Did Young Mozart Have Fun?
'A minuet... A minuet...'
Gu Byung-ook, the Dean of the College of Natural Sciences at Seohan University, had originally started his career as the chair of the mathematics department.
At one point, he had even personally traveled to the MCM—the Mathematics and Computation in Music conference—to present a paper.
It was a group-theoretic analysis of Bach's fugues, a paper that mathematically proved how the thematic transformations of a fugue formed a Klein four-group structure.
Usually, when analyzing music through mathematical structures, researchers tended to apply them to Bach's fugues, Chopin's preludes, or his nocturnes.
Other frequent subjects included Beethoven's late string quartets and Stravinsky's The Rite of Spring.
These were all highly complex compositions, offering an abundance of material for mathematical dissection.
He had chosen the fugue because its group-theoretic structure was clearly defined, allowing for a topological approach.
Even now, he still spent his spare moments analyzing Schoenberg's scores using set theory.
Yet, this incredibly simple minuet score that had appeared out of nowhere was currently shaking his mathematical intuition to its very core.
'Sigh...'
Gu Byung-ook stared blankly at the printed document.
It was a photograph of a page from a beginner's piano textbook.
There were only two pages in total.
K. 1, Minuet in G major.
An extremely short piece of only sixteen measures.
Written in 3/4 time, the arrangement of the notes was almost trivial.
And yet, the formulas packed tightly into the margins transformed that simple sheet music into a profound work of art.
To think that such a simple score—one so basic it would never have even been considered for discussion at the MCM—could yield such magnificent equations.
The moment he laid eyes on this material, which had been brought to him by the current chair of the mathematics department, he felt as if he had been struck by a bolt of lightning.
And what he heard afterward was even more shocking.
—Apparently, he's an elementary schooler. A fifth grader.
Gu Byung-ook swallowed hard, shaking his head in disbelief.
It was mind-boggling that an elementary school student could understand Fourier series to such a degree at that age, let alone apply them.
It was surprising enough that the child had mastered trigonometry and calculus, but this meant he also possessed a working knowledge of linear algebra and mathematical analysis. What was truly astonishing was how he had selectively studied only the exact concepts necessary for Fourier series.
It meant his ability to filter and grasp information was extraordinarily outstanding.
'...'
With that level of talent, the boy surely would have stood out in some math olympiad, yet it was incredibly fascinating that he had no record of any awards whatsoever.
Gu Byung-ook closed his gaping mouth and examined the formulas once more.
'Phew, let's see...'
The part representing the time signature and notes as sequences, and the pitch as numbers, was perfectly understood.
The way he arranged the melody of the first four measures of Section A into a sequence was also excellent.
Beyond that, his analysis of interval distances and his mathematical representation of stepwise motion and leaps were brilliant.
The resulting notation for the transformation of the harmonic structure was flawless.
T₀ : G Major = {0, 4, 7}
T₇ : D Major = T₇({0, 4, 7}) = {7, 11, 2}
Though a bit unpolished, it was truly marvelous.
It wasn't just intuitive calculation; he had deduced the conclusion through highly original reasoning.
Furthermore, the child hadn't stopped at proving this; he had even attempted an inverse calculation.
The moment he began to question the parallel keys and melodic leaps—which were designed to fit together so naturally—these marvelous formulas underwent an unpredictable, chaotic transformation.
'Sigh...'
The purpose of this sheet music and these formulas was to prove through inverse calculation that Leopold had heavily arranged this piece, the Minuet.
Of course, the formulas on this sheet music alone wouldn't be enough to reach a definitive conclusion.
But the approach itself was incredibly ingenious.
'And an elementary schooler did this...?'
How could he not be excited?
"Hey! Is it confirmed that he's coming?"
"I heard he's scheduled to meet the graduate student's advising professor."
"Good. Did you talk to the chair of the piano department?"
"Well, his reaction was a bit..."
"Fine. I'll speak to the Dean of the College of Music myself."
"Yes, sir!"
How long had it been since his heart beat this fast?
The eyes of Gu Byung-ook, Dean of the College of Natural Sciences, gleamed with a touch of madness.
"Uh..."
As Cheol-jun's explanation paused, Go Chang-ho swallowed hard.
A bright, cheerful piano melody was playing from the tablet on the table.
But the atmosphere in this room was anything but bright and cheerful.
"Do you understand, Teacher?"
Go Chang-ho's eyes were shaking like an earthquake.
No matter how much he listened to Cheol-jun's explanation, he couldn't understand a single thing.
It felt like he understood the words, but the things Cheol-jun wrote and drew in his notebook to "help" him understand only made his head spin more.
"So, uh... what you want to do is..."
"The original version of the Minuet! The one the five-year-old actually made."
"Ah..."
"I want to prove it!"
He didn't know if it was right or wrong, or what those formulas even meant, but wasn't this something absolutely massive?
Suddenly, he became curious about why the boy had started this in the first place.
"Uh, Cheol-jun?"
"Yes!"
"Why did you start this?"
Cheol-jun furrowed his brow slightly.
Then, he stared quietly at the sheet music covered in countless formulas.
"After I encountered this piece, I looked up Mozart. But he had to practice incredibly hard from a very young age. Apparently, his dad was really scary, too. And the reason was that they needed to make money. The nobles only gave them money if he was rumored to be a prodigy. He had to be perfect from childhood. He couldn't make mistakes, and he couldn't rest."
"..."
"Thanks to that, incredible music was made later on."
Cheol-jun scrunched up his nose before speaking again.
"...But did young Mozart have fun?"
Go Chang-ho blinked blankly.
"Thinking about Mozart's childhood, I analyzed the Minuet again."
Cheol-jun ran his finger gently across the sheet music.
The corners of Go Chang-ho's mouth tugged upward.
The beginning wasn't mathematics, and the destination wasn't just a proof.
The proof was merely a tool used in the process.
This child was definitely different from other mathematicians.
Cheol-jun's question started from the world, passed through mathematics, and returned to the world.
And he even showed musical sensibility and talent.
'Sigh... To think he started this just because he wanted to find the original song of young Mozart...'
Go Chang-ho let out a sigh of relief inwardly.
'As expected, he's not completely a STEM kid!'
Cheol-jun, catching Chang-ho's reaction, grinned and scratched his head.
"But actually, in the end, I just made it based on my feelings."
"Ah..."
"But since it seems like mathematics got me close, I want to ask someone who knows more."
As expected, he was a child with clear self-awareness.
Go Chang-ho chuckled and patted Cheol-jun's head.
Cheol-jun grinned, looking a bit embarrassed.
"So, you decided to go to Seohan University?"
"Yes. I want to know for sure if it's impossible with math. If I meet the math teacher at that university, I'm going to ask him. My tutor set up the meeting."
It was probably a mathematics professor.
If they saw the brilliant genius in those formulas on the sheet music, they would definitely try to lure Cheol-jun in...
The choice would be Cheol-jun's, but he might easily fall for an adult's sweet talk.
He couldn't send him alone.
Go Chang-ho raised an eyebrow.
"Haha. Actually, a junior of mine is a professor at that school."
"Whoa. Really?"
"Yeah. Should I go with you that day?"
"Yes!"
Cheol-jun smiled brightly.
"Ah, I said I'm not doing it!"
"Come on, Professor Kim. Just close your eyes and go fill the seat. The Dean of Natural Sciences personally asked me, that's how urgent it is. I've never seen that man get so worked up before."
An eyebrow of Kim Seong-cheol, Chair Professor of the Piano Department, twitched.
That proud Dean of Natural Sciences personally?
Isn't this a bit much just to hype up some young prodigy?
"This isn't a proof; it's going to remain a hypothesis anyway. If so, the reputation of the person validating it becomes crucial. That way, the academic community will actually pay attention. Is there anyone else at Seohan University with that kind of recognition besides you? No, is there anyone in Korea—or even worldwide—who is as respected in the piano world as you are? Hmm? Do it for my sake..."
The corner of Kim Seong-cheol's mouth twitched slightly.
Choi Han-ho, the Dean of the College of Music, caught that immediately.
This friend, who had been called a prodigy since childhood and swept international competitions, had an immense desire for recognition.
If not for the Triad kidnapping incident in China—and if he hadn't injured his hand back then—he would still be a living legend in the piano world.
Well, surviving that ordeal was a miracle in itself.
Anyway, he had taken the bait.
"If you play along just this once, I'll make sure to personally take care of the funding for musical prodigies in next semester's budget. Deal, Professor Kim?"
Kim Seong-cheol pouted and let out a sigh.
But Choi Han-ho, who had known him for a long time, could clearly see that the man was grinning inside.
"Sigh, well, it's true there's no one else quite like me. Okay. But I'm not going to dance to the tune of those number-crunchers. I will only speak the truth according to my convictions."
"Of course! Of course! That's how it should be."
Choi Han-ho, Dean of the College of Music, bantered even more playfully as he massaged Chair Professor Kim Seong-cheol's shoulders.
"Oh, honestly..."
Kim Seong-cheol's lips kept twitching.
"My goodness. Then I'll leave him in your hands."
"Yes! Don't worry, sir."
"Haha. Thank you so much for taking care of him even on your day off."
"Haha."
Cheol-jun bowed deeply.
"I'll be back!"
"Right, right. Be safe."
"Yes!"
Watching the teacher's car drive away with Cheol-jun, Hyeong-man furrowed his brow slightly.
'Maybe I should have gone with them.'
Well, since his homeroom teacher was going with him, nothing bad would happen.
'Wait. Should I call Professor Kim?'
Soon, Hyeong-man shook his head.
Cheol-jun was going to meet a mathematics professor.
The boy already detested math, so there was no need to bring it up.
Besides, if he mentioned it, the professor would probably pester Cheol-jun to play the piano, which would only bother him.
Hyeong-man smacked his lips and walked toward the elevator.
The small recital hall of Seohan University's College of Music.
On the stage sat a Steinway D-274 grand piano.
But unlike usual, two large whiteboards—completely out of place next to the luxurious piano—stood there as well.
There was also a projector screen, displaying a relatively simple sheet music.
Yoo Min-seok, a professor of education, peeked inside from the entrance and widened his eyes.
"Whoa, what is this?"
When he talked to his senior on the phone, it had sounded quite strange.
'Why is the meeting with a math professor in the music school's recital hall?'
So, thinking Senior Go might have gotten the location wrong, he had come to check it out himself.
Was this really not the place?
"Oh? You came too, Professor?"
"Huh?"
"Is the Gifted Education Center interested in this too?"
"...What?"
"Aren't you here to see the kid coming today?"
Min-seok tilted his head.
"The kid coming today?"
"You know, the elementary schooler who analyzed and even did an inverse calculation of the Minuet."
"Uh... Ah, is this the right place?"
"Yes! But how did you find out, Professor? We're still keeping it quiet."
Yoo Min-seok narrowed his eyes and looked back at the stage.
Something was going very strangely here.
"Well, his homeroom teacher is my senior."
The math professor clapped his hands.
"Wow, of course. His homeroom teacher is no ordinary person either."
"Huh?"
"If he's your senior, it's that person, right? The one who got a PhD in education from Harvard but voluntarily chose to become an elementary school teacher?"
"Ah... Yeah. That's him."
"Wow, this is amazing too."
"..."
"Anyway, the entire College of Natural Sciences is in an uproar right now. I heard the Dean is coming today too."
"...Huh? The Dean?"
"Yes! Ah, I have to go prepare the materials... See you later!"
"Uh, yeah. Sure."
Watching the math professor walk away, Yoo Min-seok blinked his wide eyes.
'What on earth is going on?'
He had heard the kid was just coming to ask a math professor a few questions.
Yoo Min-seok scratched his head with a bewildered expression.