“BLT sandwich and one coffee.”
Megan handed over the bag with a bright smile.
The student took the food, murmured thanks, and hurried away.
The cafeteria was busiest before morning classes began. To shake off the last of their sleep, math students stood in line with books tucked under their arms.
‘They must be from robotics.’
A group of students were carrying heavy tool bags.
By the window, Indian students were revising code while looking at their laptop screens, and in a corner seat, doctoral students who looked Eastern European were engaged in a heated debate over some problem.
Megan liked this kind of scene.
Unlike Harvard Square or the cafés downtown, this place was neither noisy nor artificially dressed up in glamour. It was always filled with the energy these people gave off.
Beep—
When she pressed the machine’s button, the rich scent of coffee came pouring out.
Drip, drip.
Megan’s taste in men had always been nerds.
The bird’s-nest hair of math majors, computer science students so lost in coding that they dropped USB drives into their coffee cups, the dweeby but somehow very strictly observed dress code that belonged only to them.
All of those things were incredibly attractive to Megan.
And MIT was truly a place worthy of being called the holy land of nerds. To be able to observe all kinds of nerds from around the world and even get paid for it was a blessing to her.
“Megan, two lattes!”
Her coworker shouted from behind the counter.
“Got it!”
Even as she moved her hands busily, she did not lose her smile.
She checked the order slip and wrote names on the cups.
And among the dozens of names, there was one person she considered the most special.
[Yoo, Seoha]
He always came at the same time and ordered the same thing.
“One everything bagel and a chai latte, please.”
Megan glanced at Seoha out of the corner of her eye.
‘When did he get so tall?’
When he first enrolled, he had simply seemed like a cute younger brother, but before she knew it, he had shot up in height.
‘Mm, still the best!’
Instead of a heavy jumper, he always wore a neat shirt. His shoulders still seemed not quite fully grown, yet his back was held straight.
When he stood there holding his books, he looked as if an illustration from a novel had walked into reality.
“Yes! I’ll make it extra delicious for you today too.”
For the boy who served as the vitamin in her day, Megan poured her heart and soul into making his bagel every single day.
‘He looks good today too.’
The forehead that showed when he sometimes swept back his hair, and his glossy black hair faintly lit by the sunlight, looked especially luxuriant today.
He was tall for his age, with long, slender arms and legs. His skin was pale enough to seem almost bloodless, and when he spoke, he always looked the other person straight in the eye.
A precarious charm somewhere between boy and young man, the unique freshness created by that immature atmosphere, made Megan’s heart flutter.
When he looked at her and smiled shyly, Megan felt as if she could forgive the boss even if she did not receive her day’s wages.
Of course, everyone who worked here knew that he was strictly for looking at.
“Hi, Megan. Bagel and coffee for me too.”
Megan’s mood plummeted sharply.
Recently, a strange dung fly had been clinging to Seoha’s side. Stylish clothes that were not at all nerd-like, and a sly smile.
Theo looked at her and waved.
Megan forced herself to smile as if nothing was wrong.
“Good morning.”
He said, looking at Seoha.
“I’ll pay today. I slept well thanks to you. Saved on lodging too.”
Megan’s hand, which had been brewing coffee, flinched.
‘What exactly is their relationship?’
“You don’t have to go that far.”
Seoha said, but Theo pretended not to hear.
He looked at Megan mischievously and winked.
Soon after, the two took seats at a table and began debating.
The man she had thought was a slick womanizer was conversing with Seoha with a serious expression.
Pretending to wipe coffee cups, Megan secretly stole glances at the two of them.
Mathematicians had an aura unique to them. An exclusive yet intellectual air that did not allow others to approach.
“Megan, two espressos!”
Her coworker’s shout brought her back to herself.
“Yes! Coming now.”
She always did her best at work. After all, it would break her heart to be fired from this perfect workplace.
* * *
Theodore’s belongings in the lab had increased.
When he first came here, he had brought only a single laptop, but after stopping by Walmart, he had swept up disposable daily necessities.
Once he even bought changes of clothes, he was at the point where he needed a large suitcase.
When Seoha looked at it with an appalled expression, Theo gave a faint laugh.
“Don’t worry. Starting today, I’m thinking of looking for an inn.”
“Do you have no intention of going back?”
Theo shook his head.
“I want to see the Smale problem solved before I go. And I’m suspicious whether you’ll properly publish the paper.”
Seoha, stung, turned his head away.
Theo had printed the photos he had taken with his camera in A4 size. He attached the photos to the wall in order.
“Don’t mind me. Do what you have to do.”
“Yes, thank you.”
Seoha bowed his head despite himself.
‘Thank you? For what? Why is that person so concerned about me?’
Question marks drifted through his head.
But they were soon erased from his thoughts. There was a problem before his eyes that needed solving.
Seoha continued the proof he had yet to finish on one side of the blackboard.
Scratch, scratch.
The sound of chalk cutting across the blackboard came in a regular rhythm.
When the sound seemed to stop for a moment, Theo looked back and saw Seoha drawing something in the air. Soon, he nodded and began drawing a curve on the blackboard. His hand moved smoothly along an invisible trajectory.
‘Is he seeing a space made of formulas?’
Theo felt an impulse to see the world through his eyes, even if only for a moment.
“To make the curvature zero...”
He muttered.
“If I fold the domain once more at this part, I think the balance of density will be maintained.”
As if conversing with someone, Seoha talked to himself while moving the chalk.
The formulas on the blackboard had, before long, gone beyond the scope of Theo’s understanding. He now found it exhausting to follow Seoha’s chalk.
‘Incredible concentration.’
As if cut off from the world, Seoha was completely immersed in his own.
Sweat ran down from his forehead. But he paid it no mind.
Every time he finished one formula, he nodded briefly, then immediately poured out an entirely new development.
‘Is this a development he planned in advance?’
Theo shook his head.
It could not be. The human brain did not function that way.
He was probably flowing in the direction his intuition led him.
‘There’s no plan, yet it’s perfect. How on earth is this possible?’
His mind was in turmoil.
He decided he would no longer try to understand Seoha.
The theorem that had begun on one side had, before long, covered two entire walls.
Theo moved the photos aside so as not to disturb him and began writing the draft of the paper.
[On the Smale Mean Value Conjecture in Non-Uniform Measure Spaces]
It was Theo’s first time writing someone else’s paper for them.
But if he left Seoha alone, he felt as though the artistic process of derivation he had witnessed would be lost.
Theo opened a thick notebook beside the monitor.
Some of the formulas Seoha had left behind were unrelated to the Smale problem. They were merely fragments of thought that seemed to have been written down in passing. Yet deep insight was contained within them.
Theo carefully classified those formulas and copied them into the notebook.
“To think I’d be getting help like this.”
He muttered.
As he dug into the parts of Seoha’s notes he could not understand, he found things he himself had missed while writing his master’s thesis.
There was something about Seoha’s way of thinking that deviated from the trajectory of human logic.
“This is seriously insane...”
In mathematics, a definition was a device meant to clarify limits.
But Seoha freely changed those limits according to his own needs.
Suddenly, a chilling thought came to him.
‘Don’t tell me he sets the result first and then creates definitions to fit it?’
Theo’s thought was half correct.
Only an extremely small number among mathematicians possessed this ability.
People who could see the shape and form of a function without going through calculation. Thus, Seoha’s thoughts flowed faster than logic.
‘Seeing it in person, he really is an absurd monster. Does that kid even know he possesses a privilege only a handful of people in history have ever enjoyed?’
Seoha’s solution continued until evening.
As he was writing a formula, he turned around.
“It’s time to have dinner at home. Theo, would you like to come with me?”
Theo was inwardly flustered by the sudden dinner invitation.
“I’m fine.”
A warm dinner table, a familial and cheerful atmosphere—these were all things Theo detested.
Seoha nodded, then packed his bag and left.
In the empty lab, Theo organized Seoha’s notes all night long.
And he wrote the unfinished draft of the paper.
Clack, clack.
When he entered his cheap inn room and lay down, a terrible fatigue swept over him.
But his mind was clearer than it had ever been in the past.
‘I’ve grasped the clue to my master’s thesis.’
For the next few days, similar days continued.
After Seoha finished his classes, he returned to the lab and vomited the thoughts in his head onto the blackboard. Theo chewed over each one and organized them.
It was around the one-week mark that he sensed something unusual.
Seoha’s condition was different from before.
A subtly excited air, his face flushed, his heart rate seemingly high. An inexplicable force emanated from him. It was like the gaze of a hunter going out to hunt a difficult problem.
Click.
Seoha pressed the button on the CD player on the desk.
Gentle music rang out.
A melody Theo felt he had heard somewhere before. To the mournful piano performance, Seoha steadied his breathing, then looked at Theo.
“Today, if possible, I’m planning to finish the proof of the Smale problem. It may run late, so why don’t you go back first?”
“If that’s the case, all the more reason I can’t miss it. Would my being here get in the way?”
Seoha thought for a moment, then shook his head.
“I think Theodore will be all right. You’re a fellow mathematician, and... I can’t be alone forever. And things have been much better lately too.”
“Hm?”
Clatter.
He poured the contents of his bag onto the desk.
They were calorie supplements, snacks like energy bars.
“Theo’s organization helped me a great deal.
Reading it made the path I need to take look much clearer. So later, if there’s ever anything you need from me, please call me anytime.”
Before Theo could answer, Seoha stood in front of the blackboard.
Then he began moving the chalk at a speed Theo had never seen before.
Ssssh—
Scratch, scratch.
First, he broke the space into a local coordinate system, then defined the density for each coordinate.
Where the boundaries overlapped, he wrote continuity conditions and added balancing equations so that they would cancel each other out.
‘Ah! He finished the flattening.’
Theo could feel it instinctively.
As Seoha wrote the formulas, the curve converged into a line. Then the corrected differential term showed itself.
He held his breath.
An endless sequence of theorems. Over the course of several hours, dozens of lemmas piled up as if by silent agreement. What was astounding was that even without explanation, the flow could be read.
“You look like you need hydration.”
“Thank you.”
Whenever the flow broke, Theo handed Seoha water or snacks.
“Sit down and take deep breaths. Your breathing is a little rough right now.”
“Is it?”
The boy’s superhuman concentration clearly had poor fuel efficiency.
Seoha was tiring faster than usual.
Theo observed him carefully and managed his condition.
Seoha got up again and finished the remaining lemmas.
As he organized Seoha’s notes, Theo had, before he knew it, become an expert in this field.
Among the countless theorems Seoha wrote on the blackboard, there was not a single line of formula that required elaboration. Only the theorems that had to be where they were needed piled up one by one. And at some point, the formulas on the blackboard intertwined with one another, drawing out an immense pattern.
He sensed that the time had come.
‘He’s going. Now he’s going to find the mean point.’
Theo clenched his fist tightly.
Seoha picked up speed. The flow of formulas was no longer linear. All the theorems were converging into a single point.
And the place all of this was heading toward was the center of the curve in the left corner of the blackboard.
Tap.
Seoha brought the chalk to that spot.
“I found it.”
Seoha’s bright smile, one Theo had never seen before.
“...It was perfect.”
It was an achingly beautiful proof.
For reasons he could not explain, tears flowed down Theo’s cheeks.
The point where the curvature fell to zero, the sole moment when density and domain achieved perfect equilibrium.
In the end, he had found the mean value in a non-uniform measure space.