Translator: Dreamscribe
Soft tofu stew, stir-fried spicy pork, diced radish kimchi, seaweed salad, stir-fried mushrooms, stir-fried anchovies.
The food was neatly arranged on the tray.
Though the menu looked appetizing, Yu Seo-ha’s chopsticks gradually slowed down.
‘I want to eat Mom’s cooking.’
In the end, Seo-ha couldn't finish his dinner and left some behind.
At first, it was good.
The variety of menus from the university cafeteria was fascinating, and there were many foods he couldn’t eat at home, so every day was enjoyable.
But it had already been two weeks.
Seo-ha missed his mom’s home-cooked meals that he had eaten all his life.
After leaving the cafeteria, he walked around the area once and went up to his room.
‘What is Seo-eun doing?’
He missed his younger sister so much he couldn’t bear it.
Maybe he was more dependent on Seo-eun than she had been on him, even when she cried and clung to him.
He kept recalling the image of his sister following him with quick steps wherever he went.
'I should treat her better when I go home.'
Seo-ha opened the campus notebook on his desk and flipped through the pages.
The notebook was densely filled with formulas and graphs.
[Four Color Theorem.]
The theory that any map drawn on a plane can be colored using only four colors so that no adjacent regions share the same color.
Seo-ha still couldn’t give up on this.
In 1976, Kenneth Appel and Wolfgang Haken had used a computer to prove the hypothesis to be true, but Seo-ha could not accept that as a proper proof.
“124th attempt.”
Seo-ha murmured as he picked up his pencil.
To Seo-ha, mathematics was a beautiful language where human intuition and meticulous logic met. He believed that within it, there must exist an elegant solution.
Haken and Appel’s proof was a brute-force method using a computer to check each of the 1,936 special exceptions that occur in the Four Color Theorem. While humans couldn’t possibly verify the countless resulting cases, the computer made it possible.
“That’s not a proof, just confirmation.”
Seo-ha was convinced. If Euler or Newton were alive today, they would never have accepted this.
‘There must be a way.’
Seo-ha stared at the duck attached to the end of his pencil and fell into thought.
His first attempt was when he was seven years old.
Due to his lack of mathematical knowledge, he tried by triangulating the plane and using only Euler’s formula and basic graph theory.
After about 20 failures, he became convinced. If he could use the relationship between the graph’s minimum degree and chromatic number, there must be a breakthrough.
The result was, of course, failure.
On the 50th attempt, he tried a topological approach. Eventually, he even ventured into combinatorics.
But none of them were the answer.
The complex number of cases continued to emerge, and Seo-ha could not propose a unified theory to control them all.
However, what was important to Seo-ha was the fact that he was progressing, even if only little by little.
He believed that eventually, a breakthrough would come.
Scratch, scratch.
‘What incredible concentration.’
Ji-hoon, solving problems, glanced at Seo-ha.
He didn’t even hear Ji-hoon entering the room. Not wanting to interrupt him, Ji-hoon carefully packed his workbook and stepped outside.
Two hours later.
Knock knock!
Someone knocked on the door.
Seo-ha snapped back to awareness and got up from his seat.
“Who is it?”
After a moment of hesitation, a voice came from outside.
“...It’s me, Lim Su-jeong.”
Click.
Seo-ha opened the door with a puzzled expression.
She had been in training clothes in the afternoon, but now she was wearing a skirt and coat.
“Can you come with me for a bit? I need your help.”
“Huh?”
Before Seo-ha could respond, Su-jeong grabbed the hem of his clothes and pulled him along.
It was past 9 p.m.
The outside was already covered in darkness.
Since it was vacation time, many of the buildings were empty, and the lights were sparsely lit.
They went down the stairs and headed to the lounge. From there, they went inside again, and a study room appeared.
Without hesitation, Su-jeong opened the door.
Creak.
“I brought him.”
Su-jeong gently pushed Seo-ha’s back.
Seo-ha stepped inside, bewildered.
“You took way too long!”
At Ji-ye’s scolding, Su-jeong twisted her hair and pretended not to hear.
Ko Chang-seok, Seo Ji-ye, Sung Ji-hoon.
Familiar faces appeared.
And one person who had been in the same group during the problem-solving session.
"We introduced ourselves before, right? Have a seat."
It was Kim Do-kyung, a third-year high school senior who had participated in last year’s IMO.
He had taken the lead during problem-solving before and was someone with leadership skills.
As Seo-ha sat down, Do-kyung stood up.
“Sorry for calling you suddenly. You didn’t come here unwillingly, right?”
At Do-kyung’s question, Seo-ha nodded as if to say it was fine.
“When we went to the IMO last year, honestly, our team was a mess. No one had any experience. But to be honest, there was an even bigger problem...”
Do-kyung let out a sigh.
“Our teamwork was zero. We were too busy checking each other.”
Su-jeong agreed as well.
The atmosphere during last year’s IMO, which had ended with the worst results, hadn’t been good even from the winter school stage.
“The IMO is an individual competition and a team competition at the same time. The individual scores are added up to determine the country’s ranking. We didn’t exactly interfere with each other, but we didn’t actively help each other either.”
Ko Chang-seok adjusted his glasses and chimed in.
“There was no information sharing at all.”
“The result, well, as everyone knows....”
Do-kyung’s voice was filled with regret.
“When I looked at the Chinese and American students, they were completely different. They moved like a real team. Constantly exchanging opinions while studying, and if someone got stuck, others helped them.”
“To be honest, back then, the problem was that the third-year oppas had no presence.”
Su-jeong pouted her lips.
“If there had been an overwhelmingly outstanding sunbae, we could have followed along. It's something I can say now, but everyone was at a similar level, right? You were the youngest, and Chang-seok and I were second-years, so it was hard to speak up.”
“So is that why you gathered us?”
Ji-ye showed an intrigued expression.
“Anyway, I really don’t want to fail like last year. I’m not the best at math, but as one of the older ones, I want to lead this group. What do you all think?”
At Do-kyung’s serious expression, everyone straightened their posture.
“Alright.”
“I think it’s a good idea too.”
“I don’t mind.”
Everyone agreed that something needed to be done to get a good result at the IMO.
Seo-ha didn’t really understand but nodded for now.
“These six people here are ones I arbitrarily called because I think they have the highest chance of being selected as team members. Well, I actually discussed it with Su-jeong.”
Su-jeong looked away, seeming shy.
“Well, I guess there’s no personal bias in the selection.”
“Is it based on yesterday’s results?”
During the winter school period, there were two tests.
Since feedback was exchanged after the tests, everyone here knew each other's scores.
“I think we have an overwhelming advantage this year compared to last year.”
“What is it?”
Do-kyung looked directly at Seo-ha.
“Yu Seo-ha. It’s you.”
“Me?”
“Seo-ha, for us, Olympiad past problems are honestly difficult. To be real, they’re really, really hard.”
Everyone nodded at Do-kyung’s admission.
“I’ve been preparing for this for three years, and even now, I keep hitting walls.”
Chang-seok carefully spoke while taking off and cleaning his glasses.
“Same for me. In number theory or combinatorics, I can at least see the approach, but for geometry, I have no clue.”
Ji-ye was also a talented student but was struggling with Olympiad-style problems.
“The moment I see a problem, I feel choked. I don’t even have a clue where to begin. After worrying about it for hours, I may or may not see a path.”
Geometry is the most devilish demon in the Olympiad, no, in mathematics.
“It’s not that we’re incompetent. Isn’t this actually the normal reaction? Even famous university graduate students and PhDs can’t solve Olympiad-style problems unless they’re used to them.”
Do-kyung spoke while looking straight at Seo-ha.
“But since coming to winter school, I’ve never seen you get a single problem wrong. Don’t tell me... is this easy for you?”
At first, it was just curiosity.
Because he was way too young to be here.
But when Seo-ha solved a problem that he himself had struggled with for two days in an instant, he realized that this kid was on a completely different level.
“Uh... I...”
Seo-ha stammered, flustered.
“You can be honest.”
Su-jeong’s voice, as if she already knew everything.
Ji-ye and Ji-hoon also looked at Seo-ha and nodded, signaling it was okay.
Seo-ha’s mouth slowly opened.
“Uh... I honestly don’t really understand why people say Olympiad geometry is so hard.”
Everyone’s mouths fell open.
They had heard he was good, but no one expected him to show this kind of confidence.
But it was by no means arrogance. It was simply Seo-ha’s honest impression of IMO problems.
“Wow! I never thought I’d hear something like this in my life.”
Chang-seok, normally quiet by nature, let out a dry laugh.
“I had high hopes, but seriously? You just solve it as soon as you see it?”
“Man! We should’ve recorded this.”
“Now I realize I wasn’t even bragging.”
Everyone burst into loud chatter and laughter.
Seo-ha found the scene heartwarming and laughed along with them.
“Seo-ha, you really mean that?”
Once the atmosphere settled, Do-kyung approached Seo-ha again to confirm.
“Yes.”
As he was trying to figure out what to say, Su-jeong snapped her fingers, snap!
“Do-kyung oppa! Let’s have him try that problem. The one that was going around during last year’s IMO...”
“Ah!”
Do-kyung opened his notebook, then grabbed a ruler and compass to draw a figure.
“This is a problem from the Indian Institute of Technology (IIT) entrance exam.
Last year, one of the Indian team members brought it with him while preparing for the exam. But he couldn’t solve it no matter what, so during the competition, he passed it around to students from other countries.”
IIT is the only remaining ladder of social mobility for India’s 1.4 billion people.
Graduating means Silicon Valley companies will recruit you immediately, and the entire family can immigrate to the U.S.
Naturally, the entrance difficulty is extreme.
Do-kyung continued.
“The funny thing is, no student solved this by the last day. In the end, the Caltech professor who accompanied us solved it.”
It seemed to be a problem that had been studied for a long time, as Do-kyung skillfully drew the figure.
“Here! Want to try solving it?”
Everyone had excited expressions like they were watching a fun variety show.
“Don’t feel pressured. We’re just trying it for fun.”
Do-kyung smiled.
But for something “just for fun” their gazes were too intense.
Ji-ye, Chang-seok, Ji-hoon, and Su-jeong all watched with a mix of curiosity and anticipation.
Seo-ha took the notebook. After examining it for about a minute, he picked up his pencil.
Scratch-
He drew one auxiliary line over the figure.
Do-kyung was so shocked it felt like his heart would jump out.
"You're drawing from right there?"
Scratch, scratch.
A second line, and then a third line.
Every time the pencil tip moved lightly, the drawing changed into an entirely different structure.
Su-jeong held her breath.
Even though she knew the answer, she couldn't understand the underlying principle. But Seo-ha?
Seo-ha barely did any calculations.
A brief angle notation, a few lines of ratio equations.
And lastly, he circled the conclusion and ended the proof.
“It’s done.”
Silence fell.
Ji-ye, Chang-seok, and Ji-hoon all looked to Do-kyung as if asking for confirmation of the answer.
“I-It’s correct. That’s the solution.”
Do-kyung’s voice trembled.
Everyone was stunned.
In the quiet, Ji-ye was the first to speak.
“With geometry, if you can’t solve it, you leave it blank. If you can, it’s three lines solutions.
It’s something our teacher used to say all the time, but I never thought I’d see it happen with my own eyes.”
Ji-ye looked at Seo-ha in disbelief.
Even Su-jeong, who knew Seo-ha well, hadn’t expected him to be at this level.
But Seo-ha felt no pride in any of this.
To him, the Olympiad was not the mathematics he loved.
Problems were deliberately described in complicated ways. They mixed in unnecessary conditions that weren’t used in the solution to create confusion. Figures were intentionally drawn in complex forms to hide the essential structure. Key conditions were disguised in different forms to obscure them.
Seo-ha’s exceptional mathematical intuition saw through all these tricks.
A scam that relied solely on deception and technique.
That was how Seo-ha saw the IMO.
To Seo-ha, this felt closer to a game than actual mathematics.
‘I guess there’s no helping it. They can’t exactly ask us to write research papers in an Olympiad.’
The organizers must have their own difficulties.
‘And someone truly exceptional wouldn’t fall for such tricks anyway.’
While Seo-ha was organizing his thoughts, delayed exclamations of awe burst out.
“Amazing!”
“I think this is the first time I’ve seen what people call mathematical intuition.”
“He’s so incredible I don’t even feel like trying to beat him.”
“I knew it all along.”
If he’s on our side, we’re invincible!
Everyone’s faces lit up.
“There’s a guy named Lu Yichen from China who got first place individually last year. He was a second-year back then, so he’ll be competing again this year. He was an unbelievable monster, especially in geometry.”
Su-jeong nodded.
“I remember too. He was the only one who solved the final problem. Looking back now, I guess he was someone with outstanding intuition like Seo-ha.”
“This year, Lu Yichen’s going to be in for a shock.”
Su-jeong and Do-kyung looked at each other and grinned.
“Alright, alright! Let’s not expect to coast just because we’ve got Seo-ha. We should each earn a medal too.”
At the IMO, roughly the top 10% receive gold medals, and silver and bronze are awarded at fixed ratios. In the end, about half the participants receive medals.
“Seo-ha, if it’s okay with you, could you help us study from now on? There’s so much that’s difficult.”
“Me too!”
“Me too, please!”
“Yes! I’d be happy to help if I can.”
Seo-ha nodded cheerfully.
The next day, Do-kyung informed all the winter school participants about the study group and started accepting members.
Having never taught others before, Seo-ha surprisingly achieved great results while leading the study group.
It was the first time he had to verbalize his thought process.
And through that, he began to reflect deeply on the parts he had previously glossed over with mere intuition.
Four months after winter school ended,
The final selection exam was held.
The successful candidates were the six students who had participated in the study group.