Paper-Writing Speedrun
Mom turned around, leaving the dishes half-done.
"A paper? What paper?"
"Actually, I solved the Riemann Hypothesis. I wanna write a paper on it."
In that instant, the plate slipped from Mom's hand and shattered on the sink floor.
Her eyes went wide as saucers.
"R-Really? No, really?"
I nodded vigorously.
Mom had her master's degree, so she knew full well how monumental and grueling an achievement this was.
I couldn't help but grin at her expression.
"Hold on, A-yeon. Tell me everything in detail."
We three sat at the living room table. Mom's hands were still a bit damp, and Dad looked utterly confused about why he'd been summoned.
I sat primly with my hands neatly folded on the table.
"A-yeon, can you explain it all?"
I laid it out step by step.
In my past life, right before I died, I'd cracked the Riemann Hypothesis. The night before, I'd summarized the core idea in the cloud. That's why I wanted to turn the proof into a paper.
I spoke in a flat, businesslike tone.
I hadn't mentioned it earlier because my emotions had overwhelmed me—I'd been bawling my eyes out and couldn't think straight.
"But my finger muscles aren't developed enough to type alone... so I need Mom's help."
A hush fell over the room. Mom closed her eyes and murmured softly,
"...I see. So Professor Shin pulled it off after all."
It was almost a whisper to herself.
Mom knew what the Riemann Hypothesis was. She'd felt its weight firsthand reading related papers during her master's.
How impossibly hard it was. Why the world's top mathematicians had all challenged it and given up.
Urban legends swirled about it being a devilish problem—one that drove some mathematicians to schizophrenia, others to dementia.
While Mom pondered quietly, Dad piped up.
"Wait a sec. You solved the Riemann Hypothesis?"
"Yup!"
"That problem Professor Ijun obsessed over since his PhD days? You actually cracked it?"
"Yup, that's right. My past-life self solved it right before dying."
"That's my girl! Wait, not as Yoo A-yeon, right? Doesn't matter—come here, you did great!"
"Eek! Hehe!"
Whoosh—whoosh. Dad grabbed my sides and gave me the deluxe airplane ride. As my body lifted into the air, my semicircular canals went wild, my brain hit excitement overdrive, and giggles bubbled out uncontrollably.
Airplane time ended, and Mom, done thinking, spoke up.
"Alright, A-yeon. I'll help."
My eyes sparkled.
"For real?"
"Yes. Because it's my daughter's request, not anyone else's."
Mom's face softened.
"Yesss!"
I shot my arms up in victory.
"But there's a condition."
"What?"
Mom looked me straight in the eye, her expression serious now—different from before.
"Eat meals on time. Sleep early. And never skip family time. That includes me, Dad, and A-rin."
"...That's a given."
"It's not."
Mom's voice grew firm.
"I know how Professor Shin lived while researching the Riemann Hypothesis. Three months holed up in the lab, never stepping out. No sunlight, no exercise, delivery food only, guzzling caffeine drinks by the case, barely sleeping—and even that curled up like a shrimp on a hard sofa."
"..."
I shut my mouth. I had nothing to say.
"And how did that end? He already had health issues, and it all caught up—heart attack. That wasn't just bad luck."
Memories of my past life's final days flashed by.
The lab piled with delivery containers and caffeine cans. Days-long stretches of hyper-alertness. And on the day the proof clicked, that sudden crushing pain in my chest.
I already knew the heart attack hadn't come out of nowhere.
Back when Mom was my grad student, I'd behaved myself. But after she graduated and left, with no one around, I'd gone wild in that empty lab.
"No one could rein the professor in back then because he was alone. But I'll never let that happen again. As long as I'm here, you won't live like that, A-yeon. Got it?"
"...Yeah, got it..."
I replied quietly.
I got scolded out of nowhere...
Pat-pat. Mom stroked my head.
"Good answer, A-yeon. Such a good girl."
Dad nodded beside her, arms crossed.
"I agree. Take your time with the paper—no skipping meals or sleep. Promise Dad."
Dad stuck out his pinky.
"...Tch. Fine."
I puffed my cheeks a bit.
Treating me like a kid, seriously!
Grumbling inwardly, I still hooked my pinky with his.
After teaming up with Mom, our routine settled in like this.
I drafted the paper first. Aiming for an international journal, so in English from the start.
We worked during A-rin's naps. Mom opened the laptop, and I glued myself to her side.
I dictated; she typed.
I figured it'd be smooth sailing, but an unexpected snag made it way harder.
"A Hilbert space is defined as—"
"Hold on, hold on. What?"
"A Hilbert space."
"...Hilbet?"
"Hilbet! Hilbert space!"
"Hilbert space, maybe?"
"Yes! That, that!"
The problem? My toddler tongue couldn't pronounce English right...!
Th sounds mushed into D, R half-vanished. No difference between L and R.
Mom couldn't just type what she heard—it was gibberish.
She had to decipher my words, reconstruct proper English in her head, confirm with me, then type.
Slow as molasses, naturally.
"So, 'A Hilbert space is defined as a complete inner product space'?"
"Yes! Perfect!"
"But A-yeon, if I don't get why this space specifically, I can't type the next sentence."
"Why not?"
"Your English is too cute—I won't understand the next one either."
Mom giggled.
Pffft. Realizing my pronunciation sucked, embarrassment flooded me. My face burned.
"It's okay, A-yeon. You're still little, tongue's short. It'll improve fast as you grow."
Pat-pat. Mom stroked my head.
"Hng, okay..."
Dictation-only typing was impossible. To get the paper right, Mom had to understand.
Mom. A Hilbert space is a complete vector space with inner product. Think of it as the vessel for the operator whose eigenvalues are the zeros of the Riemann zeta function. Without it, nowhere to define the operator.
That's what I meant to say. But my mushy speech failed.
"Um... complete vector space, right?"
"...Yes."
"And after 'zeros of the Riemann zeta function,' what?"
"Eigen... eigenvalue..."
"Aha, eigenvalues? Got the gist. I kinda get it."
"Then type the next sentence."
"Okay, okay."
Tap-tap-tap.
That was the drill.
To write the paper, I had to make Mom grasp the logic first.
But as a master's holder, not a PhD, she struggled with specifics. Plus my pronunciation? Communication hell.
I braced for a long haul, but...
This bottleneck was frustrating.
Haa. I sighed softly.
What could I do? Couldn't beam my brain into hers. Had to plod on, inconvenience and all.
Hold up—gonna explain the tough stuff real quick, so smarty-pants with headaches can skim. Cool?
The Riemann Hypothesis is about prime number patterns—feels like pure number theory. But with the function's flexibility, tons of approaches. Mine? Physics-based.
The "Hilbert-Pólya conjecture"—recast as a quantum mechanics energy levels problem.
That's why many see it as a physics issue.
Paper structure went like this.
First, define the right Hilbert space for the zeros. H = L²(X, dμ).
That choice was the proof's foundation.
Then build operator H on it: (Hf)(x) = i*(d/dx)f(x) + V(x)f(x).
Most crucial. For 160 years, no one found it—that's why unsolved. Its eigenvalues had to be real, matching zeta zeros exactly.
Past-life me poured three months into this.
When I explained, Mom shared her thoughts.
"Sounds physics-y... but I don't know physics."
"Still, this is the key part, Mom."
"Defining operator H?"
"Yes. Prove it meets three conditions, proof done."
"Really? That simple?"
"Yup. Each step's a beast, though."
Operator H couldn't be junk—had to satisfy three picky conditions.
Self-adjointness. Show H equals its adjoint H*.
Spectrum. All eigenvalues match the zeros perfectly.
Trace Formula. Spectral (zeros) and geometric (primes) sides equal.
So hard to find such an H—no one did, despite the million-dollar prize.
"Get it, Mom?"
"...Nope. Zero clue."
She looked deflated—uncharacteristic.
Makes sense. Back when she was my student, I'd dote, explain at her level, give hints for tough bits.
This? PhD-plus territory, even other profs struggle. Like jumping from WWE to UFC—no wonder her brain scrambled.
"Can't even follow my daughter... what a shameful mom..."
"No worries, Mom! Your job's typing my English sentences! No need to get it all!"
Pat-pat. I stroked her drooping head to cheer her. Height difference meant stretching my arm high—tough work.
"...A-yeon, maybe you building muscle is faster than me understanding?"
"Hm... maybe? But let's type the easy stuff first!"
Would Mom grokking this be quicker? Or my pronunciation/fingers improving?
Either way, not wrapping up soon.
Time flew by like a bullet.
Or nah—bullet tops 250 km/h. More like a railgun at 6,000 km/h?
Anyway, time railgun-ed away.
Before I knew it, I was five years old.