Chapter 13
Chapter 13
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Translator: Ace
Chapter: 13
Chapter Title: The Infamous Problem 6
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Seoul, Gangnam-gu. Inside the studio.
Woo-hyun stands in front of the camera, flashing his signature relaxed smile at the screen.
His neatly styled hair, casual yet unmistakably expensive clothes, and the confidence radiating from his face. He exudes the dignity of Korea's top math instructor.
Recently, he launched a new lecture series for top-tier students, and it's been an explosive hit from the start, earning him chants of "As expected of Shin Woo-hyun."
In the past, his lectures had faced criticism for being too efficiency-focused.
His know-how for guiding students to the right answer even without grasping the essence—the very thing that turned him, fresh out of college, into a star instructor overnight—didn't actually improve the students' skills themselves.
Among high schoolers, he had become the icon of "distrust in students."
"Don't trust your own heads. Don't even try to understand. Just follow my instructions like machines."
Of course, his solid fanbase and student following meant it never became a real issue.
"I've heard there's this rumor lately that I don't even consider grade 2s and below human."
Woo-hyun tries to lighten the mood while lecturing on his new Frame textbook.
With so many students, he rarely does in-person classes anymore, but he prefers live streams where he can get instant feedback.
"Calm down, everyone. It's a misunderstanding. A few years ago, I realized we're not that different at our core."
"Sigh. Karma's a bitch—even truth comes out twisted. My fault, I admit it."
"Today, I actually want to talk seriously. I think the smartest people in the world are philosophers and mathematicians. At their core, both rely on logical thinking. That's why history is full of people who excelled in both fields."
"First off, disclaimer: this is purely my subjective opinion. This world is overflowing with self-proclaimed or so-called geniuses. Put them all together, and you might hit 100,000.
Narrow it to math world figures, and it's about 1,000. People who've published meaningful papers in academia. But are they geniuses? I'd say no, unequivocally."
"Genius. Heaven's (天) talent (材). Latin 'genius' means someone endowed with special abilities by the gods. East and West, unconnected, arrived at the exact same word from antiquity. You think there are thousands or tens of thousands like that?"
"I always say this: geniuses prove it with achievements. Solving calculus at five makes you a genius? Please. Most seventeen-year-olds can do calculus. Koreans mistake precocious kids for geniuses. What's so special about doing it a bit earlier?
IQ 180, 200? Mensa certified? So what? What have they done with it? Great memory makes you a genius? Memorizing stuff you can Google? Impressive?"
"Geniuses appear once every 100 years, or 50 if we're lucky. There've been droughts longer than that, and times when a few overlapped.
Ancient: Pythagoras, Euclid, Archimedes, Aristotle. Modern: Newton, Euler, Gauss. Contemporary: Einstein, Ramanujan. Those are worth calling geniuses."
"Then there are genius-level supporters. Not geniuses themselves, but exceptional. That's your 1,000. Some have Fields or Nobels.
I knew I didn't belong there. That's why I gave up on being a mathematician. In that sense, you and I are the same. This is my honest truth—get that."
"Spot on. Modern math and physics haven't pierced beyond Einstein's theories. Why is he great?
Relativity encompasses universal gravitation. Newton nailed earthly laws; Einstein scaled it to the cosmos. What's next?"
"Figure that out in college yourselves.
Anyway, no geniuses since. That's my conclusion. But someone with potential might exist."
"He has potential, sure. But maybe, just maybe."
Woo-hyun pauses, lost in thought for a moment.
"That genius might come from Korea.
I believe past geniuses shared traits. This ties into why high-IQ folks can't become geniuses...
Intelligence is baseline. Add creativity, intuition, and most crucially, insight piercing mathematical structures. That godlike combo? Divine talent.
I know a Korean very, very close to it. But I won't name him. You know why? How do geniuses speak?"
"Alright! When that person achieves something, we'll talk then. I'll spill the tea too. You guys wasted all my time with this!"
The stream ends, and Woo-hyun leans back in his chair, staring at the ceiling.
"Genius..."
He finds himself anticipating it unconsciously.
A smirk.
From the moment he met Seo-ha, Woo-hyun had sensed it.
What he didn't tell his students: many geniuses wither away, their talents unrealized for various reasons.
Woo-hyun was determined not to let that happen to Seo-ha.
"What are you doing?"
Woo-hyun, visiting Okcheon after a long time, finally speaks up upon seeing Seo-ha's desk.
The first round of the Olympiad prelims is soon.
But the past problem books he'd sent were neatly stacked aside, clearly untouched—brand new, not a page flipped.
"Oh, that?"
Seo-ha scratches his head, embarrassed.
"Yeah, why haven't you done them?"
"I was going to, but I found something interesting."
Papers piled high in front of Seo-ha's desk, mid-problem-solving.
Woo-hyun approaches to check it out—and his face falls.
IMO 1988 Problem 6,
Let a and b be positive integers such that ab+1 divides a²+b². Show that (a²+b²)/(ab+1) is the square of an integer.
The infamous 1988 Olympiad Problem 6.
He'd meant to remove it before sending but slipped up.
Olympiads never set nightmare-level problems.
An ironclad rule since the first event in Romania in 1959.
'Except once, in 1988.'
This monster stumped even Australia's problem committee experts within time limits. Four number theory pros spent six hours and still no solution.
Marked with double asterisks (**) and a warning: "Too hard—inappropriate for contest." But the committee trusted human potential and went ahead. The results were disastrous.
And now...
"Seo-ha, how far did you get on this?"
Woo-hyun's voice trembles.
He leans in to check Seo-ha's work.
「...In particular, when b is sufficiently large, it can also be proven that a' = 0.
Thus, (a', b) is a new solution smaller than the original (a, b). This contradicts the minimality of (a₀, b₀).」
'This kid's insane!'
Seo-ha tilts his head.
"Something wrong? Logical gap?"
The core of this proof: the approach called Theory of Quadratic Forms.
Seo-ha had already grasped it.
But he went further.
"No, it's perfect."
Dissatisfied with standard proofs, he'd used Vieta jumping—an infinite descent method—for the most concise, elegant solution.
「Therefore, k must be a perfect square.」
"Why prove it this way?"
Seo-ha answers matter-of-factly.
"Assuming a minimal element exists, then constructing a smaller one for contradiction—cleanest method, right?"
A proof technique hailed as one of math history's most beautiful.
Seo-ha might instinctively gravitate to it. Unlike plebs like Woo-hyun, who just need the answer regardless of path.
Woo-hyun slumps into a chair.
'Books like that are pointless for Seo-ha.'
'I want to unleash this genius on the world.'
An intense desire he can't suppress.
'Just a bit longer. Almost there.'
Woo-hyun wished next year's Olympiad problems would be as brutal as possible.