = 2.”

He swallowed hard.

“My god. Was he trying to prove the Four Color Theorem himself?”

Chul-ho, who had been quietly listening, couldn’t hold back and interrupted.

“Four Color Theorem? What is that?”

“It’s a theory proposed by Francis Guthrie in 1852. The gist is that no matter how complex a map is, it can be colored so that all regions are distinguishable using only four colors.”

“Is it difficult?”

“Difficult? It’s beyond that. For a hundred years, countless mathematicians challenged it but couldn’t solve it. In the end, it was only proven to be true after the advent of computers.

That kind of thing isn’t really a proof. It’s more accurate to call it computation, or programming. There were many mathematicians who couldn’t accept it, but since there was no alternative, the academic community eventually accepted it. These days, no mathematician would seriously dive into this topic.”

While fiddling with the colored paper, Woo-hyun suddenly smiled as if something had clicked.

“Ah! That’s why he studied topology. To translate the map into a planar graph and define the properties of the borders and faces!”

At that moment, the door opened and Seo-ha peeked his head in.

“Mister, did you touch my colored paper?”

Woo-hyun smiled sheepishly.

Mathematicians have a strong aversion to others touching their research without permission. Judging by this prickly reaction, even at his young age, he clearly had the temperament of a mathematician.

“Ah… sorry. I’ll put everything back the way it was.”

”No, it’s okay. You can just leave it.”

The worst possible first impression.

He was clearly upset. Woo-hyun decided to approach him with a topic he might like.

“Where did you get stuck? The coloring condition?”

“Huh? How did you know? You know this game too?”

Seo-ha’s expression instantly changed, and he began firing off questions excitedly.

A game.

Woo-hyun was at a loss for words. A problem that had stumped so many mathematicians for over a century was, to this child, just a slightly advanced coloring game. But he couldn’t let himself be beaten right from the start.

“I could tell from the way you wrote down the four colors and the condition about adjacent vertices. Looks like you’ve already finished determining planarity.”

Seo-ha hesitated for a moment, then pulled out his sketchbook.

“I got stuck after that. Adjacent vertices have to be different colors, right? But when I actually tried it, if I changed the order, the colors didn’t overlap, but in some cases, I could only make it work if I used the third or fourth color.

So then I get confused about whether it can be done with just four colors. No matter how many times I rearrange it, sometimes the condition breaks on the third side.”

Seo-ha pointed with his finger to a page in the sketchbook.

It showed the process of four colors gradually overlapping in various combinations.

“Look here. If I start with blue, the two vertices at the end end up the same color, so it doesn’t work. So I started with red instead, but this time I got stuck in the middle…”

Woo-hyun said with a smile.

“That’s the trap of coloring order. Even if the graph is planar, if you pick the coloring order wrong, it’ll look like you need more colors. To avoid that, you have to use techniques like ‘inductive coloring’ or the ‘reduction method’.”

“Reduction method?”

“Yeah. You remove one vertex from a large graph and color the rest, then you put it back in and adjust it to fit the conditions. All within the four colors.”

Seo-ha’s eyes sparkled.

“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 you think. Doing it all by hand like you are will hit a limit fast. To prove the Four Color Theorem, you have to check every case. Thousands, even tens of thousands of them. That can’t really be called a proof.”

Only now, realizing the reality, Seo-ha’s expression turned glum.

But Woo-hyun, in contrast, felt a rush of exhilaration.

Amazingly, this child was following the exact same path that many of the greatest mathematicians of the time had taken in approaching the Four Color Theorem.