Chapter 53
Chapter 53
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Translator: Ace
Chapter: 53
Chapter Title: Hilbert's Infinite Hotel
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Soo-jung arrived at the dorm. But the hotel's name felt strangely familiar somewhere.
"Hilbert's Hotel?"
Her mind was foggy like mist, making it hard to recall where she'd seen it.
"Let's check it out for now."
She approached the reception desk, pulling her suitcase, dressed in a 19th-century European-style gown.
But on the counter sat a sign: 'No vacancy'.
"Ah... no rooms available."
As disappointment washed over her, a hotel staff member approached and said,
"Don't worry, lady. We're an infinite hotel."
"Huh? Then what's that?"
Soo-jung pointed at the 'No vacancy' sign on the counter.
"Aha! The hotel is full, but we can specially make a room for you."
What on earth was he talking about? Soo-jung looked puzzled.
"How?"
"Move the guest in room 1 to room 2, room 2 to room 3... and so on, infinitely shifting everyone. Then room 1 will be empty. You can stay there."
While Soo-jung stood there dumbfounded, a group of guests arrived. A man who looked like a bus driver approached the counter.
"Hey, we're from Infinite Bus Company. Can our passengers stay here?"
"No problem."
"I said Infinite Bus Company. We have infinitely many passengers."
The staff member smiled faintly and tapped the ledger with his fountain pen.
"We're an infinite hotel.
If we move all guests to even-numbered rooms, all the odd-numbered rooms will be free. No matter how many guests, they can all stay."
Soo-jung couldn't stand this seemingly pointless conversation any longer.
"If it's infinite anyway, why not just pick any empty room and go in!"
The staff stared at Soo-jung intently, then said with a stern expression,
"Lady, didn't I tell you from the start? There are no empty rooms here. If you go in on your own..."
He leaned in close and whispered in her ear.
"...you never know who—or what—you might meet in the room."
Kya-aa-aa-aak—.
Soo-jung screamed and fled.
"..."
Seo-ha was eating donuts with Soo-jung.
The cafeteria staff were even glancing over, captivated by her vivid performance.
"You had a dream like that?"
Soo-jung gulped down a glass of water, her throat parched.
"Yeah. I read about Hilbert's Paradox of the Grand Hotel before bed, and it showed up in my dream."
The paradox stated that in a hotel with infinite rooms, even if full, you could always free up space by rearranging guests according to set theory.
"You were reading something interesting. Why Hilbert all of a sudden?"
Soo-jung set down her cup and shrugged.
"I've got mentoring tomorrow. A middle schooler asked me to explain countable infinity and one-to-one correspondence."
"Ah! Great idea. Hilbert's paradox would make it intuitive."
Natural numbers: 1, 2, 3, 4, 5...
Rational numbers: 1/2, 2/3, 1/4...
At first glance, rationals seem far more numerous, squeezed infinitely between 1 and 2. But math defines set size by cardinality. The key is whether a one-to-one correspondence is possible.
As Hilbert's hotel shows, even countable infinities like natural numbers (rooms) and rationals (guests) can match perfectly.
The paradox where the part equals the whole shakes human intuition to its core—profoundly philosophical.
"Why are you interested in this too?"
Instead of answering, Seo-ha pulled a book from his bag.
[The Theory of the Riemann Zeta-Function]
Soo-jung gaped at the title, nearly fainting in shock.
"R-Riemann zeta function? You're not thinking of solving the Riemann Hypothesis, are you?"
"Not right now, but someday I definitely will. I'm still in the research phase."
To explain the Riemann Hypothesis like Hilbert's hotel:
Imagine a hotel with infinite rooms, but unlike Hilbert's, not all are occupied.
Rooms 2, 3, 5, 7, 11, 13, 17, 19...
Only prime-numbered rooms have guests.
At a glance, these 'prime guests' seem scattered randomly.
But the Riemann Hypothesis claims their placement follows an invisible mathematical rhythm.
And the key to revealing that rhythm is the Riemann zeta function.
"You believe primes hide the universe's secrets too? Most say they're random."
Soo-jung looked indifferent.
Primes have fascinated mathematicians for ages.
Yet no one has proven their pattern. Even proving Riemann would only predict distributions, not pinpoint each prime.
"Most mathematicians say primes have no exact pattern—that randomness is their essence."
Hence, primes are called the 'atoms of mathematics'—indivisible, unpredictable.
"But if Riemann is true, isn't calling it random vague? Order in chaos, maybe?"
"Less a strict law, more predicting density and flow. But that's enough for humans to uncover so much."
Noticing Seo-ha's seriousness, Soo-jung straightened up.
"Really? I think the Riemann Hypothesis is overhyped. Solving it won't break modern cryptography—primes' rules stay unknown. Number theory advances a bit, but no massive breakthrough.
Maybe it's legendary just because it destroyed so many mathematicians."
Soo-jung wanted to steer Seo-ha away from it.
Seo-ha nodded.
Some mathematicians would agree. But he had a compelling reason to solve it.
His secret dream, untold to anyone:
Discovering the 'Theory of Everything' beyond relativity.
A theory explaining all—Newton's domain for 300 years.
Einstein revealed Newton's oversight of time's relativity and proved it.
Now scholars say relativity fails quantum motion.
Time for the next theory.
(String theory's a candidate, but unprovable.)
Seo-ha believed primes' secrets transcended number theory. The zeros of the zeta function mirrored quantum chaos—the universe's rhythm.
'If there's a theory beyond Newton and Einstein, it must start with the Riemann Hypothesis.'
That's what he thought.
But this research hadn't even begun; he couldn't tell Soo-jung everything.
"Proving Riemann might solve the Goldbach Conjecture too, right?"
Soo-jung stared silently at Seo-ha for a long time, then spoke haltingly.
"Seo-ha. Please, don't."
Her voice was desperate.
"I know you're a once-in-a-generation genius. But infinity isn't just math—something destroys human intuition there.
Think again. Is it really worth it?"
Obsessing over Riemann often ends careers. (At least so far.)
The world romanticizes it as mathematicians' passion, failure, endless quest. But those who dive in?
A bottomless labyrinth, question even if an answer exists.
They wander lost, burning life in infinite darkness. Left with emptiness and regret.
Soo-jung feared Seo-ha stepping into math's abyss.
"It's worth it. I can't spill everything now, but I'll reach the primes' secrets someday."
Soo-jung closed her eyes, sighed deeply.
She knew him—he wouldn't stop till he found the answer.
"What if there's nothing at the end?"
No counterexamples yet, but Riemann might be false.
"I'll be the one who confirms it's nothing. That's enough. Someone has to peer into that abyss."
Seo-ha's voice was calm, laced with iron conviction—like it was his fate.
In that moment, Soo-jung felt she knew what to do.
Meeting Seo-ha might be destiny.
To help him—or stop him before it's too late...
Such talent vanishing would defy even fate.
"Can I do anything? Not sure if I'd help."
Her first friend, the one who revealed math's beauty.
To her, Seo-ha was special.
"Not at this stage yet. But when I'm sure I can crack it, I'll call you, noona. Help me then."
Soo-jung nodded.
She planned to study math in college but hadn't picked a focus.
'Guess I'll study number theory.'
Until that day.
"Oppa!"
Spotting Seo-ha from afar, Seo-eun dashed out of the house. She ran straight into his arms.
Seo-ha grinned, hoisting her tiny frame high.
Kyaak—.
Seo-eun squealed, flying through the air in delight.
"Were you waiting?"
"Yeah! You said you'd come today. I kept watching!"
Gripping her brother's hand tight, Seo-eun bounded inside like a puppy.
"Mom, Dad! Oppa's here!"
The house filled with joyful laughter.
Seo-ha helped with her homework, then harvested pumpkins from the garden together.
Seo-eun devoured her meat heartily, then nodded off, collapsing asleep.
Cheol-ho gently scooped her up.
"She was so excited oppa came, and now she's out."
Seo-eun slept soundly, face beaming with some dream's smile.
"Everything okay with Seo-eun lately?"
Mi-young thought a moment, then chuckled softly.
"She used to say she'd be a mathematician like you, but now she wants to be a doctor."
"Suddenly?"
"Not really—started after visiting you in the hospital. Probably shocked seeing you collapsed."
Recalling that time still filled Seo-ha with guilt toward his family.
"I'm sorry."
"Just don't let it happen again."
Seo-ha pondered Seo-eun's dream.
Grades weren't an issue—her talent rivaled gifted school kids. If lacking, he'd teach her.
Reality was the hurdle.
Parents would say it's fine, but civil servant pay plus six years of med school wasn't light.
Universe's secrets mattered, but family peace did too.
Seo-ha mulled ways to fund her tuition before college.
Thankfully, it didn't seem too hard.