Soft tofu stew, stir-fried pork, diced radish kimchi, seasoned seaweed, stir-fried mushrooms, stir-fried anchovies.
The food was neatly arranged on the tray.
Though the menu looked appetizing, Seoha's chopsticks gradually slowed.
‘I want to eat Mom’s cooking.’
In the end, Seoha couldn’t finish his dinner and left some behind.
At first, it had been nice.
The diverse menu at the university cafeteria had been fascinating, and there were plenty of dishes he couldn’t eat at home, so every day had been enjoyable.
But it was already the second week.
Seoha missed his mother’s home cooking that he had eaten his whole life.
After leaving the cafeteria, he walked around for a bit and headed back to his room.
‘I wonder what Seoeun is doing?’
He missed his younger sister so much he couldn’t stand it.
Perhaps he depended on Seoeun more than his sister, who used to throw tantrums and cry, had depended on him.
He kept picturing his younger sister scurrying after him wherever he went.
‘When I get home, I have to treat her better.’
Seoha opened the campus notebook on his desk and flipped through it.
Formulas and graphs densely filled the pages.
[Four Color Theorem.]
The theorem stating that any map drawn on a plane could be colored using only four colors such that no adjacent regions shared the same color.
Seoha still couldn’t give up on it.
In 1976, Kenneth Appel and Wolfgang Haken had proven the conjecture true using a computer, but Seoha simply could not acknowledge that as a valid proof.
“Attempt 124.”
Seoha muttered and picked up a pencil.
To Seoha, mathematics was a beautiful language where human intuition and rigorous logic met. And he believed that within it, an elegant solution must always exist.
Haken and Appel’s proof was a brute-force method that used a computer to check each of the 1,936 special exceptions occurring in the Four Color Theorem one by one. Humans could not possibly verify all the countless cases derived from it, but computers made it possible.
“That’s not a proof. It’s just verification.”
Seoha was certain. If Euler or Newton were alive today, they would never tolerate this.
‘There has to be a way.’
Seoha gazed at the duck attached to the end of his pencil and fell into thought.
The first attempt had been when he was seven years old.
Lacking sufficient mathematical knowledge, he had challenged it using only triangulation of the plane, Euler’s formula, and basic graph theory.
Around the twentieth failure, he became convinced. If he used the relationship between a graph’s minimum degree and its chromatic number, he would surely find a breakthrough.
The result was, naturally, failure.
On the fiftieth attempt, he tried a topological approach. And eventually, he even dabbled in combinatorics.
But none of them were the answer.
Complex cases kept emerging endlessly, and Seoha could not present a single theory that could control them all.
But what mattered to Seoha was the fact that he was improving bit by bit.
He believed that if he kept at it, a breakthrough would come eventually.
Scratch, scratch.
‘What incredible concentration.’
Jihun, who had been solving a problem, glanced at Seoha.
Seoha hadn’t even heard him enter. Not wanting to disturb him, Jihun carefully gathered his problem book and went outside.
Two hours later.
Knock, knock!
Someone knocked on the door.
Seoha snapped back to his senses and got up from his seat.
“Who is it?”
After a brief hesitation, a voice came through.
“...It’s me, Im Sujeong.”
Click.
Seoha opened the door with a puzzled expression.
She had definitely been in a tracksuit in the afternoon, but now she was wearing a skirt and a coat.
“Can you come with me for a minute? I need your help.”
“Huh?”
Before Seoha could answer, Sujeong grabbed his sleeve and pulled.
It was past nine at night.
Outside was already shrouded in darkness.
Perhaps because it was vacation, the building was largely empty, with only a few lights on here and there.
They went down the stairs and headed toward the lounge. Going further inside, they found a study room.
Sujeong opened the door without hesitation.
Creak.
“I brought him.”
Sujeong gave Seoha a light push on the back.
Bewildered, Seoha stepped inside.
“What took you so long!”
At Jiye’s reproach, Sujeong twirled her hair and feigned ignorance.
Go Changseok, Seo Jiye, Seong Jihun.
Familiar faces were there.
And one person who had been in the same problem-solving group.
“We’ve greeted before, right? Come sit down.”
It was Gim Dogyeong, a third-year who had gone to last year’s IMO.
He had led the problem-solving sessions before too—a person with leadership.
When Seoha sat down, Dogyeong stood up.
“Sorry for calling you out suddenly. You weren’t dragged here against your will, right?”
In response to Dogyeong’s question, Seoha shook his head as if to say it was fine.
“When we went to last year’s IMO, our team was honestly a mess. There wasn’t a single person with experience. Actually, there was an even bigger problem than that...”
Dogyeong let out a sigh.
“Our teamwork was zero. Everyone was too busy keeping each other in check.”
Sujeong agreed.
The atmosphere for last year’s IMO, which had yielded the worst results, had been bad since winter school.
“The IMO is an individual competition, but at the same time, a team competition. Each person’s scores are added up to determine the country’s ranking. But while we didn’t sabotage each other, we didn’t actively help each other either.”
Go Changseok adjusted his glasses and chimed in.
“Information wasn’t shared at all.”
“As for the result, well, you all know...”
Regret lingered in Dogyeong’s voice.
“The kids from China and the US were completely different. They really moved as one team. They exchanged opinions constantly while studying, and if someone got stuck, another person would help.”
“Honestly, the problem back then was that the third-year oppas had no presence at all.”
Sujeong pursed her lips.
“If there had been an overwhelmingly outstanding senior, we could have ridden their coattails. Hindsight is twenty-twenty, but we were all around the same level, weren’t we? You were the youngest, and Changseok and I were second-years, so it was hard to speak up.”
“So that’s why you gathered us?”
Jiye asked with an intrigued expression.
“For one thing, I absolutely don’t want to fail like last year. I’m not the best at math, but as the eldest, I want to lead this group. What do you think?”
At Dogyeong’s serious expression, everyone straightened up.
“Sounds good.”
“I think it’s good too.”
“I don’t mind.”
Everyone agreed that they needed to do something to achieve good results at the IMO.
Seoha wasn’t sure about what was happening, but he nodded for now.
“I called the six people here because I think they have the highest probability of being selected as members. Actually, I discussed it with Sujeong.”
Sujeong looked elsewhere, seemingly embarrassed.
“Well, I guess you called us without any favoritism.”
“Isn’t this basically yesterday’s midterm results?”
There were two exams during the winter school period.
Since feedback was given after the exams, everyone here knew each other’s scores.
“I think this year, we have an overwhelming advantage compared to last year.”
“What is it?”
Dogyeong looked straight at Seoha.
“Yu Seoha. It’s you.”
“Huh?”
“Seoha, past IMO problems are actually hard for us. Honestly, really, really hard.”
At Dogyeong’s confession, everyone nodded.
“I’ve been preparing for this for three years, and there are still walls everywhere.”
Changseok took off his glasses and wiped them as he spoke carefully.
“Same here. I can at least see an approach for number theory or combinatorics, but geometry is hopeless.”
Jiye was an outstanding student too, but she was currently struggling with Olympiad-style problems.
“The moment I see the problem, my breath catches. There’s no clue how to even begin. I have to agonize for hours before I can maybe see a path.”
Geometry was the most vicious villain of the Olympiad—no, of mathematics itself.
“It’s not that we’re lacking. Isn’t this actually the normal reaction? Even PhDs from famous universities can’t solve most Olympiad-type problems if they’re not used to them.”
Dogyeong looked straight at Seoha and said,
“But since coming to winter school, I’ve never seen you get a single problem wrong. Surely this isn’t easy for you?”
At first, it had just been curiosity.
He had been too young to be here.
But when Seoha solved a problem he had agonized over for two days in an instant, he realized this child was on another dimension.
“I... I...”
Seoha stammered in bewilderment.
“You can be honest.”
Sujeong’s voice implied she already knew.
Jiye and Jihun also looked at Seoha and nodded, telling him it was okay.
Seoha’s mouth slowly opened.
“I... I honestly don’t really understand why Olympiad geometry is considered difficult.”
Everyone’s jaws dropped.
They had heard he was good, but no one expected such audacity.
But this wasn’t arrogance at all. It was simply Seoha’s candid impression of IMO problems.
“Wow! I’ve never heard anyone say something like that in my life.”
Changseok, who was usually quiet, let out a hollow laugh.
“I expected a lot, but really? You just look at it and solve it?”
“Man! I should have recorded this.”
“So I wasn’t even showing off.”
Everyone chatted and laughed boisterously.
Seoha liked the sight and laughed along with them.
“Seoha, are you serious?”
Once the mood calmed down, Dogyeong approached Seoha again to confirm.
“Yes.”
While he was at a loss for words, Sujeong snapped her fingers.
“Dogyeong oppa! Let’s have him try that problem. The one that went around at last year’s IMO...”
“Ah!”
Dogyeong opened his notebook and took out a ruler and compass to draw a figure.
“This is an Indian Institute of Technology (IIT) entrance exam problem.
Last year, one of the Indian representatives brought it because he was preparing for the entrance exam. But no matter how hard he tried, he couldn’t solve it, so he passed it around to the kids from other countries during the competition.”
IIT was the only remaining ladder of social mobility for India’s 1.4 billion people.
Because graduating meant Silicon Valley companies would recruit you immediately, entire families could immigrate to America.
The difficulty of admission was naturally extreme.
Dogyeong continued,
“But the funny thing is, not a single student solved it until the last day. In the end, a Caltech professor who was accompanying us solved it.”
Perhaps because he had studied the problem for a long time, Dogyeong drew the figure skillfully.
“Alright! Want to give it a try?”
Everyone looked on with excitement, as if watching an interesting show.
“Don’t feel pressured. We’re just doing this for fun.”
Dogyeong smiled.
But calling it just for fun was belied by the burning gazes.
Jiye, Changseok, Jihun, and Sujeong were all watching with a mix of curiosity and anticipation.
Seoha took the notebook. He examined it for about a minute, then gripped his pencil.
Scratch—
A single auxiliary line was drawn on the figure.
Dogyeong felt like his heart would leap out of his chest in surprise.
“You’re drawing it right there?”
Scratch, scratch.
A second line, and then a third.
Each time the pencil tip moved lightly, the figure transformed into a completely different structure.
Sujeong held her breath.
She had known the answer yet couldn’t understand the principle. But Seoha?
Seoha hardly did any calculations.
Brief angle notations, a few lines of proportional expressions.
And finally, he concluded the proof by circling the conclusion.
“I’m done.”
Silence fell.
Jiye, Changseok, and Jihun looked at Dogyeong as if asking whether the answer was correct.
“I-it’s right. That’s the correct answer.”
Dogyeong’s voice trembled.
Everyone couldn’t hide their astonishment.
In the quiet, Jiye was the first to speak.
“In geometry, if it doesn’t work out, it’s a blank paper; if it does, it’s three lines.
Our teacher used to say that a lot, but I never thought I’d see it with my own eyes.”
Jiye looked at Seoha in disbelief.
Even Sujeong, who knew Seoha well, hadn’t expected him to be at this level.
But Seoha wasn’t proud of this in the slightest.
To Seoha, the Olympiad was not the mathematics he loved.
They intentionally complicated the problem statements. They mixed in irrelevant conditions to cause confusion. They deliberately drew complex figures to hide the essential structure. They disguised key conditions in different forms to conceal them.
Seoha’s outstanding mathematical intuition saw through all these deceptions.
A fraudulent spectacle that forced one to rely solely on tricks and technique.
That was how Seoha viewed the IMO.
Seoha thought it was closer to a game than mathematics.
‘I suppose it can’t be helped? You can’t exactly ask someone to write a thesis at the Olympiad.’
The organizers must have their own difficulties too.
‘A truly outstanding person wouldn’t fall for such tricks anyway.’
As Seoha was organizing his thoughts, belated exclamations burst out.
“Amazing!”
“I think today is the first time I’ve seen mathematical intuition that I’d only ever heard about in stories.”
“You’re so incredible I don’t even feel like competing.”
“I knew it all along.”
If he’s on our side, he’s invincible!
Life returned to everyone’s faces.
“There’s a Chinese student named Rui Chen who took first place individually last year. He was a second-year then, so he’ll probably be back this year. He was an absolute monster, especially in geometry.”
Sujeong nodded.
“I remember too. He was the only one who solved the last problem. Now that I think about it, he must have been someone with exceptionally keen intuition, like Seoha.”
“This year, Rui Chen will be in for a surprise.”
Sujeong and Dogyeong looked at each other and grinned.
“Alright, alright! Just because we have Seoha doesn’t mean we should try to get a free ride. We should each win a medal.”
At the IMO, roughly the top 10% received gold medals, with a certain ratio for silver and bronze. Ultimately, about half of the participants received medals.
“Seoha, if it’s okay, could you help us study from now on? There’s so much we don’t understand.”
“Me too!”
“I ask too!”
“Yes! If I can be of help.”
Seoha nodded gladly.
Dogyeong announced the existence of the study group to everyone at winter school the next day and recruited participants.
Seoha, who had never taught others before, achieved unexpectedly great results while running the study group.
He faced a situation where he had to verbalize his thought process for the first time.
And in that process, he was compelled to think deeply about the parts he had glossed over with intuition.
Four months after winter school ended,
the final selection exam was held.
The six people who had participated in the study group were the ones who passed.