MIT was not a university generous with transfer admissions.
Each year, it accepted at most around twenty undergraduate transfer students. Applicants numbered in the thousands, but the acceptance rate was not even a single-digit percentage.
The reason was clear.
MIT’s current undergraduate program had been designed with extraordinary care over the course of decades.
The basic science courses were arranged in a meticulous curriculum to serve as the foundation for later advanced majors and graduate study. Naturally, there was little room for a student from the outside to slip in midway.
For that reason, it was customary here for transfer admission to be permitted only in extremely limited cases.
The applicant had to be a researcher who had already proven themselves, or a student with potential equivalent to one.
“Oh, this student is remarkable.”
The admissions committee member flipping through Sujeong’s file paused.
He turned the pages back and read through the documents again. Without even glancing at her perfect GPA, he began carefully reading the research summary Sujeong had attached.
“An undergraduate was researching a topic like this?”
Number theory, graph theory, computational theory, and the combinatorial structures that bound them all into one.
Even taken separately, they were subjects at the graduate level, yet they were organically interwoven under a single line of inquiry.
Among the problems Theo had sent, there was one part that had kept nagging at Sujeong.
‘It feels connected to the computational theory Seoha used in the seminar room.’
In the process of compressing a graph’s local rules into an automaton, was transition of the number of states possible?
On the surface, it was a problem in computational theory, but she saw an entirely different direction.
‘Is this a coincidence? There’s no way.’
The period of state transitions, the exceptions that appeared only at certain lengths—Sujeong began gathering them all in one place.
When she replaced the graph’s local structure with integer sequences and expressed the transition rules as congruences, the patterns that had seemed irregular began to waver only at prime periods.
“It was worth clinging to number theory all this time.”
The number theory she had devoted herself to in order to help Seoha prove the Riemann Hypothesis was now becoming the force that sustained her own mathematics.
She decomposed the transitions using the Chinese Remainder Theorem (a theorem that allows several pairwise coprime conditions to be unified into one) and traced the growth rate of the number of states with Dirichlet generating functions.
Months of tedious research passed, and Sujeong gradually stopped showing up at school. She had no time to study again what she already knew.
Without knowing whether the sun was rising or setting, she counted coefficients of generating functions and redrew the boundaries of state spaces. Some days, she stood blankly before the blackboard all day without drinking even a sip of water.
‘I think I understand a little now. What you must have felt.’
She had a premonition that if she failed to complete this research, she would not be able to take even a single step forward as a mathematician.
And at last, one day, Sujeong discovered that there was a special rule among the coefficients that had been leaping about in disorder.
Her hand trembled as she wrote the proof on the blackboard.
「Q.E.D.」
“…I did it.”
A rush of exhilaration she had never experienced before flooded over her. This was an achievement she had reached from beginning to end by Sujeong’s strength alone.
Sujeong crouched down in the empty lecture room, hugging her knees, and sobbed.
[On Prime-Periodic Constraints Appearing in Local Automata on Planar Graphs]
The paper she published was not printed in a major academic journal, nor did it become a topic of public attention or gossip.
But for the mathematician Im Sujeong, it was the first moment she broke out of her shell and stepped into the world.
* * *
“Oh my! Sujeong, it’s been so long!”
“Hello, teacher.”
Sujeong passed by, bowing politely.
The hallway of the gifted high school she had returned to after two years was narrower than she remembered.
Sujeong stopped for a moment and looked up at the ceiling. The familiar fluorescent lights, the countless club and study group notices posted on the walls—none of it had changed from before.
The only thing that had changed was herself.
To enter the seminar room, a separate application process was required.
Though she was not quite on Seoha’s level, Sujeong too was a celebrity long remembered among the teachers and younger students. At Sujeong’s request that she needed mathematical inspiration, the principal granted her permission to enter without asking any particular questions.
‘Class ■■, Yu Seoha, completed the Four Color Theorem here.’
The notice posted beside the door told what had happened that day.
Rattle.
Sujeong opened the door without hesitation.
Step, step.
She set foot in the empty seminar room where no one was present.
The countless papers plastered over the walls, the equations and symbols filling the blackboard, the arrows and circles layered over one another in tangled masses.
“Phew.”
Sujeong let out a deep breath.
As if turning time backward, the sight carried her to a certain day in her high school years.
Even now, when she closed her eyes, what had happened that day came vividly to mind.
When she heard that something had happened to Seoha, she had immediately run to the seminar room. What she saw there was an enormous diagram that seemed to be alive and breathing.
She had thought she knew Seoha well, but that day, Seoha had the face of someone she had never seen before.
His fingertips were stained white with chalk dust.
The sight of him muttering something to himself as he wrote equations on the blackboard as if possessed overwhelmed her, and Sujeong could not bring herself to approach him.
‘What on earth is he doing?’
Sujeong desperately tried to understand the equations Seoha was writing.
She followed the flow of the formulas, traced the connections between the figures and arrows, and went over again and again in her head what the diagram meant. But back then, it was something she could not reach in the end.
‘What on earth is this?’
It was a language she had never learned.
The symbols were familiar, but not a single thing properly entered her eyes.
What Sujeong felt then was not something as one-dimensional as jealousy or a sense of defeat. It was despair surging up from somewhere far deeper, and without realizing it, she thought,
‘Ah! So this is all I amount to.’
Step, step.
Sujeong walked right up to the blackboard.
The curtain of formulas that, at the time, had blocked her approach like a solid barrier—Sujeong had come here today to dismantle it.
What happened that day had become an indelible brand on Sujeong. Herself, frightened and backing away before something she could not understand.
After looking over the blackboard for a long while, Sujeong found the point where Seoha’s proof began.
“So it’s here.”
Rattle.
She pulled over a chair and sat down, staring fixedly at that spot.
Sujeong’s eyes moved frantically as she followed the flow of the equations Seoha had written. Unlike back then, Seoha’s thoughts now seemed almost within her grasp.
‘Why were you in such a hurry?’
Unkind explanations, frequent leaps in logic.
Only then did Sujeong realize why she had been unable to understand it. Seoha had never intended to show this proof to anyone else. Since it only needed to be understood by him alone, there would have been no need to consider anyone else.
“You really are a bad kid.”
But now she could see it. She could see by what logic he had tried to solve the Four Color Theorem.
Around sunset, Sujeong looked at the blackboard one last time.
The place where Seoha’s proof had begun, and the place she had only now been able to reach.
Rustle.
She slowly rose from the chair.
Rattle.
After pushing the chair back to where it had been, she walked toward the door.
As she left the classroom, she glanced back over her shoulder. Then she gave a faint smile.
“Now I’ll go to that place.”
Today, in this place, she was finally able to graduate in the truest sense.
* * *
“Sri, what are you doing?”
The moment Seoha opened the door to the lab, he felt something was strange.
As if he had come in since dawn, Sri had taken out several boards and was continuing to organize something.
Seoha quickly scanned them.
‘Number theory?’
Congruences, prime factorization, period notation.
Lattices instead of curves, congruence constraints instead of variational conditions. It was not a field Sri usually dealt with.
“He got thoroughly beaten by an undergraduate yesterday. He asked about minimum-energy surfaces the way he usually does, but apparently that student approached it through number theory.”
Sri wore a gloomy expression.
“It’s because I wasted my time learning engineering. If I’d studied mathematics properly from undergrad…”
“Was it that shocking?”
He nodded.
It was not simply that his pride had been wounded. Sri had firmly believed that Seoha would be the last person younger than him he would ever learn from.
‘A minimum found through differentiation always has a way to escape. If you block it 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 could not understand her words all at once.
He nodded awkwardly, then went straight to the library.
‘Impressive.’
An insightful answer.
The more he chewed on it, the more things came to mind. In the end, only after staying up all night studying everything related to it was he able to fully understand what she had said.
“Why are there so many monstrous people among mathematicians?”
Sri’s shoulders slumped.
Knock, knock!
Someone knocked, then opened the lab door and came in.
“Excuse me.”
The eyes of all three people turned to the entrance at the same time.
Though her face had no makeup at all, her skin was exceptionally pale. Her eyes were clear, but there was a certain sharpness to her air.
Over a thin knit top, she wore a stylish oversized coat.
She did not look particularly dressed up, yet she was strangely eye-catching—a beauty.
“Noona Sujeong!”
Seoha sprang up from his chair in delight.
“Yeah, the person over there told me to come in today.”
With the tip of her chin, Sujeong pointed at the dejected Sri.
She thought,
‘Team Apex. Since they’re people working with Seoha, of course they must have something extraordinary about them.’
She had resolved herself.
At least one person.
She would prove that she was superior to at least one member of this team.
“Don’t you have something to say to me?”
Sujeong asked, looking at Theo.
“Hahaha!”
Theo set down the material he had been reading.
It was the paper recently published in a journal under Sujeong’s name.
The question he had thrown at her was one asking whether transition of a graph’s local states held under certain conditions. But Sujeong had not tested the possibilities by plugging in the conditions.
Instead, she had proved why, among countless cases, only transitions of this form survived to the end.
An overachievement that far exceeded the target.
Step, step.
Theo walked to one side of the lab and made a cup of coffee with the most expensive beans.
“Please, have a drink, lady.”
Sri hurried over and cleared the table.
Sujeong sat in the chair Theo held out for her, crossed one leg over the other, and lifted the coffee cup.
“Surprised?”
Having recovered her self-esteem, Sujeong had returned to her former self.
A proud and confident attitude.
“No.”
Seoha shook his head.
“I told you, didn’t I? Noona, you’re someone who’s going to become a great mathematician.”
Tears welled in Sujeong’s eyes.
“You believed in me?”
“I’ve never doubted it.”
Memories she had built up with Seoha surged into Sujeong’s mind like a raging tide.
The Seoul National University competition where she had first seen him, the IMO where they had gone together as Korea’s representatives. Back then, there had been nothing in the world to fear.
And the high school life they had spent together came back to her, scene by scene, like a panorama.
‘Thinking back, it was from the very beginning.’
The moment her heart was stolen by the beautiful proofs he unfolded, no path other than that of a mathematician had existed in Sujeong’s future.
Looking straight into Seoha’s eyes, Sujeong said,
“I am the mathematician Im Sujeong.
I want to join Team Apex.”
Seoha nodded briefly, as if it were only natural.
“It would be an honor.”