A studio in Gangnam-gu, Seoul.
Standing before the camera, Uhyeon looked at the screen with his signature easy smile.
Neatly styled hair, casual clothes that were by no means cheap, and confidence written plainly across his face.
He exuded the dignity of Korea’s representative top-ranked math instructor.
Recently, he had launched a new course for the highest-level students, and from the very start it had received an explosive response, earning praise of “As expected of Sin Uhyeon.”
In the past, his lectures had often been criticized for pursuing efficiency to an excessive degree.
His know-how helped students arrive at the correct answer even if they failed to understand the essence of the problem. It had been the driving force that turned him, a man who had only just graduated from university, into a star instructor in an instant, but it also drew criticism that it did not actually improve his students’ abilities.
Among high school students, he was an icon of “distrusting his students.”
“I don’t trust your brains, so don’t try to understand. Just do what I tell you and follow along mechanically.”
Of course, since his fandom and student base were so solid, it had never become a major problem.
[Listening to Sin Uhyeon’s lectures honestly pisses me off]
-I mean, it’s true I’m a dumbass, but he doesn’t have to say it so openly.
└But your score went up, didn’t it?
└Yeah.
└That’s why I can’t stop taking his classes.
└Put yourself in Sin Uhyeon’s shoes. He studied math at Princeton under a Fields Medalist. You think kids who gave up on math look like the same species to him?
└No no, Sin Uhyeon treats even second-tier students like bugs.
└If you get first tier, can you eat at the same table as him?
└If you’re first tier, you’re allowed to take the Frame series lectures. That’s where you become human.
“I hear there’s a rumor going around these days that I don’t treat anyone below second tier as human.”
While lecturing from his new textbook, Frame, Uhyeon attempted to shift the mood.
He had so many students that he hardly ever taught in-person classes anymore, but live lectures were a format he preferred because he could immediately hear students’ feedback.
└Isn’t that true, though?
└Info: In the past, Sin Uhyeon once said, “Why can’t you do this? If you just do what I tell you, it solves itself, and you still get it wrong? Are you even human?”
└Woof woof!
└Grr! Growl!
└Meooooow.
└Awoooooolololololololol!
“Calm down. It’s a misunderstanding. I realized this a few years ago, too, but fundamentally, you and I aren’t that different.”
└Teacher, what kind of outrageous statement is that?
└Here he goes again, insulting us lol. You think we’ll fall for it twice?
└Sin Uhyeon’s humblebragging has begun again.
“Sigh. I’ve got karma, so even when I tell the truth, it doesn’t get through properly. My fault. I admit it.”
└That’s right. Paying off karma begins with acknowledgment.
└Hahahahahaha.
└Forget that and tell us about your first love.
“Still, today I want to talk about this properly. I think the smartest people in the world are philosophers and mathematicians. Fundamentally, in terms of logical thought, the two are the same. That’s why, in the past, there were so many people who distinguished themselves in both fields at once.”
└But why does that mean we and you aren’t different, sir?
└Changing the subject again?
“First, I’ll start with the caveat that this is my extremely subjective opinion. There are far too many geniuses in this world, whether self-proclaimed or called that by others. If you gathered them all, there might be around a hundred thousand.
If you limit it to figures in the mathematical world, maybe about a thousand. People who have published meaningful papers in academia. But if you ask whether those people are geniuses, I want to say firmly that they are not.”
└Then who on earth is a genius?
“Genius. In Korean, cheonjae: heavenly cheon, material jae. In Latin, genius. It means a person with a special ability bestowed by a god. Since ancient times, it’s not as if East and West conspired together, yet they created words with exactly the same meaning. Do you think there could be thousands or tens of thousands of people like that?”
└Then who does Teacher consider a genius?
“I always say this. A genius must be spoken for by their achievements. You solved calculus at five, so you’re a genius? Don’t make me laugh. Most seventeen-year-olds can solve calculus. Koreans have a tendency to mistake precocious kids for geniuses. What meaning is there in simply doing something a little earlier than others?
Your IQ is 180, 200? Certified by Mensa? So what? What did they do with that? If someone’s memorization is a little good, are they a genius? Is it impressive to memorize information you can find just by searching online?”
└Uh-heh-heh. I’m convinced.
└Comrades, do not be deceived!
└Honestly, he’s right. Every Tom, Dick, and Harry is called a genius.
└So in the end, who is a genius?
“A genius appears once every hundred years, or once every fifty years if they appear often. There have been long periods without even one, and there have also been times when several existed at once.
In ancient times, Pythagoras, Euclid, Archimedes, Aristotle. In the early modern period, Newton, Euler, Gauss. In modern times, Einstein and Ramanujan are about the level worthy of being called geniuses.”
└The standard is insanely strict.
└This feels like humblebragging.
└So unless you’re a great man on that level, everyone’s just the same human?
“Then there’s a level of helpers who can assist geniuses. They aren’t geniuses, but they’re extremely outstanding people. Those are the thousand I mentioned earlier. Among them, there would likely be many Fields Medalists and Nobel Prize winners.
I realized that I wouldn’t be able to belong even there. That’s why I gave up on becoming a mathematician. In that sense, you and I are no different. This is my sincere feeling, so I hope you understand that.”
└Then humanity hasn’t had a genius for decades since Einstein?
“You saw that exactly. Modern mathematics and physics still haven’t discovered anything beyond Einstein’s theories. Why is Einstein great?
Because the theory of relativity encompasses the law of universal gravitation. Newton discovered laws that apply on Earth, and Einstein expanded them to the universe. What comes next?”
└Quantum mechanics.
└Quantum!
└What is this? It’s scary.
└I’m getting weirdly sucked in.
“That’s something you can look into yourselves when you go to university.
Anyway, there has been no genius since then. That’s my conclusion. But there may be someone who has the potential to become a genius.”
└I think I know who.
└That person at Princeton?
└Isn’t he Sin Uhyeon’s teacher?
└I heard he’s working on a Millennium Problem these days…
“That person has potential, too. But perhaps—just perhaps.”
Uhyeon stopped speaking and fell into thought for a moment.
“That genius might come from Korea.
I think the geniuses of the past had something in common. This is connected to why people with nothing but high IQs can’t become geniuses…
Intelligence is the foundation. On top of that, creativity, intuition, and most importantly, insight that sees through mathematical structure. You have to possess all of those. Only when someone has that fraudulent combination can it truly be called a talent bestowed by a god.
I know one Korean who is very, very close to that. But I won’t say who. You know why without me saying it, right? What must a genius speak with?”
└Achievements!
└Papers?
└A Korean, wow. If that’s true, that’s amazing.
└One of his students?
└Could be a senior or junior of his.
└If the picky Sin Uhyeon is saying that, I kind of look forward to it.
“All right, all right! Let’s talk about that again later, when that person establishes an achievement. I’ll tell you the story then, too. You guys said weird things and used up all the time!”
The stream ended, and Uhyeon leaned back in his chair and stared up at the ceiling.
“A genius…”
He found himself looking forward to it without realizing.
Heh.
From the moment Uhyeon met Seoha, he had sensed it.
There was something he had not told his students. Quite a few geniuses, for various reasons, were unable to fully display the talent they possessed and simply faded away.
At least with Seoha, Uhyeon intended to make sure that would not happen.
* * *
“What are you doing?”
Uhyeon, who had finally found time to visit Okcheon after a long while, looked at Seoha’s desk and eventually blurted out a remark.
The first preliminary round of the Olympiad was soon.
However, all the past problem books he had sent were neatly stacked to one side. At a glance, they were still in brand-new condition. It was clear not a single page had been turned.
“Ah! Those?”
Seoha scratched his head, as if embarrassed.
“Yeah. Why haven’t you tried solving them?”
“I was actually going to, but I found something interesting.”
There were piles of paper in front of Seoha’s desk, as if he was in the middle of solving a problem.
Uhyeon stepped closer and looked at what he was doing. Then his expression turned to one of belated realization.
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 notorious sixth problem of the 1988 Olympiad.
He had meant to take it out before sending the books, but it seemed to have been included by mistake.
The Olympiad never sets problems that are at the level of absolute unsolved difficulties.
That had been an absolute rule handed down since the first competition was held in Romania in 1959.
“Except for once, in 1988.”
This problem was a monster that even the experts of the Australian problem committee had been unable to solve within the time limit. Even four number theory specialists had invested six hours and still failed to find the solution.
That was why it had even been marked with a double asterisk (**) and a warning: “Too difficult and inappropriate for inclusion.” But the committee pushed ahead with setting it, saying they believed in human potential, and the result was disastrous.
And yet now…
“Seoha, how far did you get with this?”
Uhyeon’s voice trembled.
Unable to hold back, he approached and looked at Seoha’s solution.
「…In particular, when b is sufficiently large, it is also possible to prove that a' > 0. Therefore, (a', b) becomes a new solution smaller than the original solution (a, b). This contradicts the minimality of (a₀, b₀).」
“This is insane!”
Seoha tilted his head.
“Is something wrong? Was there a gap in the logic?”
The core of this proof was an approach called the Theory of Quadratic Forms.
Seoha had already grasped it.
But he had gone one step further.
“No. It’s perfect.”
As if the existing proof had not been satisfying enough, he had derived the answer using an infinite descent method known as Vieta jumping. In the most concise and beautiful form possible.
「Therefore, k must necessarily be a perfect square.」
“Why did you prove it this way?”
At Uhyeon’s question, Seoha answered as if it were obvious.
“Assuming a minimal element exists, then creating an even smaller element to derive a contradiction is the cleanest method, isn’t it?”
A proof technique called the most beautiful in the history of mathematics.
Perhaps Seoha was instinctively drawn to it. Whatever the process, it was fundamentally different from the thinking of an ordinary person like himself, who only needed to find the answer.
Uhyeon sank into a chair.
“Books like those were never necessary for Seoha.”
“I want to show this genius to the world as soon as possible.”
He could not suppress the intense desire.
“Just a little longer. Just a very little.”
Uhyeon found himself hoping that next year’s Olympiad problems would be as difficult as possible.