A Path That Isn't Lonely
A highly absurd scene was unfolding inside the police substation.
"So, if you had used Poisson brackets more intuitively to group them under the higher concept of Lie transforms, it would have been over in three lines. The von Zeipel method you applied is far too verbose and lacks beauty."
Cheol-jun furrowed his brow.
He didn't care about other things, but hearing the man dismiss the path that so many teachers had stayed up all night to beautifully pave for him made him feel incredibly upset.
It was the first time he had ever felt this way toward an adult.
He flared up without realizing it.
"If you explain it like that, only the people who already know will understand! Even if it takes a bit longer, a path that everyone can follow is much cooler!"
"Haha. You can always explain that later. Besides, those who want to follow will study and catch up anyway. First, you must present it to the world in a clean, elegant form, and then..."
"Why do the work twice? Isn't it better if everyone understands it easily the first time? Is boasting about knowing something harder really that cool?"
"My word... My boy, mathematics is..."
"It's not mathematics, it's astronomy!"
"Ha..."
"And I didn't start this to show off to anyone. I started it because I wanted to show others the path I saw."
Edward Kang let out a dry laugh. To think he couldn't detect even a shred of intellectual vanity in an eleven-year-old boy.
He really is something else...
Cheol-jun scowled as he looked at Edward Kang's smiling face.
The conversation had started with exciting questions about the Diophantine condition, but the man sitting across from him wasn't even trying to understand; he was just nitpicking.
Until now, Cheol-jun had only met adults who listened intently and nodded whenever he spoke, but this mister was different. Yet, it was strange.
Aside from being annoyed, the desire to completely crush the other person with logic gave him a strange, thrilling sensation.
Furthermore, the points the man occasionally poked at forced him to think deeply, which was actually quite fun.
This was the first time Cheol-jun had ever met someone he could converse with without having to walk on eggshells or dumb things down.
At first, he had just been incredibly annoyed, but as they kept talking, it gradually became enjoyable.
It was fascinating how, the more they conversed, the paths he had tried to build transformed into new landscapes, growing clearer and clearer.
And so, for the first time in his life, Cheol-jun was raising his voice at an adult in excitement.
Cheol-jun picked up one of the A4 sheets scattered messily across the table. It was a short, simple formula the man had coldly summarized.
"If we apply everything exactly as you've written here, how many university teachers do you think could actually follow it?"
"Well, any professor worth their salt should..."
Cheol-jun's hand grabbed another piece of paper. It was the formula he had expanded and solved in dense detail.
"Well, I like this one better! Because even with just a little understanding, it's a path anyone can easily follow!"
"Haha. But that equation is far too crude, my boy. Have you perhaps not learned algebra yet?"
"It's not crude at all!"
"Good grief... Fine, the explanation is perfect. But right now, to transform the orbit, you've used the von Zeipel generating function and manually exposed all the partial derivative terms. That is outdated and incredibly messy."
"It's clean!"
Watching the two debate blankly while munching on the snacks the police officers had given them, Min-jun and Ha-rang's faces grew increasingly distorted.
"Yep, math is seriously no fun."
"Tell me about it."
"Cram school sounds more fun than this."
"Agreed."
Beside them, the police officers sipping their instant mix coffee nodded along to the conversation, utterly clueless as to what on earth they were talking about.
One of the officers quietly approached the table.
"Excuse me, Mr. Man-sik Kang? We've verified the situation and cleared up the misunderstanding, so you're free to go now..."
But Edward Kang didn't hear a word. This delightful debate could not be interrupted. Wasn't the boy wishing for the same?
"Look, even the way you expanded the Fourier series here! If the small divisor pops out from here..."
The officers smacked their lips and let out deep sighs, while Min-jun and Ha-rang began packing their bags.
"Hey, let's just go to the PC cafe by ourselves."
"Yeah. It's not like we're getting certificates of appreciation anyway."
Overhearing their conversation, one of the officers quickly ran off and brought something back. It was a stationery set featuring a cute police mascot and some book gift certificates.
"Here, you guys did a brave thing today! A present!"
"Oh! Thank you!"
"Thank you!"
The two kids accepted the gifts with proud, smug faces.
"Cheol-jun, we're heading out first!"
"See you tomorrow!"
Cheol-jun, too engrossed in his conversation with the strange mister, didn't even hear their farewell. Min-jun and Ha-rang stared at him, exchanged funny looks, and quickly scurried out of the substation.
"Sigh, I want to leave too."
One of the officers sighed deeply, just as Cheol-jun waved two sheets of A4 paper in his hands.
"Officer! I'm right, aren't I? Which of these two is better?"
The officers quickly averted their eyes. They couldn't make heads or tails of the scribbles on either page.
◇◇◇◆◇◇◇
Gu Byung-ook, the Dean of the College of Natural Sciences at Seohan University, flung the substation door open, completely out of breath.
"Huh...?"
Taking in the atmosphere inside, Gu Byung-ook blinked. A scene he had never in his wildest dreams expected was unfolding before him.
"I'm telling you, no! If the Fourier series is expanded here, the denominator converges to zero! The orbit will just diverge! Ah, seriously, look here."
"No, it won't blow up! You just have to twist it and flip it over here!"
The whiteboard hanging on one wall of the substation—which originally had a calendar drawn on it—was now heavily vandalized with dense, pitch-black equations.
Dozens of A4 sheets lay scattered in disarray across the table, and Edward Kang and Cheol-jun were glaring intensely at each other.
It was the first time Gu Byung-ook had ever seen Cheol-jun make such a face at an adult.
"Twist and flip? Are you joking? If you ignore canonical transformation in a Hamiltonian dynamical system and forcibly warp the phase space, energy won't be conserved!"
Edward Kang slammed his hand against the whiteboard.
"Look closely! If resonance occurs here, does the torus maintaining the orbit shatter or not?"
Cheol-jun scurried over to the whiteboard. Standing on his tiptoes, he drew two overlapping donut shapes next to the equations.
Then, he waved his whiteboard marker in the air as if drawing in space.
"You only think the orbit shatters because you're keeping your thoughts flat on the board. The universe isn't flat at all! Look. If you overlap two donuts like this, twist them into a figure-eight, and plug them into this equation..."
"...A figure-eight?"
"Yes! Just as the energy is about to fly outward, it slips right into the other donut and loops back inward. Like a Möbius strip! Since the Diophantine condition is irrational, according to this equation, the orbits will never overlap and will just keep spinning forever!"
"...!"
Suddenly, Edward Kang's eyes widened so much they looked ready to pop out. He stared intently at Cheol-jun's crude drawing, then whipped around and snatched a piece of A4 paper from the desk. He began scribbling with a pencil.
Scratch, scratch, scratch!
"Wait... Bypassing the symplectic structure in the intersection space... like this? Hold on, just hold on..."
"See! I told you I was right!"
Cheol-jun placed his hands on his hips and shouted triumphantly.
"I've been telling you to twist and flip it for a while now! You're supposed to be a famous math teacher from America, but you're really bad at math."
"Wait! Quiet down for a second! I'm verifying it right now!"
The substation police officers watching this chaotic scene could only sip their instant coffee with blank expressions.
The Department Chair of Mathematics, who had run into the substation after parking, spoke up with a dazed face.
"Um... Dean?"
"Huh...?"
"W-what is going on here..."
"I don't really know either..."
Suddenly, Edward Kang lifted the A4 paper, stared at it intensely, and shouted.
"It works! It's correct! Damn it, taking that detour actually makes everything fall perfectly into place!"
Edward Kang grabbed Cheol-jun by both shoulders.
"You... did you draw this knowing all of it from the start? You completed the inflection points of this multidimensional manifold purely through the intuition in your head? Without even expanding the equations?"
"Of course I completed it because I knew! I could clearly see the stars looping and spinning beautifully without colliding!"
Edward Kang stared at the pouting Cheol-jun before bursting into a mad, breathless laugh.
"Ha, hahahaha! Unbelievable!"
His legs giving out, Edward Kang collapsed right onto the substation floor.
A bizarre laughter, a mix of sheer ecstasy and shock, filled the room.
While the officers, Dean Gu Byung-ook, and the math department chair stared at Edward Kang in utter bewilderment,
"Do you get it now?"
Cheol-jun asked, lifting his chin with a bright smile.
Dean Gu Byung-ook quickly snapped out of it, wiping away his cold sweat.
"U-um... Cheol-jun?"
Only then noticing Dean Gu, Cheol-jun bowed politely with a bright grin.
"Hello!"
◇◇◇◆◇◇◇
The Dean's Office of Seohan University's College of Natural Sciences.
Cheol-jun bowed deeply with a cheerful smile.
"Hello! I am Lee Cheol-jun, a fifth-grader in Class 5 at Hanyoung Elementary School!"
"Haha. Yes, it's a pleasure to meet you. I'm Edward Kang, and I research mathematics at Princeton University."
"Huh? But at the police station earlier, you said you were Mister Man-sik Kang..."
"Ah, that name is far too old-fashioned, so I rarely use it."
Reunited in the dean's office, the two finished their belated introductions. Staring at each other despite an age gap of over five times, they both burst into giggles at the same time.
Watching their interaction with bated breath, Dean Gu Byung-ook and the math department chair also let out soft smiles.
It seemed brilliant minds truly shared a unique connection.
As their giggles subsided, Edward Kang looked at Cheol-jun with a warm, pleased expression.
It had been a very long time since someone had stood up to him so confidently.
His colleagues at Princeton, and even veteran professors who had spent decades honing their craft, would usually nod along with his logic, or back down quickly after raising a cautious counterargument.
But this boy was different. When Edward deliberately nitpicked, the boy threw back an even bigger counterpoint.
When explaining the logic hit a wall, he drew pictures. When pictures failed, he waved his hands in the air, passionately describing the world he wanted to show.
Ha...
Honestly, it would be a lie to say he didn't feel a sense of inadequacy. To possess such extraordinary intuition and creativity at such a young age.
As a scholar, he felt a surge of jealousy so intense he wanted to curse the heavens.
Yet, an even greater emotion swept over him, completely burying those worldly feelings before they could even take root.
Wonder. It was a feeling he had rarely experienced, even in gatherings of the absolute pinnacles of the natural sciences, where only geniuses congregated.
A sudden thought struck Edward Kang. How lonely must this child have been all this time?
He knew the feeling well. Someone who saw the world so differently was destined to remain entirely alone until they met someone who viewed it the same way.
No matter how much you explain, they don't understand; you grow exhausted from explaining, and eventually, you end up walking the path only you can see, all by yourself.
Was it because of that loneliness that he approached every problem in a way that others could easily follow?
He could guess how that special class he witnessed at the elementary school had come to be. Perhaps it was a struggle to overcome loneliness...
That was why the boy had been so excited at the substation earlier. He recalled how the boy had grown even more thrilled to fire back after being nitpicked a few times.
This must be his first time. Meeting someone to whom he can freely and fully show the world inside his head.
Edward Kang nodded knowingly.
"Cheol-jun."
"Yes?"
"Was it fun talking to me earlier?"
Cheol-jun thought for a moment, then quickly nodded.
"Yes. Incredibly so."
"Why?"
"Because I had to think deeper to avoid losing. And doing that made the paths I built much clearer."
Edward Kang nodded slowly.
"I see."
Pausing for a moment, Edward decided he should at least test the waters and spoke again.
"You know, in America..."
Cheol-jun tilted his head.
"There are so many people who can have conversations like the one we had today."
Cheol-jun's round eyes sparkled.
"...Really?"
"Yes. And you can have much deeper conversations, too. Not just with people who nitpick like I did today, but with many people who can walk the path you see alongside you, and even build the next steps of that path together."
Cheol-jun knit his brows as if in deep thought.
"Over there, you wouldn't have to walk alone and lonely."
At Edward's words, Cheol-jun tilted his head.
"Uh, but I'm not lonely?"
"...Hm?"
"This time was incredibly fun!"
"..."
"I didn't walk alone! And besides, I can just make the path easier and more enjoyable!"
Edward Kang blinked. He had thought he understood this child to some extent...
"From what I saw earlier, you make paths very difficult, Professor. That must be why you were lonely."
Cheol-jun grinned.
"I'm going to make a path that isn't lonely at all! So that anyone can walk it with me!"
At Cheol-jun's pure, bright ambition, Edward Kang's mouth fell slightly open. Has there ever been this kind of genius before?
After a moment of daze, Edward let out a hollow laugh and shook his head.
"Yes. Yes, indeed! That is truly wonderful."
Edward Kang turned his head to look at Dean Gu Byung-ook. The most urgent matter now was figuring out how to debut this out-of-bounds genius to the global academic community.
"Now, let's draw up a strategy."
Dean Gu Byung-ook, whose emotional side had been awakened ever since that academic conference, quickly wiped the tears welling up in his eyes from Cheol-jun's words and nodded.
"Yes, Professor!"