I Got an Omnipotent Brain

Su-jeong arrived at the lodging. However, the name of the hotel looked somehow familiar.

“Hilbert’s Hotel?”

Her mind was hazy like a fog, and she couldn’t quite recall where she had seen it.

“Let’s just go for now.”

Wearing a 19th-century European-style dress, she pulled her suitcase and approached the reception.

However, there was a sign on the counter that read “No vacancy”.

“Ah... there’s no room.”

A hotel staff member approached the disappointed Su-jeong and spoke.

“Lady, don’t worry. We are an infinite hotel.”

“What? Then what’s that?”

Su-jeong pointed at the “No vacancy” sign on the counter.

“Aha! Although we are currently full, we can make a special room available for you.”

What on earth was he talking about? Su-jeong wore a puzzled expression.

“How?”

“We move the guest in room 1 to room 2, the guest in room 2 to room 3... like this, infinitely shifting guests, and room 1 becomes vacant. You can stay there.”

While Su-jeong stood dazed, a group of guests arrived. A man who appeared to be a bus driver approached the counter.

“Excuse me. We’re from the Infinite Bus Company, and our passengers would like to stay here. Is that possible?”

“No problem.”

“But I said we’re from the Infinite Bus Company. We have an infinite number of passengers.”

The staff member smiled faintly and tapped the ledger with the fountain pen in his hand.

“We are the Infinite Hotel.

If we move all the guests to even-numbered rooms, all the odd-numbered rooms will be vacant. So no matter how many guests there are, there’s no problem accommodating them.”

Su-jeong could no longer tolerate this seemingly nonsensical conversation.

“If it’s infinite anyway, can’t I just go into any empty room?”

The staff member stared at Su-jeong and spoke with a firm expression.

“Lady, didn’t I tell you from the beginning? There are no vacant rooms in this hotel. If you go in on your own...”

He had approached at some point and whispered in Su-jeong’s ear.

“...you never know who you’ll meet in the room.”

Kyaaaaaah-

Su-jeong screamed and ran away.

“....”

Seo-ha was eating donuts with Su-jeong.

Even the cafeteria staff were glancing over at them, drawn by her vivid performance.

“You had that kind of dream?”

Su-jeong gulped down a glass of water, as if her throat was dry.

“Yes, I read about Hilbert’s Paradox of the Grand Hotel before going to bed, and it showed up in my dream.”

The paradox of Hilbert’s Hotel was that even if the rooms in an infinite hotel were all full, depending on how the sets were rearranged, it was always possible to make room for more guests.

“You were reading something interesting. Why Hilbert all of a sudden?”

Su-jeong put down the cup and shrugged her shoulders.

“I have mentoring tomorrow. I was asked to explain countable infinity and one-to-one correspondence to a middle school student.”

“Aha! That’s a great idea. Using Hilbert’s paradox, you can intuitively demonstrate it.”

Set of natural numbers: 1, 2, 3, 4, 5...

Set of rational numbers: 1/2, 2/3, 1/4...

At first glance, since there are infinitely many rational numbers between 1 and 2, it seems like there are far more of them than natural numbers. But in mathematics, the size of a set is defined by cardinality.

The key point is whether one-to-one correspondence is possible.

As Hilbert’s Hotel shows, in countable infinity, even natural numbers (rooms) and rational numbers (guests) can be matched one-to-one.

A paradox of infinity where the part becomes equal to the whole, this is deeply philosophical and greatly shakes human intuition.

“Why are you interested in this too?”

Instead of answering, Seo-ha took a book out of his bag.

[The Theory of the Riemann Zeta-Function]

Su-jeong was so shocked upon seeing the book that she nearly fainted.

“R-Riemann zeta function? Don’t tell me you want to solve the Riemann Hypothesis?”

“Not right now, but I definitely plan to solve it someday. For now, I’m just in the research stage.”

If we were to explain the Riemann Hypothesis in the same way as Hilbert’s, it would go like this.

There is a hotel with infinitely many rooms. But unlike Hilbert’s Hotel, not all the rooms are occupied.

Room 2, 3, 5, 7, 11, 13, 17, 19....

Only the rooms with prime numbers have guests in them.

At first glance, the placement of these guests seems scattered and random.

However, the Riemann Hypothesis claims that the placement of these ‘prime guests’ is not random, but follows an invisible mathematical rhythm.

And the key to revealing that rhythm is the Riemann zeta function.

“Are you one of those who believe the secrets of the universe are hidden in prime numbers? The general consensus is that they’re irregular.”

Su-jeong had a disinterested expression.

Prime numbers had long fascinated many mathematicians.

But no one had been able to prove their regularity. Even if the Riemann Hypothesis were proven, it would only allow a precise prediction of the distribution of primes, not the exact location of each individual prime.

“The majority of mathematicians agree that there’s no exact rule to the distribution of primes. They say that this randomness is actually the essence of prime numbers.”

That’s why primes are sometimes called the “atoms of mathematics”.

They cannot be divided further, and no one knows where they will appear.

“But if the Riemann Hypothesis is true, doesn’t calling it random become ambiguous? It’s like order within chaos.”

“It’s not a law, more like the ability to predict density and flow. But even that alone can let humanity understand a great deal.”

Seeing Seo-ha being serious, Su-jeong sat up straight.

“Really? I think the Riemann Hypothesis is a seriously overrated theory. Even if it’s solved, modern encryption systems won’t collapse. We still won’t know the rules of prime numbers, and while it might lead to some progress in number theory, it’s not like we’re expecting some grand mathematical breakthrough.

Isn’t it only considered legendary because it ruined so many mathematicians?”

Su-jeong wanted to pull Seo-ha away from the Riemann Hypothesis.

Seo-ha nodded.

Some mathematicians would agree with her opinion. But Seo-ha had a reason why he absolutely had to solve it.

A dream he had never told anyone.

It was to discover the so-called “Theory of Everything” that went beyond the theory of relativity.

A theory that explained everything – for the past 300 years, that role had belonged to Newtonian mechanics.

But Einstein discovered that Newton hadn’t considered the relativity of time, and he published a theory that proved it.

Now, modern scholars claim that the theory of relativity cannot explain the behavior of quantum particles.

The time has come for the next stage of theory.

(String theory was one of the candidates, but it cannot be proven.)

Seo-ha believed that the secret of prime numbers was not just a problem of pure number theory. The order hidden in the zeros of the Riemann zeta function resembled the chaos of the quantum world – the rhythm of the universe itself.

‘If there is a theory beyond Newton and Einstein, the beginning of that stage will inevitably be connected to the Riemann Hypothesis.’

That was what Seo-ha believed.

But it was a study that hadn’t even begun yet. He couldn’t tell Su-jeong everything.

“If the Riemann Hypothesis is proven, wouldn’t that solve the Goldbach Conjecture too?”

Su-jeong stared at Seo-ha silently for a long time. Then she opened her mouth with difficulty.

“Seo-ha. Please, don’t do it.”

Her voice was desperate.

“I know you’re a genius like no other in this world. But touching infinity isn’t just a matter of mathematics. There’s definitely something in there that destroys human intuition.

Think again. Is it really something worth doing?”

Becoming immersed in the Riemann Hypothesis is practically the end of a career. (At least up to now)

The world glorifies it as mathematicians’ persistence, failure, and endless pursuit of truth, but what actually happened to the people who threw themselves into it?

A labyrinth with no end. A question whose answer may not even exist.

Mathematicians who become consumed by it lose their way and spend their lives in the infinite darkness.

All that remains is likely emptiness and despair.

Su-jeong was afraid that Seo-ha might walk into the endless abyss of mathematics and never return.

“It’s worth it. I can’t reveal everything right now, but one day, I definitely intend to uncover the secret of prime numbers.”

Su-jeong closed her eyes, then opened them again with a deep sigh.

She knew Seo-ha. He would never stop until he found the answer.

“What if there’s nothing at the end of that path?”

There hadn’t been a counterexample yet, but perhaps the Riemann Hypothesis wasn’t true.

“Then I’ll be the one who confirmed there’s nothing there. That alone is enough. Someone has to stare into that abyss directly.”

Seo-ha’s voice was calm, but it carried a deep conviction. As if to say it was his destiny to walk this path.

At that moment, Su-jeong felt like she knew what she had to do.

Maybe it was inevitable that she met Seo-ha.

Whether to help him, or to stop him before it’s too late...

Even fate wouldn’t wish for such talent to be wasted in vain.

“Then is there anything I can do? I don’t know if someone like me would be of any help.”

Her first friend, the one who helped her realize the beauty of mathematics.

To her, Seo-ha was a special person.

“It’s not at the stage where I can say anything yet. But if I ever become convinced that I can solve it, I’ll definitely call you. When that time comes, please help me.”

Su-jeong nodded.

She had planned to study mathematics further in college, but she hadn’t yet chosen a specific theme.

‘I need to study Number Theory.’

At least until that day.

***

“Oppa!”

As soon as she saw Seo-ha walking from afar, Seo-eun ran out of the house. She sprinted for a while, then jumped into Seo-ha’s arms.

Seo-ha beamed and lifted Seo-eun’s small body high into the air.

Kyaaah-

Seo-eun soared through the sky with joy.

“Were you waiting for me?”

“Yeah! You said you were coming today. I’ve been watching the whole time!”

Holding tightly onto her oppa’s hand, Seo-eun rushed back into the house.

“Mom, Dad! Oppa’s here!”

Laughter quickly filled the house.

Seo-ha helped his little sister with her studies and harvested pumpkins with her in the garden.

After eating meat heartily, Seo-eun’s head began to nod off, and soon she fell into deep sleep.

Chul-ho gently picked her up.

“She got all excited because her oppa came, and now she’s already asleep.”

A smile was spread across the face of sleeping Seo-eun, as if she were having a sweet dream.

“Has anything happened with Seo-eun lately?”

Mi-young thought for a moment, then smiled softly.

“She used to say she wanted to be a mathematician like you, but lately she says she wants to be a doctor.”

“All of a sudden?”

“Not exactly. It started after she visited you in the hospital. I guess seeing you collapse was a big shock.”

Thinking back to that time, Seo-ha still felt ashamed in front of his family.

“I’m sorry.”

“As long as you understand. Just don’t let it happen again.”

Seo-ha thought deeply about Seo-eun’s dream.

Grades weren’t the issue. Seo-eun’s abilities were on par with students at the Gifted High School. Even if she lacked in some areas, he could teach her himself.

What remained was a practical concern.

Their parents would surely say it was fine, but paying six years of medical school tuition on a public servant’s salary wouldn’t be a light burden.

Secrets of the universe were important, but so was the peace of his family.

Seo-ha began thinking about ways to prepare her tuition fee before she entered college.

Fortunately, it didn’t seem like it would be too difficult.

*****

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