A Beautiful Compromise
"Yeah, yeah, that. You remember when you prepared for the MCM (Mathematics and Computation in Music) conference? You still have all those materials, right?"
"No, wait, are you seriously showing that to an elementary schooler? And expecting him to understand? Even the geometric approach to microtones? Wouldn't just explaining the Pythagorean comma be enough?"
"Just bring everything related to music! Don't you want to see this kid?"
"Sigh, it's so heavy... Seriously. Fine, I get it."
"How long will you be?"
"Twenty minutes."
"Okay, see you then."
Cha Se-young hung up, took a sip of her iced Americano, and stared at the apartment complex across the street.
For a while, she hadn't even turned her head in this direction whenever she passed by this neighborhood.
But she had been genuinely curious.
How the boy was doing in school, how shocked his teachers were, and whether his homeroom teacher—the one she had spoken to on the phone—had developed stress-induced alopecia...
In any case, the more she consciously tried not to think about him, the more he came to mind.
Most of all, she found herself deeply missing his bright, sparkling eyes and adorable face.
She was terrified of his barrage of questions, but she still wanted to see him, which was why she had called her friend for backup.
My hair is precious.
Unlike her, her friend was a science high school graduate currently in a PhD program, so surely she could hold a conversation with such a brilliant child.
But this time, it's music?
When they had lessons together, he had been completely obsessed with stars and the universe.
Cha Se-young suddenly found herself incredibly curious about what went on inside his head.
She couldn't even begin to guess how far his question marks had stretched from a single sheet of music.
I think he reached the Pythagorean comma all on his own...
A chuckle escaped her lips.
She was picturing the look of utter bewilderment on Park Ye-ji's face—the very friend who had dismissed her claims as lies back then.
You're up next, girl. Let's see how you handle it.
The corners of Cha Se-young's mouth twitched upward.
"I-Is that so?"
Jeon Hye-min nodded quickly at Go Chang-ho's words.
As soon as the after-school piano class ended, she had rushed to the staff room to find Chul-jun's homeroom teacher.
She had never seen a child with such raw talent for the piano.
It was something she simply couldn't let slide.
She hadn't let it show during class.
She believed consulting his homeroom teacher was the first step.
But although he seemed surprised, his reaction wasn't as dramatic as she had expected.
It was to the point where she wondered if she had failed to convey the gravity of the situation.
"Um, Teacher. For a child who doesn't even know the basics to play the piano like that is extraordinary. If he's taught properly..."
"Ah, yes. I completely understand what you're saying, Teacher."
"..."
"Well, I will pass this along to his guardian, but unless they say otherwise, I would appreciate it if you could treat him like any other ordinary child."
"Pardon...?"
"I must ask this of you. Ah, but please do let me know whenever special situations like today arise."
"Ah..."
Go Chang-ho smiled warmly as he sent off the bewildered piano teacher.
Only then did Go Chang-ho shake his head, his own expression turning to one of sheer disbelief.
I barely managed to keep my cool.
He really couldn't pin the boy down.
The piano?
How on earth did his genius leap in that direction?
He shook his head, planning to ask Chul-jun gently tomorrow.
A genius who found his own path without anyone's guidance.
Suddenly, the Indian mathematician Ramanujan came to mind.
A man from rural India who had almost no formal mathematical education, teaching himself from a single textbook.
While Newton, Leibniz, Euler, Gauss, and Riemann were monumental geniuses, Chul-jun currently resembled Ramanujan.
From a very young age, Ramanujan had raised his own question marks and discovered countless formulas and theorems in the process of solving them. Even a century after his death, many of his formulas remained unproven.
Chul-jun was the same.
No one had pushed him from a young age, and he hadn't received any special training.
Yet, he raised his own questions and paved his own path toward the answers.
He would have to ask tomorrow to be sure, but the piano must have started from some question mark as well.
That was just how the boy operated.
Sigh, in the end, I'm comparing him to a mathematician again...
He couldn't think of a single non-STEM genius to compare him to.
Go Chang-ho pouted in mock frustration.
He had heard from Chul-jun.
That the boy had connected Baduk to mathematics.
Honestly, Chang-ho couldn't understand everything the boy had babbled about, but he knew for sure that Chul-jun had used math to find the optimal moves.
Chul-jun instinctively read the world by turning it into patterns.
Children with exceptionally high cognitive abilities automatically count stairs as they climb, find rules in tile patterns, and feel uncomfortable with asymmetrical arrangements.
That was simply how they saw the world.
Mathematics was the only language and tool of proof that first confirmed to that brilliant brain: What you see is correct.
He didn't know how Chul-jun had reached the piano, but he was undoubtedly approaching it mathematically this time as well.
Hmm...
Lost in thought, Chang-ho shook his head slightly.
Chul-jun and Ramanujan were different.
Ramanujan had nothing but mathematics.
He failed everything else, and his interpersonal skills were poor.
All his question marks existed solely within math.
But Chul-jun's question marks began in other fields and then connected to mathematics.
First space, then Baduk, and now the piano.
His interest lay not in mathematics itself, but in reading the world through mathematics.
And above all, the Chul-jun he saw valued relationships.
He showed none of the isolation or insularity typically seen in high-functioning gifted children.
That was why Chang-ho was so full of anticipation.
Instead of becoming a genius who shut himself away in his own world, obsessing over a single proof for his entire life, Chul-jun could become something entirely different.
Ending his long train of thought, Go Chang-ho smiled warmly.
The ultimate environment.
A free genius.
Go Chang-ho couldn't even begin to guess what kind of possibilities this would create.
Ah, first, I should let his guardian know.
Chang-ho pulled out his phone.
"Ah, yes. Yes. Well, I don't really understand it, but you're right. They're talking about math. ... Ah, yes, his former tutor came by, and she brought her friend too. I think they said she's a math graduate student... Yes, that's right. They have a piano book open, but they're talking about math. Haha... Yes, thank you for calling."
Hyeong-man scratched his head and hung up.
He glanced at Chul-jun's tightly closed bedroom door.
When he had slipped in earlier to bring them drinks, he had caught a glimpse of the sheet music. It was covered in bizarre symbols.
They looked exactly like math formulas.
Well, I'll be...
He would need to know something about it to even guess, but Hyeong-man had absolutely no idea what they were discussing in that room.
Smacking his lips, Hyeong-man plopped down on the sofa.
Through the door, Chul-jun's voice drifted out.
It sounded like an alien language.
"First, I assumed this number could be written as a fraction. If it's a fraction, we can write it as p over q. But here, p and q must be coprime, meaning they can't be simplified any further. Their only common divisor is 1. Since multiplying it twelve times must equal 2, dividing p12 by q12 must equal 2. That means p12 = 2q12. But the right side is a multiple of 2. That means the left side must also be a multiple of 2, so p must be a multiple of 2. If p is a multiple of 2, we can write p as 2k. Substituting that back in gives 212k12 = 2q12, and dividing both sides by 2 gives 211k12 = q12. Right?"
"..."
Cha Se-young glanced at her friend Park Ye-ji's face and stifled a laugh.
As expected, Ye-ji looked utterly bewildered.
"This time, since the left side is a multiple of 2, q must also be a multiple of 2. But we assumed at the beginning that p and q couldn't be simplified further. If both are multiples of 2, they can be simplified by 2. That's a contradiction. Therefore, our initial assumption was wrong. This number cannot be written as a fraction. Is this correct?"
"Th-That's correct, but we call that the Pythagorean comma..."
"So in the end, math couldn't give a perfect answer, so they just settled for a rough average?"
"Uh... right. They found a compromise. And that compromise is an irrational number."
"Then, does the fact that we can't get a perfect answer, but proved that we can't, become the actual answer?"
"Uh... you could look at it that way. In mathematics, we call that a proof of impossibility. It's not that we failed to find an answer, but rather we proved that a perfect answer doesn't exist. That proof itself is the conclusion."
Chul-jun furrowed his brow.
"Then..."
"..."
"Is the piano an incorrect instrument?"
"Huh?"
Park Ye-ji was speechless. She quickly looked at Cha Se-young.
Cha Se-young smirked.
How do you like that?
Park Ye-ji swallowed hard.
"No. It's not incorrect. They chose the best possible method while knowing it wasn't perfect. That's equal temperament."
"So mathematically, it's an imperfect instrument, but it makes such beautiful sounds."
"Ah... yeah."
Chul-jun stared down at his notebook and muttered, "That's amazing."
He had looked so grumpy and dissatisfied just a moment ago, but now his face was bright with innocent wonder.
"Pythagoras was so cool. He's everywhere!"
"..."
"But... I feel a bit bad for him."
"Why?"
"He was someone who tried to explain the whole world through math. But he had to prove with his own hands that it was impossible."
"Ah..."
Chul-jun stared quietly at his Beyer piano book.
"That must have been really hard for him."
The two math majors felt momentarily dazed by Chul-jun's words.
They had never once thought of Pythagoras in that light. But hearing this young boy say it, they found themselves nodding in agreement.
"But if we accept the Pythagorean comma, can chords and things like that be fully explained mathematically?"
Park Ye-ji snapped out of her daze and nodded quickly.
"Yes! Yes! Well, research is still ongoing, so not everything..."
She moved her laptop mouse and opened the folder she had brought.
"Look, this is the Fourier series. It's a way to decompose sound into mathematical formulas. Uh, but to understand this, you need trigonometric functions, exponential and logarithmic functions, calculus, linear algebra, and analysis. You need to know about twenty-six different concepts..."
Park Ye-ji laid out her materials on the desk one by one.
Honestly, she had been skeptical when she brought them. She wondered if she would even get to pull them out.
But she felt like she could show them to this child. She wanted to show him how incredible a single mathematical concept could be.
"These are papers and academic books presented at MCM, a conference where they calculate math in music."
Chul-jun's eyes sparkled, and Park Ye-ji swallowed hard.
Is this really okay?
Handing graduate-level textbooks to an elementary schooler.
Moreover, concepts like the mathematical definition of consonance, convergence issues, and the boundary with neuroscience were still active areas of research with no definitive conclusions.
If someone dumped all of this on her at once, she would have been completely overwhelmed...
"Wow! There's so much to look at!"
But this boy was different. He was actually thrilled.
In truth, she had pulled them all out hoping for this exact reaction.
"Thank you!"
He really was as incredibly cute as she had heard. A warm smile spread across her face.
"Can I ask you more questions if I get curious in the future?"
"Huh? Oh, of course!"
"How much do I owe you?"
"What?"
"For the books and the tutoring."
Park Ye-ji quickly waved her hands.
"No, no. This is nothing..."
"My dad said nothing in this world is free!"
"Then... how about you come visit my university with me later? We'll call it even for the books and tutoring!"
"Your university?"
"Yeah. I want to introduce you to some other people. Ah, with your guardian's permission, of course."
"Okay!"
Watching them talk, Cha Se-young raised her chin and squared her shoulders.
See that? I was his first teacher!
Cha Se-young ran a hand through her hair. Feeling the texture, she was certain her hair was growing back nicely.
For Chul-jun, his world with his dad had been everything.
He had almost no contact with the outside world, and no relationships with other people.
Chul-jun hadn't viewed this as a deficiency. In that tiny world, he had been perfectly safe and happy. That was all he needed.
But suddenly, an incredibly vast world had opened up to him.
It had been barely over a month since he arrived in South Korea, yet the number of people connected to him had exploded.
The things he had learned had grown exponentially, and the things he had to learn had grown just as much.
Everything was thrilling.
The world was much bigger and far more interesting than he had imagined.
Baduk, math, music, and people were all problems waiting to be solved.
And it was so fascinating and fun that everything connected back to mathematics.
Then, he had run into a rather formidable wall.
Fourier series?
He didn't know why, but he didn't want to avoid this wall.
For the first time since coming to South Korea, his very own question mark had appeared.
He wanted to understand music perfectly through math alone.
This is going to be so much fun.
Chul-jun beamed as he looked at the books and folders piled on his desk.
It was the first world of proof Chul-jun had ever encountered.
"Ah, yeah. Yeah. He's been in his room ever since he got home today too. ... No, no. He eats fine. He does everything he's supposed to. Brushed his teeth, took a shower. Sometimes he's late because he's playing Baduk with a friend, but they say he's doing great at school with no issues. Oh, they had a race and he came in first. Yeah, the piano arrived last week. ... I don't know if he's good. He plays by himself with headphones on. I asked him to play just one song, but he's playing hard to get... Haha. No, it's not like he only plays the piano. He spends way more time sitting at his desk. Ah, that tutor and her friend came by the day before yesterday too. They insisted on not taking anything, but I made sure to give them some pocket money for transit. They said they'd take him to Seohan University later to show him around. Huh? This weekend? Let's see... Ah, is Chul-jun's friend's Baduk tournament this week? ... Oh! Right. Park Jin-gyum's son, the one you mentioned. He said he's going to watch it with his teacher and friends. Yeah, got it. Talk to you later."
Hyeong-man hung up, scrunched his nose, and listened closely to Chul-jun's room.
Plink, plonk. He could hear the faint sound of the electronic piano keys being pressed.
Huh...
He was dying to know what the boy was playing.
...Hmm?
The sound of the keys stopped, followed by the scraping of a chair.
He was probably sitting at his desk again, writing something down furiously.
What on earth is he doing in there...
Hyeong-man scratched his belly and lay down on the sofa.
Then he turned on the TV.
Keeping the volume very low.