Just a Verbal Argument
A dormitory at a university in Seoul, where the Korean Mathematical Olympiad (KMO) summer school was being held.
This place, which gathered the most brilliant math prodigies from all over the country, was burning even hotter with an invisible war of nerves among the students than the sweltering midsummer heat.
“Hey, how did you guys solve geometry question four from yesterday afternoon?”
“Me? I just applied Menelaus's theorem, drew exactly two auxiliary lines, and the answer popped right out.”
“Ugh, that's too messy. I set up coordinates with trigonometric functions and cut it down to three lines. The professor was totally shocked when he saw my solution. This year's IMO (International Mathematical Olympiad) national representative spot is definitely mine.”
During break time, the high school prodigies gathered in the lounge, flushed and spitting as they bragged about their intellectual superiority.
Who used a harder theorem, who solved it faster.
The intellectual vanity and elitism of teenagers called the future of Korean mathematics filled the narrow lounge.
In a corner slightly away from the noisy crowd, Jeong-woo sat crookedly in his chair, watching the bragging high schoolers and chuckling to himself.
“Hey, did you guys hear what the TA and the professor were talking about so seriously during lunch?”
A sophomore from Seoul Science High School, who occupied the center of the lounge, lowered his voice, acting like he was sharing top-secret info.
He was the one consistently topping the mock exams in this summer school.
As the other high schoolers gathered around with interest, the science high school student shrugged and spoke again.
Jeong-woo also listened in.
“Apparently, Seohan University's math department had a massive disaster.”
“Disaster? What kind of disaster?”
“Some grad student uploaded a 250-page piece of trash paper to arXiv, claiming to have solved the many-body problem using pure mathematics. But apparently, they spent dozens of pages just solving basic von Zeipel functions. They wrote the paper completely through brute-force labor.”
“Crazy. Seohan University?”
“Yeah! And Professor Kim Sang-wook, the corresponding author, couldn't even respond and went completely off the grid.”
“No way!”
As another student chimed in with shock, the first student clicked his tongue.
“Some dumb grad student who doesn't even know the rules of academia is just trying to draw massive attention. Even the kids at our school don't write like that when doing research papers. The level is just...”
The sophomore was piecing together fragments of information he'd overheard from the TAs, basking in intellectual superiority as if they were already part of South Korea's mainstream academic elite.
He glanced at Jeong-woo.
“Hey. Did you even understand any of that? What are you smirking at?”
“Ah, no.”
“Haha. Right. You probably don't even know what von Zeipel is yet, do you? Anyway, you're in seventh grade, right? I've seen you around, you've got some skills. Just follow my lead. If you pass the second round, I'll look after you all the way through winter school.”
Jeong-woo smiled brightly.
“Yes! Thank you!”
But inside, he was laughing.
“So, if they ask you directly about the small denominator elimination part, are you going to write down all these formulas in front of them and explain?”
Edward Kang's question made Cheol-jun furrow his brow.
That seemed impossible.
This time, the math teachers helped him, but at the symposium, explaining it all by himself would be too much.
“Look, I acknowledge the picture you're trying to paint. It's very beautiful. Your intention is incredibly good. But you also need to know how to paint the picture the academic community wants so they can properly recognize your intention. You have to be able to claim, ‘I can do harder things, but I think this looks more beautiful!’”
Cheol-jun quickly nodded.
He understood exactly what he meant.
“That's why you need to know category theory, abstract algebra, tensor analysis, and linear operators. So that when scholars criticize your lack of elegance, you can respond immediately.”
Cheol-jun's gaze turned to the books piled on the table.
He had avoided them because he thought they made the path unnecessarily difficult and complicated, but listening to Edward, he realized he needed to know them to persuade others.
“I'll study them!”
“Haha. It's not something you can master overnight. For now, I'll just point out the concepts necessary for the formulas used in this paper...”
Cheol-jun shook his head.
“I want to understand all of it.”
Cheol-jun's round eyes sparkled.
—Ah! If I pick up a sniper rifle, I win!
—Then let's have a match with snipers!
In Rival, to truly crush an opponent, one had to master every single weapon.
“Ha, well, yes, it's good to know everything. But you still need to focus on what I point out first.”
“Yes!”
Edward Kang stared at the small child.
Right now, Professor Kim Sang-wook was shielding him from the academic onslaught, so it probably hadn't sunk in yet.
‘Hmm...’
Cheol-jun's genius was undeniable.
No matter what question was asked, he defended it cleanly with his own logic.
But when the symposium actually opened and hostile questions poured in, will this small child be able to handle it with composure?
That was his biggest worry.
He heard Cheol-jun only had a few presentation experiences, and none of them were high-pressure.
“Cheol-jun.”
“Yes?”
“Aren't you scared?”
Cheol-jun tilted his head.
It wasn't a fight with guns or knives, nor was it a life-threatening situation. It was just a verbal argument. Why would he be scared?
“Do... do actual physical fights break out at symposiums?”
“...Fights?”
“Like, throwing punches...”
“No. No, of course not. It would be a disaster if that happened.”
Cheol-jun smiled brightly.
“Then I'm not scared at all.”
“...Huh?”
“At worst, it's just losing a little verbal argument. Though, I don't plan on losing.”
Edward Kang was temporarily speechless.
Looking at the brightly smiling child, he blinked blankly.
‘Just losing a little verbal argument?’
For scholars, losing a debate was not a trivial matter.
Having the knowledge and beliefs you spent your entire life building denied and torn down in a public forum watched by scholars from all over the world meant a fatal blow to one's academic life, a devastating humiliation, and the collapse of one's pride.
That's why scholars verify their logic dozens of times to avoid a single loophole, build defensive arguments, and desperately defend themselves with cold sweat running down their spines under the sharp attacks of questioners.
That immense pressure was an innate fear shared by all intellectuals, one that even Edward Kang himself, a Fields Medalist, could not escape.
Yet, the eleven-year-old boy in front of him defined the essence of all that pressure so clearly and lightly.
‘Ha, just a verbal argument...’
Edward Kang finally realized.
He had been completely mistaken.
To this child, mathematics was not a means to prove his status.
It wasn't a tool to show off intellectual vanity to others.
It was simply a beautiful path he wanted to walk with people, a joyful game where he could confidently call out to those insisting on a different path, "Hey, try walking this way too!"
A child with no reputation to protect, no pride to lose.
A mind filled only with the fundamental purity of exploring knowledge.
A deep smile slowly spread across Edward Kang's face.
‘Right. There's no way someone with nothing to lose would be afraid.’
Rather, the ones who should be afraid were the old masters of the world, trembling to protect their petty reputations and haughty pride built over a lifetime.
He couldn't even imagine how much their hearts would be lacerated by the sharp truths this fearless genius boy would innocently pour out in front of the blackboard.
Edward Kang let out a hearty laugh, his shoulders shaking.
“Hahaha! Yes! You are absolutely right. It's just a verbal argument!”
“Hehe.”
Edward Kang's eyes gleamed.
It seemed time to cast the net for the fish gathered around the bait.
“Really? A paper?”
Choi Yeon-mi, visiting Hyeong-man's house after a long time, opened her eyes wide upon hearing the news.
She had been incredibly busy lately working on a rookie idol group, so she was only just hearing about this.
“But is that really such a big deal?”
Hyeong-man shrugged.
“Do you know who Edward Kang is?”
“...”
“He's with Princeton...”
Choi Yeon-mi's eyes widened as if remembering something.
“...A rock group?”
“Sigh...”
“I'm starting to get offended. Why are you looking at me like that?”
Hyeong-man shook his head and continued.
“He's a Korean who won the Fields Medal...”
“Fields Medal? What's that?”
“Sigh, it's the Nobel Prize of mathematics... No, actually, it's an even more prestigious award.”
Choi Yeon-mi wrinkled her nose.
She didn't know exactly what it was, but she got the gist.
“Okay, so he's a world-famous math doctor?”
“Yeah. Anyway, even that amazing person recognized Cheol-jun. He's even getting one-on-one lessons from him lately. That's why he went to the university today too.”
“So, you're going to turn that cute kid into a stuffy scholar?”
“Cheol-jun says it's fun.”
“Ah, I don't really like it. Doesn't seem like it makes money.”
“Tsk, tsk.”
When Hyeong-man clicked his tongue, looking at her like she was a materialist, Choi Yeon-mi pouted.
“So, is Cheol-jun going to become famous? Is he going to appear on those prodigy shows?”
“Haha, well. I don't really want him to be exposed clumsily... But he does need to become famous. That world is apparently quite complicated, so just being smart isn't enough. They were talking about generating buzz or something...”
Choi Yeon-mi smiled as if she understood perfectly.
“I get it. Become famous first. Then, even if you take a dump, people will call it art. Something like that, right?”
“Hey. You really... talking about taking a dump. I don't know about that, but anyway, they said we need to build up his fame first so those stubborn scholars can't push Cheol-jun around.”
Choi Yeon-mi's brow furrowed slightly.
Then, she arched an eyebrow.
“Media play?”
“...Huh?”
“You mean like manipulating the press?”
“Well, it sounded like something like that.”
Choi Yeon-mi tilted her chin up.
“That's our specialty.”
“Ah...”
“Let me know if you need help. Our PR team is incredibly good at that. ‘The K-Genius!’ Oh, that has a nice ring to it. Should I ask Playground headquarters? Even famous soccer or baseball players roll around with managers these days.”
“Really? Even if they aren't celebrities?”
“Yeah. Having a company involved makes it easier to handle various situations, and even if they get exposed to the media, their image is managed systematically.”
“...Oh?”
Hyeong-man's eyes widened.
Indeed, if Cheol-jun were to step forward, he would inevitably draw media attention.
It was something both he and Cheol-jun had braced themselves for to some extent. If a trustworthy company managed that side of things, the risks would be drastically reduced.
Watching Hyeong-man's reaction, Choi Yeon-mi grinned.
“Even scholars are celebrities once they become famous.”
Hyeong-man looked at her, impressed.
“That's actually a great idea.”
Sometimes, Lady Choi was actually helpful.
This felt reassuring.
Paris, France, École Normale Supérieure (ENS) Department of Mathematics.
Professor Renoir, a Bourbaki school mathematician, looked displeasedly at Jacques, a researcher who was frantically solving equations.
“Jacques. Abandoning abstraction for such primitive brute-force labor. What on earth are you doing?”
“Professor, well, I found a paper on the many-body problem... It's unrefined, but there are absolutely no errors.”
“The many-body problem?”
“Yes. It completely resolves the small denominator problem.”
Without a word, Renoir snatched the pen and began expanding the equations.
Scribble, scribble.
After quite some time, when he reached the topological transformation section on page 142, his pen abruptly stopped.
‘...Why does this forcibly cancel out here?’
Renoir's brow furrowed.
Surprisingly, as the equations expanded, they became trapped in a flow that had initially seemed crude, only to be helplessly and smoothly pulled toward the correct answer.
“...Indeed. The logic of the proof is quite flawless.”
Renoir tapped the equation.
His face was ice-cold and rational, showing neither excitement nor anger.
“But Jacques. We must never recognize this as mathematics. It must be rejected during the peer review stage.”
“What? But Professor, the logic is flawless...”
“Logic? This is not a theory that explores truth.”
Renoir stood up, rubbing his temples as if exhausted.
“Think carefully. Where does the power of modern mathematics come from? It is universality. A single abstract, elegant formula we create becomes the backbone that solves hundreds, thousands of problems in physics, astronomy, and economics. That is why the world reveres pure mathematics as the pinnacle of academia.”
“...”
“But what about this person's equations? There is only this one path. It cannot branch out to other problems, nor can it be applied. It is a path solely for the many-body problem of that specific orbit. If the academic community certifies this bizarre, closed brute-force labor as a great achievement, what do you think will happen?”
Political calculations and a sense of crisis flashed through Renoir's mind.
“The paradigm will flip. Academic research funding will leave our French School, which studies elegant structures, and pour into low-grade applied mathematics that clings to crude calculations and variable control. Future scholars will no longer seek universal theories; they will be desperate to assemble these single-use machines just to get immediate answers.”
Only then did Jacques realize what Professor Renoir was afraid of.
This was not a simple matter of pride.
It was an ideological war to protect the academic hegemony held by the mainstream of modern mathematics and the very raison d'être of pure mathematics they had built over a century.
“This paper is a plague that will eat away at the roots of modern mathematics. The academic community will likely conclude that it should simply be ignored. Fortunately, the corresponding author is a nobody. It will just be buried.”
Just then, another researcher looking at a monitor on the other side of the lab shouted.
“Pr-Professor! It's Edward Kang! Edward Kang of Princeton just posted on his blog!”
“...Hmm?”
At the mention of the Fields Medalist's name, Renoir's eyebrow twitched.
The researcher read the screen, gulping.
“Uh, well... It's a statement from Edward Kang. He says he currently completely understands and supports the entire proof process of the many-body problem paper written by Lee Cheol-jun of Seohan University...”
“What?”
“And...”
The researcher gulped before continuing.
“He says if people fail to see the essence of this paper and waste time whining about elegance, he will personally go and meet Lee Cheol-jun... And if anyone wants to refute this paper...”
Professor Renoir quickly stared at the monitor.
"Instead of whispering cowardly from behind, I hope you will come and discuss it directly with Lee Cheol-jun in front of a blackboard."
Professor Renoir's brow furrowed.