“I’m home.”
“Welcome back. You haven’t eaten, have you?”
“Yes, I’m hungry, Mom.”
Swish—
Seoha set down his bag and washed his hands.
“Oppa! Did you have a tea party at the lab again today?”
The moment he sat at the dinner table, Seoeun asked with sparkling eyes. Cecilia had gifted tea leaves to Seoeun. Thanks to that, a new routine had been added to the time he spent with his younger sister.
“Yeah, we drink tea every day.”
Perhaps due to Cecilia’s influence, the beverage trend in the lab lately was shifting from coffee to black tea.
“Let’s eat.”
Miyeong brought out the food.
On the table sat freshly boiled soup, various seasoned vegetables, and a mackerel grilled to a golden crisp.
‘Ah, this is nice.’
Ordinary and warm.
Seoha picked up his spoon and took a sip of the soup. The warmth flowing down his throat felt as though it were calming his brain cells, which had been worked up into a frenzy.
“The tea leaves Cecilia gave me, I drank them with my friends last time and everyone said they were amazing! I told them about the tea party, and they were all jealous of me?”
Whether she was happy that her older brother had come home early, Seoeun chattered away without pause. Seoha thought that the impression left by a real English aristocrat’s tea party must have been quite intense.
“Thanks for the meal!”
After the meal, he helped Seoeun with her studies.
His younger sister’s math skills were improving by the day. Seoeun enjoyed proving problems in her own way.
“Oppa, here the circle and the line meet. So the coordinates are…”
Perhaps because they had played with shapes together since childhood? She preferred drawing graphs or figures when solving algebraic equations to find the answers.
“That’s right. Well done.”
Seoha looked at Seoeun with warm eyes.
The moment she reached the answer on her own without needing an explanation. Seoha loved seeing his sister like that.
Study time was over, and now it was time to be alone.
Thud, thud.
Seoha climbed the stairs and grasped the door handle.
Click.
The moment the door closed, his expression turned cold and sank.
“Hah… hah…”
He leaned his back against the door and breathed roughly. Then he hurriedly pressed the button on the CD player sitting atop his desk. A winter piece flowed out quietly.
‘Calm down.’
Deoki, who had been quiet for a while, was lately trying to break free from control.
It wanted to rush in through his optic nerves right now and leap onto the plane of the zeta function. It wanted to throw itself into and swim amidst the infinite zeros lying upon the critical line, within that perfect matrix of formulas.
He could guess the reason. It was because he could now see the rough path toward proving the Riemann Hypothesis in his head. Just as one could not expect patience from a beast with succulent prey before its eyes, this was an unavoidable phenomenon.
Creak.
Seoha gritted his teeth.
‘Not yet.’
Deoki’s rampage had left his family with deep trauma.
Moreover, even if he were to set it free now, there was no guarantee he could sprint to the correct answer in one go. He didn’t know how many days it might take, nor did he feel confident that he would be able to return properly.
“Deoki, wait. The problem won’t run away. It’s a problem that has waited nearly 200 years. What’s a few more months?”
Seoha closed his eyes and muttered to himself.
Tomorrow too, he would sit at the table Mom prepared and eat. While helping Seoeun with her studies and protecting his daily life, he had to stand before that door. Not be drawn to the difficult problem like a moth to flame, but open the door of his own accord.
Deoki’s voice rang out, seeming to mock him.
‘It seems like you want to solve it more than I do? Stop refusing and just dive in. You’ll be the first in humanity to witness the moment all zeros align under a single rule. How ecstatic would that be?’
Seoha glared at the plush doll sitting in the corner.
The ridiculous figure of a beaver wearing a duck mask. Its eyes flashed as though peering through Seoha’s abyss.
‘Family? Daily life? They are lighter than dust before this great truth. Let’s write the proof for months until our finger joints are crushed. Compared to the ecstasy to be tasted at the end, everything else is trivial, no?’
Swish.
Thwack—
Seoha picked up a pillow and hurled it mercilessly at the beaver.
“You’re right about one thing. I want to prove this just as much as you do. But I’ll do it my way.”
His throat was parched. It was suffocating.
The painful hunger of holding one’s breath underwater for several minutes, just before bursting to the surface.
Seoha staggered and sat on his desk. Then he opened his notebook.
Scratch, scratch.
Seoha’s pupils dilated strangely.
Beyond his pupils, instead of his room, an infinitely stretching plane. The moment Seoha’s pen touched the paper, the lined-up zeros began to expand three-dimensionally.
And lines soared up from the paper, intertwining to unfold a vast topological space. The dream that even Grothendieck and Alain Connes, masters of geometry, had been unable to achieve despite devoting their entire lives—it was being newly created in Seoha’s hands.
Noncommutative geometry and arithmetic geometry.
Seoha’s pen crossed the sea lying between two continents. A bridge was placed along the pen, and a great continent rose in the center.
Noncommutative algebra, Hilbert space, spectral theory.
Mathematical theories born from quantum mechanics met Seoha’s intuition and were reorganized into a new language.
* * *
The next day, the lab.
Seoha was eating a donut. Apparently it wasn’t his first, as chocolate bar wrappers and cookie packages were piled up beside him.
Theo glanced at them out of the corner of his eye.
“Seoha, did something happen last night?”
Seoha took a bite of the donut and turned his head.
“My body is craving sugar, I suppose. I can’t eat like this at home.”
Three chocolate bars, two packs of cookies, and the donut currently in his hand. The usual Seoha would have been fine all morning with just a cup of tea.
Theo’s gaze turned to the blackboard. There, fourteen lines of equations were written. But he couldn’t understand at a glance what those short formulas meant.
Seoha made an awkward expression.
When he woke up in the morning, his body had felt as though he had run a marathon the day before. His fingertips were numb, and the area behind his temples throbbed with a dull buzzing.
“Son! Are you okay?”
At the breakfast table, Miyeong studied Seoha’s complexion and hurried over to feel his forehead.
“You feel like you have a fever?”
“N-No, Mom! The heater must have been too strong.”
Seoeun tilted her head.
“Hmm? But I was cold?”
Seoha waved his hand with a smile.
The team members trickled in one by one.
“Good morning!”
“Did you see outside? The weather is amazing today!”
“I bought sandwiches today… Hmm?”
“Suri! Your desk is a mess again. How many times did I tell you to throw away those parts…”
Cecilia came in holding two teacups.
Clack.
She set down a teacup filled with plenty of honey and milk on Seoha’s desk. Her gaze was fixed on the blackboard.
“…When did you write this?”
“I came in early this morning.”
Cecilia walked heavily to the front of the blackboard. Theo was already staring intently at the blackboard from the side. She too set down her teacup, crossed her arms, and began reading the fourteen lines of equations.
An unusual atmosphere.
Sujung, Suri, and Ben joined the formation in turn.
The notation of étale cohomology. The language of Grothendieck. Yet it was defined upon Alain Connes’s noncommutative space. Cecilia’s eyes narrowed. These two did not mix. At least not in the mathematics she knew. That was exactly why she had come here fully prepared, but…
“Seoha, can you explain?”
At Cecilia’s request, Seoha nodded.
His long explanation.
Clink.
By the time the teacups had been changed three times, the team members could finally grasp the concept.
“It’s not a completed theorem yet.”
“Of course.”
Theo stroked his chin. The equations were infused with the thoughts of several great masters.
‘Amazing. But…’
The idea of transferring the role of vector bundles to the noncommutative world through projective modules and defining cohomology upon it was beautiful, but this theory required many lemmas.
Seoha must have known intuitively that this hypothesis held true. But gaining academic recognition was a different matter. There had to be no flaws in any condition.
“Poincaré duality, finite dimensionality, compatibility with base change. Each of these requires independent proofs. Probably a few more besides these.”
Seoha nodded.
Cecilia’s eyes trembled fiercely. Only a few days ago, the gate toward the Demon King’s castle had finally opened. What had leaped out from there was a monster from the Four Heavenly Kings who controlled space.
“Kwahahaha! You worm-like scum! Disappear and become dust of spacetime!”
His voice seemed to echo in Cecilia’s ears.
A legendary demon that even the previous generation of heroes—Hilbert, Grothendieck, and Alain Connes—had failed to overcome. She had prepared herself for years of fierce battle, but her party possessed the greatest hero in history.
The battlefield scenery appeared before her eyes.
The hero walked out heavily, leaving the front lines alone. And—
“Seoha, wait!”
It was too late.
Seoha’s sword moved without hesitation.
The first slash.
Noncommutative algebra.
Kwa-kwang—
The moment the hero drew his sword, a shockwave swept across the ground. The commutative plains (commutative: a property in which the result does not change based on the order of operations) that the heroes of old had fought upon split apart, and new terrain surged upward.
Twisted land where the result changed based on the order of multiplication—a ground the monster had never stepped upon before.
“How dare this wretch!”
The monster roared in fury.
The following blade.
A six-line theorem drawing out dual structures from the spectrum of the Dirac operator.
“Kwa-eek!”
The monster screamed.
The hero’s sword changed direction. A formula restoring geometric structure by placing noncommutative algebra upon Hilbert space.
A single inequality serving as the core pierced through the entire structure. Exactly like finding and stabbing through the gap between the scales on a giant monster’s neck.
Six more slashes followed.
A total of fourteen slashes dismembered the monster.
It was truly overwhelming force.
“Kuaaaaak!”
Finally, the last line was written.
A powerful blow bisecting its thick neck!
Its head snapped off, and the monster’s enormous body toppled forward.
“…Did we get him?”
The Suri in her imagination subtly leaned forward and asked.
Cecilia jumped in surprise and turned to glare at him. Suri, who had been quietly looking at the equations, shuddered under her chilling gaze for no reason.
Rumble…
It wasn’t over.
The monster’s body seeped into the ground, and complex formulas were drawn. Its body scattered into dozens of small pieces. And each fragment crept into the corners of the blackboard, donning the shells of lemmas.
“Second phase.”
Cecilia muttered quietly to herself.
Commutator estimates, trace class convergence, injectivity of module maps, existence of spectral gaps, compatibility of index pairs, and many other theorems.
He had summoned his minions.
The Four Heavenly King rested, hiding his shattered main body behind the summoning circle.
“There are a lot.”
“Indeed. But if we work hard starting now, it won’t take too long. First, I’ll take the most troublesome one…”
At Cecilia’s words, Seoha picked up the chalk as if embarrassed. But she raised her hand to stop him.
“No! From here, it’s our turn.”
Theo looked at her and nodded.
Seoha’s hyper-focus mode had very poor fuel efficiency. The two thought differently, yet their intentions strangely aligned.
Cecilia glared at the list of lemmas with a grim expression.
While he rested, his comrades would hunt the minions.
That was the standard practice for a hero’s party.