“Excuse me!”
Theodore slid down the corridor at a run.
Each time he rounded a corner, his loose-fitting coat flapped like wings.
“Watch it!”
“Hey, don’t run!”
“What’s with that guy?”
Students hurriedly dodged out of the way, afraid he might crash into them.
[Let’s Do It Together, Blackboard Cleaning! - Today at 18:00! For everyone’s clean blackboards :)]
“Damn it.”
The smiley face on the poster seemed to be mocking him.
When he rounded the final corner, he saw students wearing green aprons. Whether the school had made them itself or not, the sight of them pushing out enormous industrial brushes while wearing masks that looked like oxygen respirators was terrifying.
They looked ready to erase everything without leaving a trace.
Rattle, rattle.
“Wait!”
Theo spread both arms and blocked their path.
“You can’t erase it right now! There’s an extremely important research sketch on the blackboard in that corridor.”
Apron A narrowed his eyes.
“I haven’t seen you before. Who are you?”
“Theodore Lanford, Stanford Department of Mathematics.”
“…I feel like I’ve heard that name somewhere.”
“If you study math, of course you have. Look it up later and be moved. For now, just wait ten minutes—no, twenty!”
Apron B shrugged.
“That’s difficult. If our schedule gets delayed, the next team has to wait too.”
At that moment, Theo’s patience hit rock bottom.
“Then wait!
Is you lot waiting ten or twenty minutes more important than an important proof in the history of mathematics disappearing?”
The students flinched at Theo’s outburst.
“No, that’s not what we meant…”
“All right. We’ll just rest here for a bit.”
Theo went to the department office and borrowed a high-resolution camera.
The equipment manager stubbornly insisted that they could not lend equipment to a student from another school, but after Theo persuaded him that he had to record Seoha’s notes, he finally handed over the expensive camera.
“Is it all done now?”
When he returned, Seoha was looking at the blackboard in the same pose as before.
As if he did not like the theorem he had just written down, he frowned, then continued writing equations again with a serious expression.
At the sight of his calm demeanor, Theo felt as if a fire were about to burst in his gut.
In the brief time he had been away, one whole section of the blackboard had already been covered in formulas.
Theo scanned the blackboard with his eyes.
Fortunately, it was something he had seen somewhere before.
“That theorem you’re writing right now…”
“Yes.”
Seoha answered without even turning around.
“It resembles an approach Smale once attempted.”
Smale was a mathematician who had received the Fields Medal.
Seeing a young mathematician develop logic similar to that of a giant of twentieth-century analysis, Theo felt complicated emotions.
“I don’t think this path is wrong.”
Contrary to how he looked, he had a stubborn streak.
Well, with a brain like that, it was only natural.
“Oh? Smale gave up in the end, you know. If the domain twists, the derivative vanishes.”
Theo casually gave him a hint.
The reason Smale had failed was because the space he had tried to handle was not completely homogeneous.
In a space where the domain was curved, a derivative could not express the rate of change.
Once curvature appeared, the tangent formula at each point went awry.
No matter how smoothly the function continued, the directions of those tangents were not consistent, so even if one tried to average the rate of change, vectors in different directions would intervene and cancel one another out.
For a moment, he felt puzzled. Could Seoha really not know something he knew?
‘He definitely knows…’
Seoha nodded and continued the proof. Then, as if it were nothing, he tossed out a single sentence.
“I plan to make the domain uncurved.”
For an instant, Theo wondered if he had heard wrong.
“What?”
“Not by unfolding the space, but by adjusting the density so that it appears flat. By changing the coordinate system itself.”
Theo felt as if his breath had stopped.
Adjusting the density of space meant redefining the measure itself of a topological space where curvature existed.
To make the curvature of a space flat, one had to assign different weights and deformation rates to every single point.
In other words, it meant rewriting the metric tensor—the mathematical tool that defines the distances and angles of a space—for every coordinate that composed the space.
If even a single point of error occurred in that process, the continuity of the entire function would collapse. Geometrically, that space would turn not into a surface, but into a torn cloth.
‘He’d have to use Riemannian geometry, calculus of variations, probability theory, measure theory, and topological invariants all at once.’
The process was so dizzying it made his head grow faint. Even if he spent his entire life on it, he had no confidence he could pull it off.
Seeing the boy carry it out as if it were nothing, Theo felt something close to fear.
‘Is this truly an ability permitted to human beings?’
There was always a valid reason why a difficult problem remained a difficult problem.
Every unsolved problem had one foot in a boundary region beyond the reach of human thought.
That was why, in essence, it rejected human approach—a place like a spiritual sanctuary, so to speak.
And yet the boy was now trying to go there. Without any preparation, he was about to walk in with muddy feet and trample the holy ground without hesitation.
“Is that really possible?”
Instead of answering, Seoha began writing new formulas on an empty blackboard.
From this point on, even Theo could not follow easily. But he had a feeling he knew what Seoha was trying to do.
“I just sketched it out for now, but I think it’ll roughly work.”
‘Sketched? That? He thinks it’ll roughly work?’
His mind felt as though it might overload trying to accept words that defied common sense.
But he had no time to be confused.
Rattle, rattle.
He heard the sound of wheels rolling toward them.
Apron A adjusted his mask and waved at Theo.
“Time’s up! We have to work now too. We’ve got a lot of assignments to do tonight!”
A few more people had joined them from behind.
Two enormous brushes entered the corridor side by side.
Seoha also looked at them and waved.
“Yes! I’ll erase it cleanly now!”
Seoha smiled innocently. Then he picked up an eraser and tried to erase the “sketch” he had just written.
At that moment, something in Theo’s head snapped with a ping.
“No!”
A roar that burst out like a Lion’s Roar thundered through the corridor.
Grab.
Theo reflexively seized Seoha’s wrist.
“What do you think you’re doing right now?”
“Shouldn’t I erase it? They must be busy too…”
Seoha pointed at the aprons.
“Do you know what you’re trying to erase right now?
It’s a problem Smale devoted his entire life to and still never saw through to the end. It’s a difficult problem that dozens, hundreds of mathematicians attacked and still couldn’t solve.
And now you’re going to erase it because it’s cleaning time?”
Seoha blinked.
“Uh… No, that’s not it. The contents are in my head anyway.”
“Do you remember every last detail? Can you really be sure that no information will be lost if you erase it?”
Overwhelmed by Theo’s force, Seoha unknowingly took a step back.
When Theo turned around, the students holding the brushes also swallowed hard.
But unlike what they expected, Theo smiled gently and took a credit card out of his wallet.
“Hey, friends. You’re working hard. Can I buy each of you a coffee?”
The volunteers’ faces brightened.
“Yes, thank you.”
“I was just desperately in need of caffeine. Perfect timing.”
“We’d be grateful if you did!”
Theo gave a faint smile and patted them on the shoulders.
“Go buy coffee and sandwiches for everyone. In the meantime, I’ll organize these with that guy. Once you’re done eating, you’ll be able to start work right away.”
Seoha was impressed by his skillful handling of the situation.
‘Oh! An adult.’
There was the composure of a mature member of society in Theo’s actions.
“…”
After they left, the corridor grew quiet.
Theo smoothly changed his expression and took out the camera. His hand trembled faintly as he removed the lens cap.
Click.
Theo began taking photographs.
He divided the blackboard vertically, assigned numbers, and photographed each section in sequence.
“The bottom right corner was the start.”
“Good.”
Click, click.
As he took pictures, Theo tried reconstructing Seoha’s logical development in his head.
After watching for hours, the flow naturally came into view. It was a theorem far more high-dimensional than he had expected.
“Here, you set the density as w(x), and the average rate of change… Ah! So that’s why you were trying to substitute it with a probability space and find a fixed point.”
Seoha nodded.
“Yes. I think a fixed point must exist. Though I don’t have a perfect proof yet.”
Click.
“Listen carefully. When you research something, you must leave records.
Memories are bound to fade, and an intuition that seems obvious may never return to you later.”
Click.
Perhaps because he was speaking from experience, his words were strangely persuasive.
“Gauss was reluctant to write papers. In the case of non-Euclidean geometry as well, he already knew the principles, but he never published them.
Thanks to that, just how many years was the development of geometry delayed?”
Theo could not bring himself to like people like Newton or Gauss.
Newton’s eccentricities were famous, but Gauss had not exactly been normal either. Of his research, even by the most generous estimate, only twenty percent had actually been published as papers. The rest vanished completely from the world with his death.
“Such irresponsible people.”
‘To waste a God-given mind like that.’
Whether Seoha knew Theo’s thoughts or not, he looked at him with a resolute expression and said,
“Yes! If I make an important discovery, I’ll be sure to present it to the academic world.”
‘What?’
Wasn’t that the same as saying he would just throw it away if it was not important?
Theo was convinced that Seoha had not understood what he meant. The way these people thought was something he, who belonged in the category of ordinary people, could never understand.
Seoha looked at the blackboard.
There was not a trace of doubt on his face as he stood before the theorem he had written.
Click.
Finally, Theo captured Seoha’s face in a photograph.
From the end of the corridor came the sound of the students laughing.
“The coffee’s here.”
“Bagels are all right too, aren’t they?”
While he was here, it seemed he would have to eat bagels often.
* * *
“Come in.”
Seoha guided Theo to his research room.
Because, as an outsider, Theo had nowhere to rest.
“This is a nice research room.”
Theo came in, looking around.
“They said I could use it only until the project ends, but the deputy director said it would take a few years.”
Thud.
Theo sank down onto the sofa.
He was tired.
It had truly been a long day.
“Would you like some cold water?”
As Theo looked around, his gaze stopped in one place.
Beside the trash can, several crumpled sheets of paper were sticking out.
“What’s this?”
Rustle.
[Dynamical Center of a Function]
Surprise flashed through Theo’s eyes.
This was a formula that defined the point where the second derivative was minimized—in other words, the place where a function changed in the most balanced way.
Seeing that, Seoha spoke as if making an excuse.
“Ah! That’s something I thought of while researching average points. I just tried it for fun.”
“Damn it…”
Theo clutched at his hair.
“This is an idea that could later be expanded all the way to the oscillatory stability of nonlinear functions. It’s the kind of problem physics would treat as important too.”
Why did God love such absentminded human beings so much?
He truly resented the heavens.