Translator: Dreamscribe
"Alright, is everyone on board? Seo-eun, did you fasten your seatbelt properly?"
Chul-ho turned around from the driver’s seat to check.
From his tone of voice, Yu Seo-ha could sense a slight excitement.
At some point, Seo-ha’s schedule for math competitions had become something like family trips. Thanks to the support from Okcheon County, they no longer had to worry about the costs.
"Yes!"
Seo-eun raised both hands and responded cheerfully.
"Here’s Seo-ha’s bag, and Seo-eun’s clothes are packed properly too...."
Mi-young seemed to have something on her mind, so she got out of the car and checked the trunk once more.
"Do we really need such a big bag for just one day?"
As a man from the countryside, Chul-ho couldn’t understand this world.
National-level math competitions were mostly held in Seoul.
Seoul might not be an ideal travel destination for city dwellers, but to country folks like Seo-ha’s family, it was a whole new world every time they went.
Especially Mi-young and Seo-eun had completely fallen in love with Seoul’s charm.
"Still, you never know."
Mi-young hummed a tune as she rearranged the luggage and closed the trunk.
Vroom.
The car set off.
Seo-eun, unable to hide her excitement, began singing a song she learned at kindergarten. When Seo-ha praised her for doing well, she got even more proud and started dancing along.
‘Already the fourth time.’
After the current competition held at Seoul National University, Seo-ha had decided not to participate in any more contests aimed at regular students.
Having won the Grand Prize in all three previous competitions, Seo-ha had already become the eye of the storm among people in the mathematics field.
However, this was limited to the academic community, and to the general public, mathematics was of no interest at all.
‘Maybe one reason is that we completely failed at the Olympiad....’
This year, Korea ranked 7th overall, behind the United States, China, Russia, India, Iran, and Hungary.
Only Lim Su-jeong managed to barely save face by ranking 3rd individually.
Compared to the past, when there were no notable mathematical achievements but test scores were still high, this result was seriously lacking.
As soon as they unpacked at the tourist hotel, Seo-eun jumped straight onto the bed.
She seemed fascinated by the large bed, bouncing up and down like it was a trampoline, then rolling over to the side.
Mi-young pulled out a note with things to buy, hoisted the sprawled-out Seo-eun onto her back, and went outside.
Seo-ha briefly considered whether he should participate in more competitions for the sake of his family, but quickly shook his head after recalling what Woo-hyun had said.
“It’s already enough. Anything more is a waste.”
Seo-ha thought the same.
At first, it had been fun, but now all the problems were too similar.
He wanted to solve questions that would inspire more of a sense of challenge.
Seo-ha brought his right thumb up to check his pulse.
One.
Two.
Three.
‘Good. No problems.’
Obsessive-compulsive disorder is a type of anxiety disorder.
In most cases, heart rate increases when symptoms appear.
Seo-ha kept checking this constantly.
***
"Oppa! Do well on the test!"
Maybe because of the cold weather, Seo-eun’s cheeks were red.
Seo-ha held his little sister’s cheeks with both hands to warm her up. Feeling the warmth, Seo-eun’s face relaxed.
"I’ll be back soon. Let’s eat something delicious later."
"Okay!"
The heavy auditorium doors opened and Seo-ha stepped inside.
For a moment, a strange feeling washed over him.
Glance, glance.
He could feel people looking at him from all directions.
‘What’s going on?’
Feeling awkward, Seo-ha walked further inside to find his seat. With every step, he could hear blatant whispers.
"That’s him, right?"
"He’s taller than I expected. I thought he was in middle school."
It was clear that the results from the last competition had been made public.
Suppressing his discomfort, Seo-ha sat down. He took out his favorite pencil and cutter knife, sharpened the lead, and did some light stretching.
He twisted his back and looked behind him....
"Eek-!"
Seo-ha quickly covered his mouth and looked forward.
A ghostly face was staring intently at him from behind.
‘Who is that? Why is she looking at me like that?’
A pale face, sharp eyes.
The glare was intense and far from ordinary. A chilling hostility made Seo-ha shudder.
Ding-dong-deng-
The bell rang, and the test began.
Seo-ha’s mood brightened.
Since recognizing his obsessive-compulsive symptoms, Yu Seo-ha had been making steady efforts.
Training himself to consciously turn off the automatic calculations running in his head was as painful as holding his breath underwater.
But now, there was no need for that anymore.
He could freely spread his thoughts onto the paper.
Scratch, scratch.
Seo-ha’s hand moved without hesitation.
Su-jeong, who had been staring at him, finally began to focus on her own test paper.
Seo-ha’s pencil danced across the sheet.
Like a prisoner released from a long captivity, he began to ride the wave of thoughts freely.
The formulas came to life.
The curves of function formulas spread out.
A parabola soared with an elegant arch and landed smoothly, and the wave of trigonometric functions continued endlessly.
The exponential function started off slowly, almost crawling along the bottom, then suddenly shot up explosively.
‘Aha!’
He thought he understood the intent of the test maker.
Using the properties of convex functions, this seemingly complex expression could be simplified into a single line.
But Seo-ha didn’t choose to do that.
‘The essence of this problem is symmetry.’
A curve spread out in his mind, extending endlessly to break through the structure the test maker had intended. And finally, he discovered the cyclic symmetry hidden deep within.
A brilliant idea flashed in his mind.
It was to consider the inequality as a geometric object in n-dimensional space.
Excited, Seo-ha began to move his pencil. When the algebraic expression was translated into geometric language, the true nature of the problem revealed itself in an entirely different form.
A proof that even the test maker couldn’t have anticipated was unfolding under Seo-ha’s hand.
***
Su-jeong scanned over the test paper.
Each problem caught her eye. They were all problems she could solve.
‘Thank goodness.’
A wave of relief came over her.
But then, a question popped into her mind.
‘Why am I feeling relieved?’
In the past, exams had been events she looked forward to with anticipation. Because she knew that sweet fruits always followed at the end of every test.
But now?
At some point, a strange feeling had taken root inside her.
A sense of defeat, a sense of inferiority.
Su-jeong shook her head roughly.
‘No. I’m not afraid of things like this.’
Su-jeong knew herself well. That kind of thing was nothing. She was never weak. Even if adversity came, she could get back up right away and overcome it with a smile.
The scariest thing would be admitting to herself that she was just an ordinary person.
Since the first time she lost to that kid, everything had changed.
She needed to focus, but her mind was a mess.
‘When did I start liking math? What was the reason?’
The answer: because it was hard.
A dry laugh escaped her lips.
She liked being able to easily handle things others found difficult.
Of course, along with that came the shower of praise.
Dad, Mom...
She knew that although they pretended to stop her on the outside, they were actually prouder of her than anyone else.
Problem 1.
[Given real numbers a, b, c > 0 such that a + b + c = 3, prove that the inequality √(a² + 1) + √(b² + 1) + √(c² + 1) ≥ 2√3 holds.]
It was a problem that could be easily solved using the Lagrange multipliers or the Arithmetic Mean - Geometric Mean inequality.
But Su-jeong didn’t pick up her pencil.
Just by looking at his back, she could tell.
The boy in front of her was completely immersed, excitedly moving his pencil.
Su-jeong clenched her teeth.
‘I can do it too.’
She wouldn't choose the safe route. Simply following the model answer wouldn’t get a perfect score.
Su-jeong looked at the problem again.
√(a² + 1)... She thought she could interpret this form as the norm of a vector.
‘Wait, should I try using the Minkowski inequality?’
Probably no one here had even thought of using that.
Scratch, scratch.
Su-jeong’s pencil moved busily.
Time passed.
No matter how far she carried the calculations, she kept making errors.
‘Did I write the sign wrong? A calculation mistake?’
No, she had taken the wrong path.
‘Focus, Lim Su-jeong.’
Su-jeong lightly tapped her cheeks and started again from the beginning.
A little more carefully.
Tick, tock.
‘Why can’t I solve this?’
Normally, this kind of problem wouldn’t have taken her ten minutes.
‘Should I just solve it the usual way?’
No.
She had a feeling that if she did that, the result would turn out just like last time.
She wanted to submit a solution so shocking it would leave the judges wide-eyed. Just like the reaction from the teacher when they saw Yu Seo-ha’s answer.
But unlike her intentions, her mind kept forcing other thoughts on her.
‘What is it that I’m lacking?’
Knowledge?
She was the youngest person in twenty years to make it to the International Olympiad, more than that elementary schooler?
Technique?
She was confident she had mastered all the solution methods and applications of every past Olympiad question.
Experience?
She could say with certainty that no one her age had participated in more competitions than she had.
Then what could it possibly be?
One possibility rose up in her mind.
But she immediately denied it.
The problem is now.
There’s no room for other thoughts.
She had believed she could solve it for sure, but every line of calculation led to a dead end.
A seemingly simple inequality now felt like a massive wall. The countless formulas written from her pencil filled the paper, but the proof remained incomplete.
Tick, tock.
Time passed without mercy.
“Thirty minutes remaining.”
The proctor’s calm voice echoed through the exam hall.
Su-jeong’s heart began to pound.
That meant she had spent two and a half hours stuck on problem one.
For a moment, Su-jeong felt a desire to just solve everything the usual way and be done with it.
At the same time, she had the chilling feeling that if she did that, she would never be able to beat Yu Seo-ha for the rest of her life.
‘I’ll give up the perfect score.’
Su-jeong threw everything else aside and clung to the proof for problem one.
Su-jeong, who had been called a math prodigy since the age of three.
Under the same conditions (age), she was certain she could take first place in the International Olympiad. And she intended to.
Scratch, scratch.
The sound of pencils filled the room.
Everyone was wrapping up their answers. But Su-jeong’s hand, suspended in midair, was trembling.
Drop.
A small droplet fell onto her test paper.
Drop, drop.
The densely written formulas began to smudge.
In the end, Su-jeong was unable to finish the proof.
“Time’s up. Everyone, put your pencils down.”
Su-jeong lifted her head and looked forward. Her face, stained with tears, was unsightly, but she couldn't think of anything.
His calm manner of organizing his test papers looked peaceful.
He moved his hand, gently picking up his pencil and placing it into his case.
The duck with the mischievous expression hanging from the end of his pencil seemed to be mocking her.
“Damn duck....”
Su-jeong muttered under her breath.
If she let him go like this, she might never get another chance to see him again.
Her chest felt so tight it was about to burst. She couldn’t even breathe properly.
He submitted his test paper and began walking out.
Srrrk.
“Wait a minute!”
As he brushed past her, Su-jeong instinctively grabbed Seo-ha’s hand.
*****
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