I Got an Omnipotent Brain

Studio located in Gangnam-gu, Seoul.

Standing in front of the camera, Woo-hyun looked into the screen with his signature relaxed smile.

Neatly styled hair, casual yet by no means cheap outfit, and a face radiating confidence.

The dignity of the Republic of Korea’s top math instructor is fully evident.

Recently, he launched a new lecture series aimed at top-tier students, and from the beginning, it has received an explosive response, earning him praise like, “As expected of Shin Woo-hyun.”

In the past, his lectures were often criticized for focusing excessively on efficiency.

His know-how that helped students arrive at the correct answer even without understanding the essence, this was the driving force that turned him into a star lecturer right after graduating from university. However, there were comments that it did not actually improve the students’ skills.

He was an icon of ”student distrust” among high school students.

“I don’t trust your brains, so don’t try to understand. Just follow my instructions mechanically.”

Of course, his fan base and student foundation were so solid that it didn’t cause any major issues.

[Listening to Shin Woo-hyun’s lectures legit pisses me off]

-I mean, it’s true I’m dumb as hell, but does he really have to say it so bluntly?

└But your scores went up, right?

└Yeah yeah

└That’s why I can’t stop listening.

└Put yourself in Shin Woo-hyun’s shoes. He studied under a Fields Medalist in Princeton’s math department. You think he sees math failures as fellow humans?

└No no, Shin Woo-hyun treats even 2nd-tier students like bugs.

└Can I sit at the same table if I become 1st-tier?

└If you’re 1st-tier, you’re allowed to listen to the Frame Series lectures. From there, you’re considered human.

”I heard a rumor going around lately that I don’t even treat anyone below 2nd-tier as human.”

Woo-hyun tried to change the mood while lecturing from his new textbook, Frame.

There were so many students that he rarely did in-person lectures anymore, but he still preferred live lectures because he could receive immediate feedback from the students.

└Isn’t that basically true?

└Information: Shin Woo-hyun once said, “Why can’t you solve this? If you just do what I say, it works. And you still get it wrong? Are you even human?”

└Woof woof!

└Grr! Grrrr!

└Meoooow.

└Awooooooooo!

“Calm down, everyone. That’s a misunderstanding. I realized this a few years ago myself, but fundamentally, you and I aren’t that different.”

└No, teacher, what kind of blasphemy is that?

└He’s about to humiliate us againㅋㅋㅋ. We’re not falling for it this time.

└Here comes Shin Woo-hyun’s fake humility again.

“Aigoo. Because of my past deeds, even when I speak the truth, it doesn’t come across properly. That’s my fault, I admit it.”

└Yes, redemption starts with admitting your sins.

└ㅋㅋㅋㅋㅋㅋㅋ

└Forget that, just tell us about your first love.

“Still, today I really want to talk properly. I think the smartest people in the world are philosophers and mathematicians. In essence, both rely on logical thinking, so they’re fundamentally the same. That’s why there were many people in the past who excelled in both fields.”

└Then why are you saying you’re not different from us?

└Changing the subject again?

“I’ll preface this by saying this is a purely subjective opinion of mine. There are too many people out there who call themselves or are called geniuses. Maybe if you gathered them all, it’d be around 100,000 people.

If you limit it to figures in the math world, it’s probably around 1,000. These are people who’ve published meaningful papers in academia. But if you ask me whether they’re geniuses, I would firmly say no.”

└Then who exactly is a genius?

“Genius. In Korean, the word is made up of the characters for ‘heavenly’ (天) and ‘talent’ (材). The Latin word ‘genius’ means someone with a special ability granted by the gods. It’s not like the East and West coordinated this in ancient times, but they created words that mean exactly the same thing. Do you think there could really be thousands or tens of thousands of such people?”

└Then who do you think is a genius?

“I always say this. Genius must be defined by achievement. Solving calculus at age five makes someone a genius? That’s ridiculous. Most seventeen-year-olds can solve calculus. People in our country tend to mistake precocious kids for geniuses. What’s the point of doing something slightly earlier than others?

An IQ of 180 or 200? Certified by Mensa? So what? What have they actually done with that? If you have a slightly better memory, does that make you a genius? Is it impressive to memorize information that’s all readily available online?”

└Ughhh. That actually makes sense.

└Comrades, don’t be fooled!

└Honestly, he’s right though. Everyone and their dog is called a genius these days.

└So then, who is a genius?

“A genius appears once every hundred years. At most, once every fifty years. There were long periods where there were none, and sometimes multiple 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 only ones worthy of being called geniuses.”

└That standard is ridiculously strict.

└This just sounds like more fake humility?

└So basically, if you’re not on that level, you’re just an ordinary human?

“There’s also a level of contributors who assist geniuses. They’re not geniuses themselves, but they’re extremely outstanding. These are the 1,000 people I mentioned earlier. Many among them are Fields Medal or Nobel Prize winners.

I knew I wouldn’t even make it into that group. That’s why I gave up on becoming a mathematician. In that sense, there’s no difference between you and me. That’s my sincere belief, so I hope you understand.”

└Then humanity hasn’t had a genius since Einstein?

“Exactly. Modern mathematics and physics still haven’t found 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 to Earth, and Einstein expanded those to the universe. So what comes next?”

└Quantum mechanics.

└Quantum!

└What, I’m scared now.

└Why is this so fascinating?

“You should explore that yourselves once you get to college.

Anyway, since then, there hasn’t been a genius. That’s my conclusion. But maybe, just maybe, there could be someone who has the potential to become one.”

└I think I know who you’re talking about.

└That person at Princeton?

└Isn’t that Shin Woo-hyun’s mentor?

└I heard they’re working on solving the Millennium Problems these days....

“That person certainly has potential. But maybe, just maybe-”

Woo-hyun pauses, falling into thought.

“A genius might emerge from Korea.

I believe past geniuses have something in common. This ties into why someone with just a high IQ can’t become a genius....”

Intelligence is the foundation. On top of that, you need creativity, intuition, and most importantly, the insight to perceive mathematical structure. You have to possess all of this. Only with such a fraudulent combination can it truly be called a talent bestowed by the gods.

I know one Korean who is very, very close to that. But I won’t say who it is. You know why, even if I don’t say it, right? How do you prove someone’s a genius?”

└By achievements!

└Papers?

└A Korean? Whoa, if it’s true, that’s incredible.

└Is it one of his students?

└Could be a sunbae or hubae.

└The fact that the picky Shin Woo-hyun says this makes me curious.

“Alright, alright! Let’s talk about that later, once that person achieves something. I’ll spill the story then. You guys derailed the whole thing and wasted all the time!”

The stream ended, and Woo-hyun leaned back in his chair, staring at the ceiling.

“A genius...”

He found himself expecting something, without even realizing it.

Smirk.

From the moment he met Seo-ha, Woo-hyun had sensed it.

There was something he hadn’t told his students. That there are more geniuses than one might think who, for various reasons, fail to show their full potential and quietly fade away.

Woo-hyun was determined not to let that happen to Seo-ha, at the very least.

***

“What are you doing?”

Having taken time out of his schedule to visit Okcheon for the first time in a while, Woo-hyun couldn’t help but speak as he looked at Seo-ha’s desk.

The first round of the Olympiad qualifiers was coming up.

But the previous exams and workbooks he had sent were neatly stacked in one corner. Clearly untouched. Not even a single page flipped.

“Ah! That stuff?”

Seo-ha scratched his head in embarrassment.

“Yeah, why haven’t you tried them?”

“I was going to, but I found something interesting.”

Seo-ha’s desk was piled high with sheets of paper, seemingly in the middle of solving problems.

Woo-hyun approached to see what he was working on, and then his expression froze.

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 notoriously infamous 1988 Olympiad Problem 6.

He meant to take it out before sending the problems, but it must have slipped in by mistake.

The Olympiad never includes problems of extreme difficulty.

That has been an absolute rule passed down since the competition first began in 1959 in Romania.

“Except for just one time, in 1988.”

This problem was a monster that even experts from the Australian problem committee failed to solve within the time limit. Even four number theory specialists spent six hours on it and still couldn’t find a solution.

Because of that, it was marked with double asterisks (**) and labeled “Too difficult and unsuitable for inclusion,” with a warning. However, the committee insisted on trusting human potential and pushed ahead with it. The result was disastrous.

And now...

“Seo-ha, how far did you get with this?”

Woo-hyun’s voice trembled.

Unable to hold back, he stepped in and looked over Seo-ha’s work.

「...Specifically, when b is sufficiently large, we can show that a’ 0.

Therefore, (a’, b) becomes a new solution smaller than the original (a, b). This contradicts the minimality of (a₀, b₀).」

‘This crazy kid!’

Seo-ha tilted his head.

“Is something wrong? Was there a flaw in the logic?”

The core of this proof lies in an approach called the Theory of Quadratic Forms.

Seo-ha had already grasped this.

But he went one step further.

“No, it’s perfect.”

Apparently not satisfied with the standard solution, he used an infinite descent method called Vieta Jumping to derive the answer. In the most concise and beautiful form possible.

「Therefore, k must be a perfect square.」

“Why did you choose this method of proof?”

In response to Woo-hyun’s question, Seo-ha answered as if it were the most natural thing.

”The method of assuming the existence of a minimal element and creating an even smaller element to derive a contradiction is the cleanest.”

One of the most beautiful proof techniques in the history of mathematics.

Seo-ha might be instinctively drawn to this. His thinking is fundamentally different from that of an ordinary person like himself, who believes that as long as you get the answer, the process doesn’t matter.

Woo-hyun sank into a chair.

‘Seo-ha didn’t need books like that.’

‘I want to show this genius to the world as soon as possible.’

He can no longer contain the intense desire.

‘Just a little more, just a little bit longer.’

Woo-hyun found himself hoping that next year’s Olympiad problems would be as difficult as possible.

*****

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