Translator: Dreamscribe
MIT was not a university generous with transfer admissions.
The number of undergraduate transfer students accepted each year was twenty at most. Applicants numbered in the thousands, yet the acceptance rate didn't even reach a single digit.
The reason was clear.
MIT's current undergraduate curriculum had been ticulously designed over the course of several decades.
The foundational science courses were carefully structured to serve as the groundwork for advanced major coursework and graduate-level study that followed. There was simply little room for an outside student to wedge themselves in midway.
For that reason, transfer admissions were permitted only in very limited cases, as was the custom here.
The student had to be an already proven researcher, or one with potential on par with that.
"Oh my, this student is remarkable."
The hand of the admissions committee mber reviewing Su-jeong's file paused.
He flipped back through the pages and read the docunts again. Without so much as a glance at her perfect GPA, he carefully read through the research summary Su-jeong had attached.
"An undergraduate was researching a topic like this?"
Number Theory, Graph Theory, Computation Theory, and the combinatorial structure that wove them all together.
Each topic, taken separately, was already at a graduate level, yet they were organically interwoven under a single line of inquiry.
One part of the problems Theo had sent kept nagging at Su-jeong.
'I think it's connected to the Computation Theory Seo-ha was writing about in the seminar room.'
Is a transition of state numbers possible in the process of compressing a graph's local rules into Automata?
On the surface, it was a problem of Computation Theory, but to her, an entirely different direction was visible.
'Is this a coincidence? No way it could be.'
The periodicity of state transitions, the exceptions that appeared only at specific lengths. Su-jeong began gathering all of them into one place.
When she substituted the graph's local structure into integer sequences and expressed the transition rules as congruence equations, a pattern that had seed irregular revealed itself as wobbling only at pri periods.
"All that ti spent on Number Theory paid off."
The Number Theory she had devoted herself to in order to help with Seo-ha's proof of the Riemann Hypothesis was now serving as the force that supported her own mathematics.
She decomposed the transitions using the Chinese Remainder Theorem (Chinese Remainder Theorem * a theorem stating that several copri conditions can be unified into one) and tracked the growth rate of state numbers using the Dirichlet Generating Function.
Months of grueling research. Su-jeong gradually stopped showing up at school. She had no ti to spare studying things she already knew.
Without knowing whether the sun was rising or setting, she counted the coefficients of Generating Functions and redrew the boundaries of the state space. So days, she stood blankly in front of the chalkboard all day without drinking a single sip of water.
'Now I think I understand a little. What it must have felt like for you.'
She had a premonition that if she couldn't complete this research, she would never be able to take a single step forward as a mathematician.
And then, at last, one day, Su-jeong was able to discover that a special rule existed among the coefficients that had been bouncing around in disorder.
Her hand trembled as she wrote the proof on the chalkboard.
「Q.E.D.」
"...I did it."
A surge of elation she had never experienced before washed over her. This was an achievent she had reached entirely on her own, from start to finish.
Su-jeong crouched down in the empty lecture hall, wrapped her arms around her knees, and sobbed uncontrollably.
[On Pri-Periodic Constraints Arising in Local Automata of Planar Graphs]
The paper she published did not make it into a major journal, nor did it beco the talk of the town, passed around on people's lips.
But for the mathematician Lim Su-jeong, it was the mont she had cracked through her shell and erged into the world for the first ti.
* * *
"Oh my! Su-jeong, it's been so long!"
"Hello, teacher-nim."
Su-jeong bowed her head politely and walked past.
The hallways of the Gifted High School she was visiting again after two years felt narrower than she rembered.
Su-jeong paused for a mont and looked up at the ceiling. The familiar fluorescent lights, the countless club and study group flyers plastered on the walls, all unchanged from before.
The only thing that had changed was herself.
Entering the seminar room required a separate application process.
Perhaps not to Seo-ha's extent, but Su-jeong was also a well-known figure, long talked about among teachers and underclassn. When Su-jeong requested access, saying she needed mathematical inspiration, the principal granted her entry without further questions.
'■■th class Yu Seo-ha, completed the Four Color Theorem in this room.'
The notice posted beside the door told of what had happened here that day.
Rattle.
Su-jeong opened the door without hesitation.
Step, step.
She set foot in the empty, deserted seminar room.
Countless sheets of paper affixed to the walls, equations and symbols filling the chalkboard, arrows and circles tangled in layers upon layers.
"Whew."
Su-jeong let out a deep breath.
These sights carried her back to a certain day of her high school years, as though turning back ti.
When she closed her eyes, the events of that day still rose vividly before her.
Upon hearing that sothing had happened with Seo-ha, she had imdiately rushed to the seminar room. What she had seen there was an enormous diagram that seed almost alive, as if it were breathing.
She had thought she knew Seo-ha well, but on that day, he wore the face of soone she had never seen before.
His fingertips were stained white with chalk dust.
Muttering sothing to himself, he had been writing equations on the chalkboard as though possessed. Overwheld by the sight, Su-jeong could not bring herself to go near him.
'What on earth is he doing?'
Su-jeong had desperately tried to understand the equations Seo-ha was writing.
She followed the flow of the expressions, chased the connections between shapes and arrows, and traced over what the diagrams ant again and again in her mind. But back then, it was sothing she could never reach.
'What is all this?'
It was a language she had never learned.
The symbols were familiar, yet not a single thing properly registered in her eyes.
What Su-jeong had felt then was not sothing as simple as jealousy or a sense of defeat. It was a frustration welling up from sowhere far deeper than that, and before she knew it, a thought had co unbidden.
'Ah, this is the limit of what I am.'
Step, step.
Su-jeong moved up close to the chalkboard.
The curtain of equations that had blocked her approach like an impenetrable barrier back then. She had co here today to dismantle it.
What had happened that day had beco an indelible mark on Su-jeong. The version of herself that had recoiled in fear before sothing she could not understand.
Su-jeong looked over the chalkboard for a while before finding the point where Seo-ha's proof began.
"There it is."
Rattle.
She pulled up a chair, sat down, and stared intently at that spot.
Su-jeong's eyes darted rapidly, tracing the flow of the equations Seo-ha had written. Unlike before, his thinking seed almost within her grasp.
'Why were you in such a rush?'
The sparse explanations, the constant leaps in logic.
Only then did Su-jeong realize why she hadn't been able to understand this. Seo-ha had never intended to show this proof to anyone else. Since he only needed to understand it himself, there had been no need to consider anyone else.
"You really are a terrible kid."
But now she could see it. The logic by which he had tried to solve the Four Color Theorem.
As the sun began to set, Su-jeong took one last look at the chalkboard.
The place where Seo-ha's proof had begun, and the position she had only now been able to reach.
Swish.
She slowly rose from the chair.
Rattle.
After pushing the chair back to its original place, she walked toward the door.
As she stepped out of the classroom, she glanced back over her shoulder. And she smiled faintly.
"Now I'll co to where you are."
Here, today, she was finally able to graduate in the truest sense of the word.
* * *
"Sri, what are you doing?"
The mont Seo-ha opened the lab door, he sensed sothing was off.
Sri must have co in since dawn; he had pulled out several boards and was working through sothing.
Seo-ha quickly scanned it.
'Number Theory?'
Congruence equations, pri decomposition, periodic notation.
Lattices instead of curves, congruence constraints instead of variational conditions. This was not Sri's usual area.
"This guy got wrecked by an undergrad yesterday. He asked about Minimal Energy Surfaces the way he always does, and apparently the student approached it through Number Theory."
Sri wore a dejected expression.
"It's because I wasted ti studying engineering. If I'd done proper math from undergrad..."
"Was it that much of a shock?"
He nodded.
It wasn't simply a matter of wounded pride. Sri had been absolutely convinced that Seo-ha would be the last person younger than him he'd ever have to learn from.
'A minimum found through differentiation always has a way to escape. If you block it off with integers, you don't have to worry about that.
The minimum energy I'm thinking of isn't a value that can't go any lower. It's a state that can no longer move.'
Sri had not been able to understand her words right away.
He had nodded awkwardly and headed straight to the library.
'That's impressive.'
An insightful answer.
The more he turned it over, the more ideas kept surfacing. In the end, he stayed up the entire night studying all the related material before he could fully understand what she had said.
"Why are there so many monsters among mathematicians?"
Sri's shoulders slumped.
Knock, knock!
Soone knocked, then opened the lab door and stepped inside.
"Excuse ."
All three pairs of eyes snapped toward the entrance at once.
Even without a trace of makeup, her skin was strikingly pale. Her eyes were clear, yet carried an air of sharpness about them.
A sleek, oversized coat was draped over a thin knit.
She hadn't put obvious effort into dressing up, yet she was the kind of beauty that drew the eye nonetheless.
"Su-jeong noona!"
Seo-ha sprang from his chair as though bouncing up with delight.
"Yeah, soone over there told to co in today."
Su-jeong pointed with the tip of her chin toward Sri, who was sunk in his gloom.
She thought to herself.
'Team Apex. If they're the people working alongside Seo-ha, they must each have sothing exceptional about them.'
She made up her mind.
At least one.
She would prove that she was better than at least one mber of this team.
"Don't you have anything to say to ?"
Su-jeong asked, looking at Theo.
"Hahaha!"
Theo set down the docunt he had been reading.
It was a paper recently published in a journal under Su-jeong's na.
The question he had posed was a problem asking whether a transition of a graph's local states held true under specific conditions. But Su-jeong had not plugged in conditions and weighed the possibilities one by one.
Instead, she had proven why, among the countless cases, only this particular form of transition survived to the end.
An achievent that soared far beyond the goal.
Step, step.
Hisssss...
Theo walked over to one side of the lab and brewed a cup of coffee using the most expensive beans.
"Here you go, my lady."
Sri hurried over and cleared off the table.
Su-jeong sat in the chair Theo held out for her, crossed one leg over the other, and picked up the coffee cup.
"Surprised?"
With her confidence restored, Su-jeong had returned to the person she once was.
Haughty yet self-assured.
"No."
Seo-ha shook his head.
"I told you, didn't I? You're soone who's going to beco an incredible mathematician."
Tears welled up in Su-jeong's eyes.
"You believed in ?"
"I never doubted it, not even once."
mories she had built with Seo-ha ca flooding into Su-jeong's mind like a tidal wave.
The Seoul National University Math Competition where she had first seen him, the IMO they had attended together as Korea's national representatives. Back then, there was nothing in the world that scared her.
And the high school days they had spent together ca back to life, scene by scene, like a panorama.
'When I think about it, it was from the very beginning.'
The mont his beautiful proofs had stolen her heart, every path other than becoming a mathematician had ceased to exist in Su-jeong's future.
Su-jeong looked straight into Seo-ha's eyes and spoke.
"I'm the mathematician Lim Su-jeong.
I want to join Team Apex."
Seo-ha gave a short nod, as though it were the most natural thing in the world.
"The honor is ours."
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