Before long, a new name had been added to the lab plaque.
Rumors that Sujeong had joined Team Apex spread rapidly throughout MIT.
[Team Apex Lab]
-Seoha Yoo, Theodore Ranford, Srinivasa Krishnan, Sujeong Lim
The team hadn't accepted a single new member since Theodore and Srinivasa. Because of that closed-off nature, it was a place rife with rumors.
"Hey, did you hear?"
Someone spoke in a low voice from the back of the lecture hall.
"I heard Apex gained a person?"
"Is it a postdoc?"
"No, an undergrad. A transfer student."
"What?"
At his words, the other person's eyes went wide.
"That's insane! Who on earth is it? That's a place where even PhD candidates got rejected one after another!"
"There she is."
He pointed to a female student sitting in the very front row, lost in deep thought.
Normally, Sujeong would have enjoyed such rumors without showing it—the curiosity and envy mixed in the whispers, and even the wary gazes directed at her.
But right now, she didn't have the luxury for that.
After Sujeong's recruitment was decided, Sri and Theo guided her to the archive room.
Creak—
When they opened the door in the corner of the lab, stacked boxes came into view.
Sujeong had steeled herself before stepping inside, but the moment the door opened, she was rendered speechless.
Boxes piled waist-high, file cabinets numbered along the wall, and a large whiteboard densely covered with paper titles.
Next to each item was a short memo.
—Excessive dependence on initial conditions.
—Local convergence observed, but difficult to extend.
—Interval where limit interchange is impossible confirmed.
—Counterexample found; discarded.
"Are all of these reference materials?"
The two nodded.
"About half. The rest is data we've accumulated during our research. We also verified every single reference paper ourselves."
Stability theory, nonlinear flow, variational problems...
Sujeong clicked her tongue at the sight of papers on such a wide range of topics stacked like mountains.
"You were doing this kind of research?"
It was research on a scale that could overturn the entire fields of mathematics and engineering.
And it was already considerably advanced. Sujeong sat in a chair and reviewed the progress so far.
"You must have had a really hard time."
Sri and Theo shrugged their shoulders.
*You have no idea. Now you're going to be doing it too.*
Even without putting it into words, the meaning came across clearly.
Sujeong suddenly shivered at a chill she felt.
"If only this were everything..."
At Theo's words, Sujeong raised her head in surprise.
"Surely you don't mean there's more?"
Sri approached silently and opened his laptop.
Click.
He clicked on 'Oracle' inside a secret folder. Inside were countless subfolders.
Meeting minutes, interim reports, simulation logs, and experimental files that hadn't even been assigned version numbers.
All records generated while carrying out the project with the City of New York were inside.
Click.
When he opened one subfolder, records organized by date stretched on endlessly.
"This project will resume soon too. So since you're a team member, you'll need to know all of it, right?"
Theo winked one eye with an impish expression.
*Ah, so that's why!*
There was a rumor she had heard countless times since coming to MIT.
Team Apex, a super-elite team centered around Seoha, but with a rumor that recruitment had stopped long ago.
Sujeong finally understood the reason.
"I'll start right away."
It was an amount of studying she had never done in her life, but it was a fight in the way she had fought all her life.
And Sujeong was someone sufficiently tempered for this fight.
*I can do it!*
She didn't want to disappoint Seoha, who had believed in her.
* * *
Beep beep beep—
Tap.
6 AM.
At the sound of the alarm, Seoha's eyes snapped open.
Shhh—
Scrub scrub.
After quickly showering, Seoha carefully went down the stairs from the second floor.
The moment he grabbed a piece of bread in the kitchen and was about to leave the house, he sensed movement behind him.
"Seoeun! Why are you up already?"
Seoeun was holding Justin, looking at Seoha with an expression as if she were about to cry.
"...These days when I wake up, you're not here."
The ears of the beaver she hugged tightly drooped, just like Seoeun's mood.
"So I thought if I woke up a little earlier, I might get to see you..."
For Seoeun, who loved morning sleep, waking up 5 or 10 minutes earlier every day was no easy task. After repeating that for several days, she had started opening her eyes before Justin's morning alarm went off.
"Seoeun."
"Hmm?"
Messy hair, a face still heavy with sleep, yet stubbornly keeping her eyes open to look at him.
Seoha set down the bread and crouched in front of Seoeun.
*How should I comfort her?*
He hadn't been able to play with her often lately, so she seemed to have built up some resentment.
A new game?
Should he promise to teach her how to ride a bicycle?
In the end, Seoha decided to ask Seoeun directly.
"Sorry I've been busy. I have to head out now, but is there anything you want?"
As if she had been waiting for those words, Seoeun's eyes sparkled.
"There is one thing!"
"What is it?"
"But they said it's incredibly hard to get."
"Tell me. Since it's what you want, I'll do my best."
"Really?"
"I can't make any guarantees, but."
*There's a much bigger and more amazing medal than this.*
Seoeun hadn't forgotten what Sujeong had said.
"The Fields Medal!"
Just thinking about it made Seoeun smile brightly, revealing her still-growing front teeth.
Seoha was momentarily at a loss for words.
"Uh... uhm."
When is the next Fields Medal awarded?
Is it possible?
Objectively speaking, the probability of winning is about fifty-fifty.
Considering age, there's a good chance they might not award it this time.
If that happens, what's needed is an achievement so great the organizers simply cannot refuse.
"Oppa?"
At Seoeun's voice, Seoha came to his senses.
"Yeah, I'll definitely get that for you. As a present for your tenth birthday!"
Her eyes grew round.
Then, looking at the clock on the wall, she quickly said,
"Then there are 649 days, 17 hours, and 20 minutes left?"
"That's right. Exactly."
Seoha nodded.
"Promise!"
"Promise."
When Seoeun thrust out her pinky, Seoha found himself making the promise before he knew it.
On the way to school by bicycle,
the image of his sister hopping about joyfully lingered in his mind.
"A deadline has been created."
Strength naturally entered his hands on the handlebars.
* * *
During Team Apex's regular meeting time,
Seoha set down the chalk and stepped back.
The entire lab was filled with formulas Seoha had written.
*Already this far?*
The stalled organization was gradually unraveling.
Theo stroked his chin with a pleased expression.
*The solution to the minimal energy surface exists.*
That was a fact Seoha had already proven—a perfect proof with no room for counterexamples.
That alone was a tremendous discovery, but the problem lay in what came next.
*Existence is only the beginning.*
*It exists.*
But no one knows where.
No one knows what path to take, or whether that path is the only direction.
Theo glanced at Sujeong.
Long hair tied tightly with a hair tie, a dark gray hoodie that didn't require worrying about minor stains. It was Sujeong's battle attire since her gifted high school days.
She was silently scanning the equations Seoha had written.
Her eyes moved busily, as if unwilling to miss a single line.
Even while digesting MIT's grueling undergraduate curriculum, she was keeping up with the research Team Apex had accumulated.
"We can't go any further down from here."
With the addition of Sujeong's perspective as a number theory expert during the preliminary investigation, the very terrain of the discussion had changed.
Gradient, limit, convergence.
The minimal energy problem that he and Sri had been thinking about was a proposition that only held upon continuous flow. But Sujeong had dotted it with integer conditions, one by one.
When integer conditions are added, there appear points beyond which one can proceed no further—states where energy is low but transition is not permitted. A minimum defined not by value but by the irreversibility of state.
"Huh?"
Seoha, examining the formula he had written, tilted his head and picked up the eraser.
"W-wait!"
Theo hurriedly raised his camera and recorded the traces Seoha left behind.
Click!
Click!
Cold reason settled in Seoha's eyes.
*Ambiguous.*
This problem had too many uncertain points from the very start.
The doubts he had harbored from the beginning surfaced one by one in Seoha's mind.
Can this solution be approached as the limit of a continuous flow?
Or is a discontinuous leap required at a specific point?
Does the variational flow actually converge to the minimum point?
And can all of that process be drawn without a single logical flaw?
Seoha bit his lip slightly.
The form of mathematics and proof he desired could only be found by stripping away all the fog enveloping the mountain range.
*It must remain not as a feeling, but as a necessity.*
There was a hint in the materials the team members had prepared.
Seoha began writing formulas again.
Graphs and diagrams drawn as if sliding.
*Show your true form!*
Sri and Sujeong watched with blank expressions.
"Shh!"
Theo brought his index finger to his lips, as if telling the two not to interfere.
The atmosphere in the lab had already changed.
Seoha was completely immersed in the problem.
It was so quiet that he could even hear the current buzzing from the fluorescent lights.
Scratch, scratch.
Intuition could be a starting point, but it was never the destination.
Ambiguity was the enemy of proof; it had to be stripped away.
Scratch, scratch.
Several candidates that could be solutions remained on the blackboard.
Different forms, different conditions.
Their energy was all minimal, and mathematically, they were all valid proofs. But an indescribable sense of unease made him hesitate.
*A disguise?*
Seoha's gaze slowly swept across the blackboard.
As graphs and surfaces overlapped, a vast mountain range unfolded in his mind.
Rumble—
When integer conditions were added, ridge collided with ridge, sending out thunderous roars.
The fog was still thick, but Seoha's eyes could pierce through its true nature.
"Now I understand."
Fog was not a phenomenon created by lack of information, but by the superposition of structures.
It was an illusion created when different solutions overlapped with the same value. And among them were points that could never be reached in the three-dimensional world.
Seoha turned around.
"As expected, the solution was not singular.
However, the existing minimum and the reachable minimum are different. We need to find a solution that can survive actual mathematical calculation."
A solution that exists but has no path to it.
That was the true nature of the fog they had been facing ever since they began the challenge.
Theo looked at Sri and Sujeong.
*A proper team has been completed.*
In this room were gathered rare talents who trusted Seoha's intuition and would not slow his pace.
Sujeong narrowed the path with number theory, and Sri supported the theory with calculations and simulations.
And he was a topologist and an analyst who verified the logical consistency of what they presented.
*Yes. With this team.*
How far could they go?
A thrilling shudder ran down Theo's spine.