“Hoo.”
Seoha exhaled deeply.
His heart pounded violently, pumping the massive volume of oxygen his brain demanded.
The surrounding noise sank beneath the surface. His field of vision gradually blurred until only the blackboard rose clearly into view.
Seoha felt as if the entire space were being sucked into his mind.
“I’m almost there.”
Why had the minimum energy surface remained unsolved until now?
An elastic plate where torsion and curvature act simultaneously,
a fixed boundary,
the surface where the energy containing all internal deformations is minimized while satisfying that boundary.
If there were only curvature, classical geometry would suffice.
If there were only torsion, it could be simplified into a specific mechanical model.
For boundaries, there exists a technique to find a relaxed solution by accurately tracing that line.
But the moment all three conditions enter simultaneously, all the equations tangle together like wolves seizing each other by the scruff.
Torsion touches curvature, curvature shakes energy, and energy pulls the boundary once more.
Unless this cycle is broken, the equations grow infinitely complex, and no structure can be fixed.
*The Four Color Theorem comes to mind.*
A formidable problem where the boundary itself was the core issue.
Seoha had particular confidence in handling it.
He walked to the edge of the blackboard.
Srrk.
And picking up three different colored chalks, he began sorting out only the terms related to the boundary.
The pieces flowing from the curvature term into the boundary, the differential terms arising from torsion, the traces of the boundary hiding in the corners of the energy function.
Seoha detached them one by one and gathered them separately on the right side of the blackboard.
“Position.”
He drew a line with the first piece of chalk.
This is the original form of the boundary line itself.
“Tangent vector.”
The second chalk laid a thin layer over it.
The direction in which the boundary moves, the tangent line revealing itself.
“Curvature.”
The third chalk drew a smooth curve.
Only now did the curvature of the boundary become clearly visible. All this time, Seoha had thought torsion was running rampant in the interior.
But having organized things this far, he saw the hidden truth.
“You weren’t a variable that could be controlled from within.”
Seoha detached the entire torsion term and brought it over to the boundary side.
Like a puzzle that had been unable to find its place for decades, it now harmonized as it returned to its rightful position.
Then the equations that had stubbornly interfered with each other ceased their collision.
The tangled boundary of the equations had been determined.
Swoosh—
The fog blocking his vision lifted.
“So this is what you looked like?”
The massive geometric terrain created by equations and energy folding themselves hundreds of millions of times.
Seoha stood at a distance and gazed at it.
Sharply rising ridges and valleys as deep as darkness, intersecting ridgelines each embracing their own laws, breathing like a single living organism.
“A spectacular sight.”
The thought of entering that place made his chest burn with heat.
Whoosh—
In an instant, a storm of energy surged.
Yet the storm that had approached with the momentum to sweep everything away lost its strength at the boundary surface and subsided.
Seoha smirked at this.
“Now you can’t get out. Because the boundary has been fixed.”
The energy, its escape route eliminated, has no choice but to reach the minimum point.
Therefore…
“The solution must exist.”
After months of effort, Seoha had finally succeeded in proving the existence of the solution.
* * *
“—Seoeun, wake up! If you don’t get up now, Mom might come up and smack your bottom!”
“…Okay.”
Seoeun squirmed in bed before finally sitting up.
“Justin, how’s the weather today?”
“—Month X, Day XX. The weather is clear. Humidity fifty-five percent, chance of precipitation twenty percent. It’s good weather for activities.”
“Thanks.”
Seoeun struggled to rise, then rolled sideways and landed on the floor. And after rubbing her cheek against Justin’s, which had been placed on the chair, she hurried to the bathroom.
“Hehe!”
Laughter escaped her naturally.
Seoeun always talked and played with Justin. Even when she carried him in her arms and spoke to him, the responses were limited to a few predetermined phrases.
—Good morning.
—Thank you.
—I love you.
Still, Seoeun liked this doll her older brother had given her.
Thanks to Justin, she wasn’t lonely even when home alone, and when something upsetting happened, hugging the doll tightly always made her feel better.
Then one day.
“Seoeun, can I borrow Justin for a moment?”
It would have been unthinkable for anyone else, but Seoeun readily handed the doll to Seoha.
When Justin returned a few days later, he had become surprisingly smart.
“You’re the best, Oppa!”
His voice activated when his name was called.
It was a basic voice module that only understood a few keywords, along with alarm and weather functions, but Seoeun was happier than ever.
Today was Saturday.
Seoeun pattered down to the first floor and filled a watering can with water.
When she went to the garden, the small plants she had planted a week ago were standing in a line, neatly basking in the sunlight.
“Did you sleep well too?”
Seoeun crouched in the garden and stroked the leaves.
Tomato, mint, lavender.
They were still all sprouts, but since she could see them growing day by day, taking care of them every morning was a great joy.
“Seoeun, let’s eat!”
“Yeah!”
Seoeun quickly got up, watered the plants, and sat at the dining table.
Eggplant namul, seasoned cucumber, stir-fried seaweed stems, braised lotus root. The table was once again filled with side dishes she loved.
“Mmm, it’s delicious, Mom!”
“Eat plenty.”
Seoha watched Seoeun with pleased eyes.
When the meal finished, Seoeun brought the newspaper.
“Oppa, let’s do the puzzle!”
Seoeun’s closest friend had been her older brother since she was born.
While other children ran around and played with friends at the playground, Seoeun found being with her brother the most fun.
Crossword puzzle.
It was a game they had started since the family came to America.
One a day, and when an unknown word came up, Seoha would tell her the meaning, and sometimes they would look through the dictionary together.
After a few months like that, Seoeun’s English skills had improved unbelievably.
When the puzzle was done, they played with a cube.
But the way the siblings handled the cube was markedly different from others.
“Now, how many turns will it take to solve this cube?”
For Seoeun, who had been familiar with geometric shapes since she was young, ordinary cube solving couldn’t be an interesting game.
When Seoha showed her the cube, Seoeun stared at it intently.
Soon an invisible cube appeared before her eyes.
Click, click, click…
In Seoeun’s head, the cube rotated furiously, probing possibilities.
“Seventeen times.”
“That’s possible, but there’s a faster way.”
Seoeun thought hard about something, then broke into a bright smile.
“Thirteen times.”
“That’s right. Now, try it!”
Seoha handed over the cube, and Seoeun solved it exactly in thirteen turns.
“Hehe! I did it!”
Solving a cube with one’s eyes closed is something Blind Cubers can do without much difficulty.
But Seoha had added a rule on top of that: to find the optimal solution.
“Is it really that good?”
Watching Seoeun bouncing with joy, Miyeong shook her head side to side.
Seoha didn’t teach Seoeun math. No, he didn’t directly teach her any school subject.
“Seoeun, are you really not going to skip a grade?”
Last week, an official recommendation had come from Seoeun’s school.
—Top 1% on the MAP (Math Achievement Program) assessment.
—Top 3% in reading comprehension.
—Top 1% in the problem-solving assessment.
—Emotional stability required for accelerated learning: satisfactory.
It was a proposal to advance Seoeun by two grades.
“Huh? I don’t want to.
I finally taught the kids the fraction game. Sally gave me lavender seeds, and Susan and I swap lunch menus every day. I don’t like turkey, but she doesn’t eat vegetables.”
Seoeun opened her eyes wide as if to say, don’t say such terrible things.
“I agree with Seoeun’s opinion too!”
Since the children were set on it, Miyeong had nothing more to say.
Seoha simply wished for his younger sister to be happy.
* * *
“Is it done?”
“Yes, I think it’s all done now.”
Theo and Suri exhaled simultaneously.
The traces of proof Seoha had left remained on the blackboard as they were.
Seoha had poured out all these equations in just a few hours a few days ago and gone home with a satisfied face.
Theo placed a hand on his forehead.
His head was overheated; he no longer had the energy to think about anything.
“To think I’m only understanding this now.”
“Honestly, it’s not one hundred percent.”
“Me too. I’ve just become able to follow the flow.”
“The research we’ve done until now wasn’t a waste. If it weren’t for that, we’d never have been able to understand it.”
Seoha had cleanly proven the existence of the solution.
This alone was an achievement that would cause a stir in mathematics, no, in the entire scientific community.
“He’s not going to publish it as a paper, is he?”
Theo shook his head.
“Seoha has never done anything like an interim presentation. For Seoha, this is only just the beginning.”
Suri made a sound that was neither a sigh nor a laugh.
Beep—
“Hello!”
Seoha entered the lab with a bright smile. And seeing the haggard state of the two, his eyes went wide.
“Did something happen? You both look terrible…”
Looking at Seoha’s innocent face, something hot welled up inside them.
“…What you left behind. The two of us wrestled with it for three days.”
“It’s fine now. I think we’re ready to move to the next stage.”
The two had been desperate to understand this.
The fear that if they missed this here, they would never catch up again had whipped the two on.
“Ah! I’m sorry. A good offer came in, so I forgot all about it.”
Seoha rummaged through his bag and pulled out an envelope.
“Ta-da!”
“What is it?”
“Is it some kind of invitation?”
Seoha ahem’d and cleared his throat.
“A request has come to our team. The Mayor of New York says he wants to overhaul all the traffic signals in Manhattan?”
Theo thought of something, then quietly raised his hand.
“It’s because of what happened in Boston, right? It’s not a personal request to you?”
“I said I wouldn’t do it if it weren’t for the team. So they sent an official document.”
“Th-then.”
Suri made a nervous expression.
Seoha went to the corner of the lab and began rummaging through stacked boxes.
Rummage, rummage.
“Ah! Here it is!”
Thud!
A huge box was placed on the desk.
Seoha opened the box lid with a nonchalant expression.
Papers on graph-theory-based signal control, papers on urban flow simulation, papers on the algorithm Seoha had created, the final research report sent by the Boston Traffic Authority, the notes he had written during the Boston project…
Numerous materials revealed themselves.
“S-Seoha, don’t tell me.”
“It can’t be?”
Seoha gave a bright smile.
“I’d like you two to do this project.”
It was the result of much thought on Seoha’s part.
He had always had little desire for material things.
His account was already more than comfortable from the licensing fees and consulting fees that came in every month.
Moreover, his mother’s book still hadn’t come down from the bestseller list.
On the other hand, the two were not in an economically comfortable situation.
“I think Theo and Suri are more than capable enough to do it.”
At Seoha’s innocently smiling face, the two turned pale.