“All right, is everyone in? Seoeun, is your seatbelt on properly?”
Cheolho turned around from the driver’s seat to check.
Seoha could detect a slight excitement in his father’s tone.
At some point, Seoha’s competition schedule had become something akin to a family trip. Thanks to Okcheon County’s support, they no longer had to worry about expenses.
“Yes!”
Seoeun answered, raising both hands high.
“Seoha’s bag is here, and I packed Seoeun’s clothes properly too….”
As if something was bothering her, Miyeong got out of the car to check the trunk once more.
“We’re only going for a day anyway. Do we really need such a big bag?”
To Cheolho, a country man, it was a world he could not understand.
National-level competitions were mostly held in Seoul.
Seoul might not have been an ideal travel destination for city folk, but to country people like Seoha’s family, it was a strange new world no matter how many times they visited.
Miyeong and Seoeun, in particular, had completely fallen for Seoul’s charm.
“Still, you never know.”
Miyeong hummed as she organized the luggage, then closed the trunk.
Vroom.
The car set off.
Unable to hide her excitement, Seoeun began singing a song she had learned in kindergarten. When Seoha praised her for doing well, she grew cocky and even started dancing.
*This is already the fourth time.*
Seoha had decided that this competition, being held at Seoul National University, would be the last general student competition he would participate in.
Having won the grand prize in all three previous competitions, Seoha was already at the center of a storm among figures in the mathematics world.
But this was limited to academic circles; to the general public, mathematics was not an object of interest at all.
*The Olympiad fiasco is probably one of the reasons too….*
This year, Korea’s overall ranking was 7th, after the United States, China, Russia, India, Iran, and Hungary.
Only Im Sujeong had barely saved face with an individual 3rd place.
It was a sorely lacking result even compared to the past, when they had done well on exams despite lacking meaningful mathematical achievements.
As soon as they unpacked at the hotel, Seoeun dove straight onto the bed.
Finding the large bed fascinating, she bounced up and down on it like a trampoline, then rolled to the side.
Miyeong took out a note with shopping list items written on it, hoisted the face-down Seoeun onto her back, and went outside.
Seoha briefly considered participating in a few more competitions for his family, but then recalled Uhyeon’s words and soon shook his head.
“It’s already enough. Any more would be a waste.”
Seoha thought the same.
It had been fun at first, but the problems were all more or less similar.
Now he wanted to tackle problems that stirred his spirit of challenge.
Seoha brought his right thumb to his wrist to check his pulse.
One.
Two.
Three.
*Thank goodness. No problems.*
OCD was a type of anxiety disorder.
In most cases, heart rate increased when symptoms appeared.
Seoha had been checking this constantly.
* * *
“Oppa! Good luck on your test!”
Perhaps because it was cold, Seoeun’s cheeks were red.
Seoha cupped his younger sister’s cheeks with both hands to warm away the cold. Seoeun’s face relaxed at the pleasant warmth.
“I’ll be back soon. Let’s eat something delicious later.”
“Yeah!”
The heavy auditorium door opened, and Seoha stepped inside.
He felt a strange sensation in an instant.
Glance, glance.
He felt eyes looking at him from all around.
*Why is this happening?*
Feeling awkward, Seoha walked inside to find his seat. With every step, blatant whispers reached his ears.
“That’s him, right?”
“He’s taller than I thought. I thought he was a middle schooler.”
The results from the last competition must have been announced.
Suppressing his discomfort, Seoha sat down. He took out his favorite pencil and a utility knife, sharpened the lead, and did some light stretching.
As he turned his waist to look behind him….
“Eek!”
Seoha hastily covered his mouth and looked forward.
From behind, a ghost-like face was staring holes into him.
*Who is that? Why are they looking at me like that?*
A pale face, sharp eyes.
The glare was far from ordinary. Goosebumps rose at the terrifying hostility.
Ding-dong-dang—
The bell rang, and the test began.
Seoha’s mood improved.
Since recognizing his OCD symptoms, Seoha had put in considerable effort.
Training himself to consciously turn off the calculations that ran automatically in his head had been as painful as holding his breath underwater.
But now there was no need for that.
He could simply spread his thoughts freely onto the paper.
Scratch, scratch.
Seoha’s hand moved without hesitation.
Sujeong stared at that sight for a moment before turning her focus back to her own test paper.
Seoha’s pencil moved across the paper as if dancing.
Like a prisoner freed from long captivity, he began riding the waves of thought freely.
Formulas came alive and moved.
The curves of function formulas spread outward.
A parabola soared, drawing an elegant arch, then settled down softly, and the waves of trigonometric functions continued endlessly.
The exponential function, creeping gently along the bottom at first, suddenly shot up explosively.
*Aha!*
He felt he understood the problem writer’s intention.
Using the properties of a convex function, this seemingly complex expression could be simplified into a single line.
But Seoha did not do that.
*The essence of this problem is symmetry.*
Curves unfolded in his mind, advancing endlessly, breaking through the structure the problem writer had intended. And eventually, he found the hidden cyclic symmetry deep within.
A brilliant idea flashed in his mind.
It was to think of the inequality as a geometric object in n-dimensional space.
Seoha began moving his pencil with an excited heart. When he converted the algebraic expression into geometric language, the essence of the problem revealed itself in a completely different form.
A proof that even the problem writer would not have anticipated was unfolding above Seoha’s hand.
* * *
Sujeong scanned her test paper.
Every single problem caught her eye. They were all problems she could solve.
*Thank goodness.*
A sense of relief washed over her.
Suddenly, a question arose.
*Why am I feeling relieved?*
To her past self, tests had been enjoyable events worth counting down the days for. Because she had always known that sweet rewards would undoubtedly follow when the test ended.
But now?
At some point, a strange emotion had taken root inside her.
A sense of defeat, of inferiority.
Sujeong shook her head roughly.
*No. There’s no way I’d be afraid of something like this.*
Sujeong knew herself well. Such things were nothing. She was never weak. Even if adversity came, she could quickly rise and overcome it with a smile.
The scariest thing was admitting to herself that she was an ordinary human being.
Ever since she lost to that child for the first time, everything had changed.
She needed to concentrate, but her mind was a mess.
*Since when did I like math? What was the reason?*
The answer was because it was difficult.
A snicker escaped her.
She had liked herself for easily and skillfully doing what others found difficult.
Of course, the praise that poured down afterward as well.
Dad, Mom….
They pretended to dissuade her outwardly, but she knew they were prouder of her than anyone else.
Problem 1.
[For real numbers a, b, c > 0 satisfying a + b + c = 3, prove that the following inequality holds: √(a² + 1) + √(b² + 1) + √(c² + 1) ≥ 2√3.]
It was a problem easily solved using Lagrange multipliers or the AM–GM inequality.
But Sujeong did not pick up her pencil.
She could tell just from his back.
That the child in front of her was immersed in something, moving his pencil with excitement.
Sujeong gritted her teeth.
*I can do it too.*
She would not choose the safe path. Following the model answer exactly was not a true perfect score.
Sujeong gazed at the problem again.
√(a² + 1)… She felt this form could be interpreted as a vector norm.
*Wait, should I try Minkowski’s inequality?*
Probably no one here would have thought of using it.
Scratch, scratch.
Sujeong’s pencil moved busily.
Time passed.
No matter how she continued calculating, errors kept occurring.
*Did I get the sign wrong? A calculation mistake?*
No, she had taken the wrong path.
*Concentrate, Im Sujeong.*
Sujeong lightly slapped her own cheek and started over from the beginning.
A bit more carefully.
Tick, tock.
*Why won’t this work?*
Normally, such a problem would not have taken even ten minutes.
*Should I just solve it the way I always do?*
She could not.
She had a feeling that doing so would yield the same result as last time.
She wanted to submit a shocking answer that would make the judges’ eyes widen, just like the reaction her school teacher had shown upon seeing Yu Seoha’s answer.
But contrary to her heart, her head kept forcing other thoughts on her.
*What am I lacking?*
Knowledge?
That she, the youngest qualifier for the International Olympiad in twenty years, could be lacking compared to that elementary schooler?
Technique?
She was confident she knew all the solution methods and applications of every past Olympiad problem.
Experience?
She dared assert that no one her age had participated in more competitions.
Then what on earth?
One possibility arose in her mind.
But she immediately denied it.
The problem was right in front of her.
She had no leisure to think of other things.
She had thought she could definitely solve it, yet every calculation reached a dead end.
The seemingly simple inequality felt like a massive wall. Countless formulas from her pencil tip filled the paper, but the proof itself could not be completed.
Tick, tock.
Time flowed on mercilessly.
“Thirty minutes remain until the test ends.”
The proctor’s calm voice echoed through the test hall.
Sujeong’s heart began to pound.
It meant she had been fixated on Problem 1 for two hours and thirty minutes.
For a moment, Sujeong felt a desire to solve everything the way she usually did and just be done with it.
At the same time, she had a premonition that if she did so, she would never be able to beat Yu Seoha for the rest of her life.
*I’m giving up on a perfect score.*
Sujeong threw everything away and devoted herself to proving Problem 1.
Sujeong had been called a math prodigy since she was three.
She was confident that under the same conditions—age—she could definitely take first place at the International Olympiad. And she had planned to do so as well.
Scratch, scratch.
The sound of pencils filled the air.
Everyone was finishing their answers. But Sujeong’s hand was frozen in mid-air, trembling.
Plip.
A small drop of water fell onto the test paper.
Plip, plip.
The densely written formulas began to smudge.
In the end, Sujeong could not finish the proof until the very end.
“Time’s up. Everyone put your hands down.”
Sujeong raised her head and looked forward. Tears blurred her vision, and she looked pathetic, but she could not think of anything.
His figure calmly organizing his test paper looked peaceful.
His hand moved to carefully pick up his pencil and put it in his pencil case.
The duck with a mischievous expression hanging from the end of the pencil seemed to be mocking her.
“Damn duck….”
Sujeong muttered under her breath.
If she let him go like this, she did not know when she would see him again.
Her chest felt so tight it might burst. She could not even breathe properly.
He submitted his test paper and walked out.
Swoosh.
“Wait!”
The moment he brushed past her, Sujeong unconsciously grabbed Seoha’s hand.