Sujeong rarely goes home these days.
She spends most of her time in the lab and lecture halls, and what time remains she often passes sitting in the library or a café.
Today was another one of those ordinary days.
A café overlooking the Charles River.
Sujeong sat in a corner seat, looking down at her notebook.
The sight of a beautiful Asian girl lost in thought, her silky, fine hair falling over her shoulders, drew the eyes of the people around her.
Stage Two,
Causal Inference.
The patterns were already sufficient.
At which intersections accidents occurred, during what time periods delays surged, which variables moved along with them. Statistics did not lie.
The problem came after that.
Why?
Sujeong spun her pen in a circle, then stopped.
There was a wide gap between correlation and causation. Especially in a system on the scale of a city. Rarely did a single cause correspond neatly to a single effect.
And it was not a change that appeared gradually, either. In most cases, its nature changed all at once.
“Stepwise.”
Sujeong left a small note on one side of her notebook.
Nothing happens up to a certain point, and then, the moment a single condition is met, the entire system changes.
A signal difference of mere seconds, a dispatch delay of just one minute, one hour of daylight saving time.
Those trivial differences overlap, and at some point push the city into an entirely different phase.
“This is troublesome. Can I really get it done by this weekend?”
She had boasted for no reason that she would have it ready by the next meeting.
Sujeong lifted her head and stretched.
Her body, stiff from sitting so long, loosened with a series of cracks.
There’s no answer to this with differentiation.
Only now did she understand why Seoha had chosen this method.
There was no way to express this with a continuous function.
The form of the city as revealed by numbers was a gigantic staircase structure, cut apart by laws, rules, standards, and thresholds.
Still, it’s worth trying.
No matter how complex it was, she felt certain that if she grasped the structure properly, she would be able to reach the answer.
Sujeong closed her eyes and tried to organize the thoughts she had had so far.
“Excuse me, are you a math major?”
At the unfamiliar voice that suddenly reached her, Sujeong turned her head.
Brown curly hair and gold-rimmed glasses. He was a man with an intelligent impression. As if to show off that he was a Harvard student, bright crimson badges were attached to his notebook and bag.
Sujeong nodded.
“Yes, I’m studying mathematics.”
He smiled brightly.
“What a coincidence. I’m a math major too. It looks like you’re having trouble with an assignment. Would it be all right if I helped?”
Sujeong looked straight at him.
Tall, with a handsome face. Confidence could be felt in his gestures and tone. He probably had not even considered the possibility that he might be rejected.
“There’s no need.”
Perhaps finding rejection refreshing, he showed even more interest in Sujeong.
He glanced at the watch on his wrist and said,
“Then let’s do this. It happens to be dinnertime. You come out with me now, and we have dinner together. While we’re at it, we can discuss the assignment you’re working on. It’ll certainly be better than studying alone.”
“Or…”
“Or?”
“Is it an assignment with a deadline?”
“Yes.”
“If it isn’t rude, I’ll solve it for you right here. You only have to give me as much time as you save.”
Though it did not have a particularly strong science-and-engineering image, Harvard’s mathematics department was among the very best in the world.
If MIT was strong in application, she had heard that Harvard valued theory and philosophical depth. When Sujeong showed interest, the man took it as a sign of agreement.
“May I see the problem?”
He strode over and sat in the chair across from her.
A wicked thought crept up in Sujeong’s mind.
What kind of face would he make if he cried? If I gave him a problem he couldn’t even touch, would he get embarrassed and run away first?
Normally, she would have laughed off such an incident, but several days of sleep deprivation had summoned the version of her from the days when she had been infamous as the Demon King.
Back then, trampling boys who got cocky with her under mathematics had been part of her daily routine.
Good thoughts. Good thoughts.
Sujeong shook her head and brushed off the temptation.
“Thank you for the offer, but I’ll decline that too. An assignment only has meaning if you solve it yourself.”
Screech.
When Sujeong pushed back her chair and stood, he looked impressed.
“Are you an MIT student?”
“Yes.”
“I thought so. My name is Ted. I feel like we’ll be seeing each other again soon.”
“Sujeong.”
She gave her name briefly, gathered her bag, and walked out.
She was praising herself for holding back so well when a remark from behind grated on her nerves.
“How about taking my phone number? Are you really sure you don’t need my help?”
That smug expression.
The patience she had barely been holding on to finally snapped.
Sujeong strode back and sat down in front of him. Ted’s face was full of expectation.
“I can’t show you my assignment. It’s under a confidentiality agreement, so don’t misunderstand.”
Doubt appeared on his face.
“A confidentiality agreement?”
“Ted, if you’re a mathematician too, you must remember at least a few problems you really suffered over solving. Right?”
“Of course. There’s one I solved a few days ago. It was really difficult, but I managed it in the end. It took me a whole week, though.”
“Give me that problem now.”
“What?”
“Hurry. If I can’t solve it, then whether it’s dinner or a date, I’ll do whatever you want.”
Ted gulped.
“You promised?”
He took a notebook out of his bag and began writing the problem.
Ted laughed quietly to himself.
To think she would react like this to a casual joke. It was a charm he had never seen in other women.
Scratch, scratch.
What he wrote down was a matrix problem.
A considerably high-level problem that asked about diagonalization, spectrum, and iterative operations all at once.
I suppose this is the level of an ordinary undergraduate.
If it had been her right after entering university, she might have struggled quite a bit. But now, not a chance. Did this person know that setting a problem revealed one’s level far more nakedly than solving it did?
Sujeong picked up her pen and wrote down the formula in one breath.
He looked horrified.
“I’m done. There’s no need to check. I know it’s right anyway.”
Less than five minutes later, Sujeong set down her pen.
“Ah…”
He could not continue, his mouth hanging open.
“Did you want to win my respect through mathematics? I won’t deny it. I like people who are good at mathematics. Unfortunately, that doesn’t seem to be you.”
He stared hard at Sujeong’s face.
“…Now I remember. Logia Ranker Im Sujeong. A member of the MIT team that proved Minimum Energy Theory.”
This was Cambridge.
Turn your head, and you could see Harvard and MIT students everywhere. Most of them wore the same confident look as Ted.
They considered themselves special, and were restless for an opportunity to prove it.
Just like…
Like me before I met Seoha.
Sujeong decided to give him sincere advice.
“I know one extraordinary genius.
When I’m beside that person, I feel as if I’m nothing at all. The knowledge I’ve built up through a lifetime of effort collapses from just one question he tosses out. At times like that, I still get so frustrated I cry, you know?
But at the same time, I grow greedy. I want to see the world he sees together with him. This may be a little different from the desire to become good at mathematics. Because what I mean is that I want to become part of that lofty, fierce world he loves.”
Ted stared blankly at Sujeong.
“One thing is clear to me now.”
“I’m glad.”
Had her feelings gotten through?
Sujeong nodded with a satisfied face. Above the sky there was another sky, and mathematics was the most elegant language for interpreting this world. So do not get distracted and work hard.
This was the advice she had wanted to give to her childhood self, and it would surely help Ted as well.
But what came out of his mouth was something she had not expected at all.
“I meant that I clearly understand I’ve been rejected. Who on earth is this enviable man?”
Sujeong’s face flared bright red.
“No, that’s not what I meant!”
Sujeong waved her hands in denial and tried to hide her fluster, but she could not conceal her face, which had turned as red as a ripe apple.
“Anyway, don’t forget what I said!”
Sujeong fled the café as if running away.
The night wind blew in from the river. The cold air seemed to cool the heat in her face.
Was I thinking that?
When she had first met him, he had been an insurmountable wall to Sujeong. After that, he had become her most reliable colleague, and at the same time, the ideal she wanted to resemble.
Since when, exactly?
She looked back on what she had said to Ted.
And she could not hide her shock.
Because she had ended up confessing that all the efforts she had made until now were ultimately a means of reaching him.
The moment she saw Gyeoul’s name appear on Seoha’s phone screen, her chest had throbbed painfully.
Sujeong shook her head hard.
“That doesn’t matter. Causal inference first!”
She thought that if she became an irreplaceable resource to him, everything would be solved.
Because then, in any case, they would spend their lives together.
Her head spun.
Sujeong walked quickly down the nighttime street. Equations mixed together in her mind and whirled like a storm.
Step structure, discontinuity.
As she breathed in the cold air, the tangled thread seemed to unravel all at once.
She could think of the city as gears. Multiple small cogwheels turning, ultimately moving a large gear. And the moment that gear moved one notch, all the gears connected to it changed phase simultaneously.
“I found it.”
A smile spread across Sujeong’s lips.
The several days of sleep deprivation, and even the absurd incident with the man named Ted, all evaporated from her mind.
Only one goal, the desire to solve the problem Seoha had given her, ruled her thoughts.
Sujeong ran.
It was the first time she had ever felt such a powerful urge to solve a problem.
Bang—
When she roughly opened the lab door and entered, the familiar scent of coffee and paper reached her. And, as always, Seoha was standing in front of the blackboard.
Without even turning his head, he continued writing dense equations across the board.
Sujeong caught her breath and approached his back. Seoha flinched and stopped his hand.
“What brings you here at this hour?”
The same indifferent voice as usual. But Sujeong knew. Within that indifference were trust and expectation toward her.
“I found a way.”
Without even thinking to put down her bag, Sujeong picked up a piece of chalk. And she began writing equations several times faster than she had when solving Ted’s problem.
“We divide the state space, then substitute the Probabilistic Transition at each stratum into the threshold function.”
Scratch, scratch.
The sound of Sujeong’s chalk echoed through the quiet lab.
Seoha watched her back in silence with an intrigued expression. Logic extending without hesitation, a development that felt refreshingly clear.
After being absorbed for a long while, Sujeong put a period on the equation and turned around.
“Hah, hah.”
She was breathing hard.
As if trying to read his reaction, Sujeong observed Seoha’s face.
“How is it?”
Seoha’s stiff expression slowly loosened. And at last, he smiled brightly.
“It’s absolutely excellent.”
Sujeong felt as though all her efforts until now had been rewarded.