“Thirty minutes?”
Seoha looked startled.
Gyeoul smiled faintly, as if she had expected as much.
When Gyeoul had finished playing, what she had seen was Seoha with his eyes closed, absorbed in the music.
At first, she had felt a little proud that a classical music novice was listening to her performance so seriously.
But when he still hadn’t opened his eyes after five minutes, she began to worry.
Was he in pain somewhere? Or had her playing not been good enough, so that his “peace of mind” hadn’t fully settled?
That was when Seoha muttered in a low voice, barely audible.
“…Encode the boundaries. The transition rules are local… Four… Ducky, I think I figured it out.”
Sensing that something was unusual, Gyeoul approached Seoha and examined him closely.
Behind his closed eyelids, his eyes were constantly moving. His right hand seemed to be holding an invisible pen. It moved slightly, ceaselessly writing something in the air.
‘Image training?’
But why now?
Getting happy on her own, worrying on her own…
She suddenly felt like an idiot. But before that, another thought came to her.
She couldn’t understand what Seoha’s words meant, but perhaps this was an important moment for him.
Special inspiration did not always come.
Through music, she had experienced moments similar to this.
When she had briefly taken lessons from a famous German pianist, he had told her:
“The human brain can barely distinguish between actually playing and playing in one’s imagination.
Simply visualizing it in your head improves your skill. Not only do you come to understand the flow of the piece better, even the movement of your fingers improves. Of course, that’s when you focus as intensely as you would in a real performance.”
That was why she had watched over Seoha for thirty whole minutes.
“So, it looked like you were thinking about something. Did you get results?”
For some reason, Gyeoul felt as though even the energy to get angry had drained out of her.
‘This kid’s head must be completely filled with math right now.’
When a competition approached, she too thought of nothing but her performance. So although it felt like she was losing out somehow, she decided to forgive him generously.
“Yeah, I really got a huge result.”
Seoha showed his teeth and laughed brightly.
Gyeoul hesitated for a moment, then took something out of her bag.
“What’s this?”
A CD in a transparent case.
On the outside, handwritten words had been written in silver marker.
[STUDIO Moon, Han Gyeoul Private Session]
—Stabilization Track.
—For personal listening only. No external distribution.
“I’m going overseas next month because of a competition. I recorded it in case you might need it.”
Gyeoul had not forgotten that he had tried to record her performance.
Seoha took the CD, not knowing what to do. Then, as if he had made up his mind, he spoke.
“Han Gyeoul.”
“Yeah?”
“Today, I only caused you trouble. I’m really sorry.
There’s a problem I’ve been thinking about for over seven years. I really, truly want to solve it, but I always hit a wall, and it was painful. But today, thanks to you, the hardest part was resolved.”
Gyeoul’s eyes widened in surprise.
“Seven years? Then just how old were you when…”
“So what I want to say is… thank you, really. I’ll definitely repay this favor next time.”
A small arc formed on Gyeoul’s lips.
“All right. I don’t know what it is, but I hope you solve it soon.”
“Once I solve it, you can ask me for anything. If it’s something I can do, I’ll do my best to grant it.”
“Really? No taking it back?”
“Yeah.”
Gyeoul sent Seoha, who seemed to be in a hurry, off first.
Then she opened the piano cover and tried playing Debussy’s Clair de Lune again.
The moment she pressed the pedal halfway and sounded the first note, the tension in her stiff shoulders loosened. Earlier, even as she played, the frustration had not gone away, so what had changed?
Now she felt freer than ever.
* * *
Seoha’s steps toward the dormitory grew faster and faster.
The night air was pleasantly cool.
‘I need an environment.’
Seoha wanted to begin his research right this instant. But there were more than a few things that bothered him before he could do so.
First and foremost, he needed a space where no one would disturb him.
He intended to unleash Ducky on this research.
‘Home won’t work, and the dorm is even more difficult. If there’s a blackboard or a board, that would be perfect. I don’t know how many days it’ll take, so I need a place where I can wash up too. Most of all, it has to be a place no one comes to.’
The start had to be Friday afternoon.
It was the time when most students went home. He should be able to secure at least two and a half days until Monday.
If he happened to need more time, he could submit a sick leave request.
After returning to the dorm, he played the CD Gyeoul had given him.
Gyeoul’s performance flowed out softly.
‘A studio recording really is different.’
The sound quality was so good that he felt as though he could hear Gyeoul’s breathing between the passages.
When he closed his eyes, it fell far short of a live performance, but it definitely had some calming effect. In an emergency, it would be more than enough to serve as insurance.
Starting the next day, Seoha began searching for a location.
The first place he considered, a shared seminar room, was already booked.
The music room was excluded because there were many preparatory-course students nearby. The project room had expensive equipment, so it was locked at night.
‘Is school no good? Then let’s look outside.’
When he went to a study café in front of the school, he was told that one person could not enter alone because an accident might happen.
‘Another dead end today.’
Leaning back against his bed, Seoha put earphones in his ears.
Track 1 — Clair de Lune.
Seoha had come to like this piece.
It was a piece he had first heard through Gyeoul’s performance, but perhaps because it had given him inspiration, it felt new every time he listened to it. His breathing began to settle.
Then a place suddenly came to mind.
‘Ah! There’s the classroom Professor Kim Jiyun uses.’
That place was a dedicated seminar room for university advanced placement, so classes were only scheduled there on Tuesday and Thursday mornings. From Friday afternoon through the weekend, he should be able to use the whole thing. It was located at the far corner of the hallway, so almost no one passed by.
At the front was a huge blackboard, and there were two more movable whiteboards. The windows were narrow, and there were two layers of blinds, making it an optimal place to block outside gazes.
As befitted a research room, the preparation room in the back had running water. Washing up briefly should be possible there.
And the most important point was that it was a place Seoha could access.
Since he had an advanced placement student card, if he said he had a presentation to prepare for and wanted to study on his own, he could get permission from the management center.
Once the location was decided, his heart grew impatient.
‘Still, I should get the professor’s permission.’
Of course, he would not say that he planned to use it overnight. He only had to inform the management center of that.
The next day, Seoha contacted Professor Kim Jiyun and asked for help.
Surprisingly, when Seoha said he had something to research, she readily gave him permission to use the classroom over the weekend.
‘I might stop by later, you know?’
That remark bothered him, but the day she came to school was Tuesday.
Seoha was confident he could finish everything before then.
Now all that remained was supplies.
On Thursday afternoon, Seoha dragged the large suitcase he used when going home and headed to a large supermarket.
Unfortunately, there were no school meals on the weekend.
Seoha thought about what food he would need to survive for three days.
One pack of bottled water containing twenty 500 ml bottles, and some ion drinks as well so he wouldn’t lack sodium. When he saw dried jujubes, he thought of home. He picked up a bag along with mixed nuts.
He bought chocolate and biscuits that could be stored at room temperature, as well as several instant porridges. He also picked up a few energy bars and protein bars that people who worked out would probably like.
‘Is this enough?’
When he stood in front of the counter, the cashier saw his suitcase and smiled slightly.
“Are you going on a trip?”
Seoha smiled awkwardly and mumbled an evasive reply.
After finishing the payment and stepping outside, the suitcase was quite heavy.
Little smell, no dishes, plenty of nutrients.
‘Supplies complete!’
He had spent almost all his allowance, but he was satisfied.
He clenched his fist and made a small fighting pose.
For Seoha, who had almost no experience traveling, this was the best he could do.
* * *
Ding-dong-deng—
On Friday, the bell announcing the end of class rang.
The atmosphere in the classroom heated up at once.
“What are you doing this weekend?”
“I have a family gathering.”
“What about you?”
“Lucky. I have to do all the assignments I put off.”
The hallway was crowded with students going home.
Seoha waved goodbye to them, then headed to the management center.
The staff member on duty sitting at the desk stared at Seoha’s student ID, then checked the Post-it note attached to the front. Then he nodded.
“Please make sure to return it when you’re done using it.”
Seoha politely accepted the card key he handed over.
“Yes!”
The sun dipped between the buildings.
At the time when the students were leaving through the main gate, Seoha walked toward a different destination.
Beep—
When he held up the card key, the door opened smoothly.
Perhaps because it had not been used yesterday, a cool air lingered inside the classroom. Seoha first approached the windows and lowered all the blinds.
He rearranged the tables into a U-shape and set one chair in the center. Then he placed all the materials he had prepared on top.
He took out the books he had borrowed from the library one by one. And the last things remaining were more than one hundred notebooks.
Seoha stared at them quietly, then picked up the notebook at the very top.
Rustle.
When he turned the page, colored paper was pasted here and there. And formulas were written alongside them.
Thinking about it now, it was an absurd theory. An extremely one-dimensional theorem.
Back then, he had truly thought that this would make a proof possible.
[Four Color Theorem, I’ll prove it no matter what!]
Letters written in uneven handwriting.
It was probably from around when he was eight years old.
“Hooo.”
Seoha exhaled deeply.
At first, it had definitely been light curiosity.
When had the coloring game he had begun half as a joke turned into a goal he absolutely had to achieve?
Every time he hit a wall, notebooks piled up.
And with every failure, his own knowledge increased as well.
Slap—
Seoha struck his own cheeks with both hands.
‘Don’t get sentimental.’
Seoha divided the notebooks into three piles.
First were the materials to be discarded.
The one-dimensional ideas he had attempted in the beginning, like the area conservation hypothesis and the angle-sum matching trick, were of no help at all to the proof.
The second pile was on hold.
Ideas like adjacency indices and directional indices might perhaps have some use.
The third pile consisted of notebooks that could be actively utilized.
Boundary Pattern Dictionary (Draft), List of Local Rules, Research on Parity Invariants.
These were worth looking at again.
He took out chalk and organized them, then placed the two whiteboards to the left and right.
‘There’s enough paper too.’
Seeing the box filled with A3 paper put him at ease.
Once the seating was set up, he made a supply station in the corner.
Water bottles, paper cups, the CD player he had borrowed from the audiovisual room, and the food he had brought were taken out and placed on the table in order.
Finally, he sent a text home.
Miyeong was very disappointed by her son’s message saying that he would study at school this weekend, but since it had happened during exam periods before, she did not seem to pay too much attention to it.
Gulp.
Suddenly, nervousness washed over him.
‘What if it doesn’t go the way I imagined?’
Even so, it couldn’t be helped. Seoha intended to see this through to the end this weekend no matter what.
Seoha closed his eyes and concentrated his mind.
One minute, then two minutes passed.
At that moment, Seoha’s eyes flashed open.
“Ducky, let’s begin.”