Translator: Dreamscribe
Anonymous Board,
[Duck Lord, are you going far away?]
-There are suddenly scary people wandering around the school. It seems our Duck Lord has accomplished something amazing, but what are we supposed to do now?
He’s not going to suddenly fly off to America or say, “I can’t play with you guys anymore because you’re not on my level!” and toddle off to college, right?
I’m just really worried. I’ve become someone who can’t live without the Duck Lord now.
└Ah... no!
└But thinking that our Duck Lord is being recognized makes me feel good, though.
└That’s true. If Duck Lord takes it on, even a coloring problem is nothing ㅋㅋㅋ
└What if Elijah Cronen suddenly cages Duck Lord and takes him away?
└Seeing our school on the news felt surreal for me too. Still, I had the thought, “Of course!” It feels like Duck Lord could do anything.
└What if he ends up solving all the Millennium Problems too?
└Then I’m going to brag to people ㅋㅋㅋㅋ that I went to the same school as Duck Lord.
└If that happens, wouldn’t he rise to the ranks of saints like Pythagoras?
└Don’t you think that’s a fitting place for Duck Lord? ㅋㅋㅋ
└Duck Lord, are you watching this? If so, wag your tail so we can see it!
***
[If I were to wake a thousand years from now, the first thing I would ask people is this:]
“Has the Riemann Hypothesis been proven?”
-David Hilbert, at the 1900 International Congress of Mathematicians in Paris.
I had a strange dream.
An old bald man I’d only seen in pictures appeared in my dream, grabbed me by the collar, and demanded to know what had happened with the Riemann Hypothesis.
David Hilbert, a German mathematician, presented 23 unsolved problems for 20th-century mathematicians to tackle at the conference held in Paris.
More than a hundred years have passed since then. Of the 23 problems, 13 have been solved, 7 have been partially resolved, and 3 remain unsolved to this day.
‘Why did Grandpa Hilbert grab me like that? Does the Riemann Hypothesis have some kind of lingering spirit attached to it?’
Perhaps the most famous problem in the history of humanity.
The greatest minds of the 20th century all tackled the Riemann Hypothesis.
But no one was able to break through that impregnable fortress.
Maybe that’s why Hilbert grabbed me by the collar in my dream?
“What the hell have you all been doing for 100 years? Why hasn’t it been proven yet?!”
The old man’s thunderous voice sounded like it was shouting right next to me.
Shiver-
My body felt chilly. I should probably take some of the herbal medicine Mom gave me.
I was discharged from the hospital after a week.
Before I returned to school, Mom looked at me with a firm expression and said,
“If something like this happens again, let’s just go back to Okcheon together. I’m not just saying this, so remember it well. I’ll drag you back if I have to.”
I felt ashamed. I didn’t want to make her worry...
I promised my mother that nothing like this would ever happen again.
Only after getting that promise from me several times did she return home with my younger sister.
Seeing Seo-eun’s eyes well up with tears, saying she was sad to be apart again, made my heart ache.
“Let’s play a lot together during vacation, oppa!”
We linked our pinky fingers and made a promise.
When I got back to the dorm, the building was empty.
‘Ah, it’s class time!’
Today was Thursday. I decided to rest two more days and start attending classes next week.
‘Hm?’
When I opened the door, I found a pile of cards stuffed under the door.
I opened them one by one, and they were all from people I knew.
[Seo-ha, come back soon so we can play soccer together!]
[It feels weird with the window seat on the third floor of the library empty. It’s like an NPC disappeared.]
[This is the newspaper club. Are you still not interested in an interview?]
[Hey! Don’t go too far. We have to at least see your back to follow you!]
[When you’re back, let’s meet at the music room.]
I felt a lump in my throat.
For a while, I kept them carefully tucked between the pages of a book.
‘Class probably isn’t over yet.’
With nothing to do, I trudged down the path toward the music room.
At the hospital, no one had given me a pen or notebook. Whether there was some agreement among the adults, they didn't even bring me books to read, so I had to frequent the children's library at the hospital.
That’s when I thought of the piano.
I asked for a sketchbook and drew keys on it that were the same size as real ones.
All that was left was to practice.
As I passed through the path and opened the door to the music room, a cool air and the scent of chalk rushed in.
Clack.
When the light was turned on, the piano sparkled like black waves.
I opened my bag and took out the sketchbook keyboard I had brought from the hospital.
Sitting on the hospital bed, I had practiced piano all day long using this paper keyboard.
Following the image in my head, I tapped the actual keys.
I lightly pressed the “C” key with my thumb.
Ding-
Left hand C-G, right hand E-D-C.
I repeated the movement I had practiced thousands of times on paper. It wasn’t easy at first, but I gradually got used to it. Reading the manual had also helped a lot.
Ducky had been quiet since that day.
But I knew he hadn’t disappeared. The hunger that had scratched at my nerves like fingernails on metal had merely been satisfied for a moment.
For now, it seemed I could go on without much difficulty.
[Theme of Duckie] was a melancholy piece.
Ducky especially liked piano sonatas, particularly the structure where the left hand laid down the same pattern in a low register during a slow movement, while the right hand gradually revived the melody little by little.
As the bass line descended one note at a time and paved the way, the melody added its tones later.
'A safe descent.'
That was how it felt.
Was that the kind of thought I had while sinking into my consciousness?
Then it rose violently in search of light.
“You’re pretty good at playing.”
When I turned my head, Gyeo-ul was there.
Unlike usual, she had her hair tied back in a ponytail and was wearing sneakers.
Her face was slightly flushed, as if she had been out of breath.
Gyeo-ul came in with a casual expression and placed her bag on the chair.
***
“I was passing by and heard the piano.”
She explained her reason first, as if offering an excuse.
Seo-ha decided to thank her first.
“The CD you gave me, it really helped a lot. I owe you for so many things. Is there any way I can repay you?”
Gyeo-ul glanced sideways at Seo-ha.
“That problem you said took seven years… you ended up solving it, right?
I’ll hold on to that favor for now. I think I’ll need it later. More than that, keep playing the piano.”
Gyeo-ul lightly pressed Seo-ha’s wrist and adjusted the angle.
Seo-ha took a breath and began playing [Theme of Duckie] again.
“It’s a piano sonata? Did you compose it yourself?”
“Yeah.”
“I like it. You once told me that people who are good at music often have a knack for math too, right? I think the reverse might be true as well. Your left and right hand separation is really good.”
To use both hands separately, the brain’s two hemispheres have to alternate sending signals to each other.
For Seo-ha, it was something that came naturally, like part of his daily life.
“Really?”
“Yeah, you’d be surprised how many people can’t do that. I don’t know much about math, but I like the piece you composed.”
“I didn’t expect that.”
Seo-ha had thought the piece Ducky composed was too dark and static.
“The musical theme is clear. Your left hand keeps striking steadily like a clock, and the melody changes little by little over it. This method of laying variations over an ostinato (*a repeated bass line) is from the Passacaglia or Chaconne family of the Baroque. It’s kind of like Bach.”
Seo-ha stared blankly at Gyeo-ul. That was exactly what Ducky had referenced.
"It's amazing that you can tell just from listening."
Seo-ha sincerely admired her. Gyeo-ul seemed pleased with the expression on his face.
“But the harmony also has a Romantic feel. This is interesting in a lot of ways.”
When Seo-ha turned his head toward her, Gyeo-ul quickly straightened up. Since she was helping from behind the keyboard, the two had gotten a bit too close.
“Alright! Let’s try again. It’s not finished yet, right? When the piece is complete, make sure you tell me. I want to try playing it.”
Gyeo-ul glanced at her watch.
The minute hand had already passed the reserved practice time.
But since what she was doing now wasn’t much different from practice anyway, she figured it didn’t matter.
***
Advanced Mathematics Institute, 3rd Floor Meeting Room,
Seo-ha received a phone call early in the morning. It was a polite request for him to come in for some inquiries.
‘Do they have questions about the verification?’
As he sat in a chair and waited for a bit, Elijah Cronen personally opened the door and entered. He was holding two large mugs with steam rising from them.
Clack.
“Cocoa okay with you?”
“Yes!”
When Seo-ha came face to face with someone he had only seen in academic papers, he couldn't help but feel nervous.
He had heard the man was incredibly intimidating, but he maintained a gentle expression throughout and asked about trivial things.
Questions like what subjects he studied at school, how he learned math when he was young, whether he had any friends.
In the end, unable to hold it in any longer, Seo-ha spoke first.
"Um.... Didn't you want to ask about the proof?"
Cronen laughed loudly.
“Hahaha!”
Seo-ha didn’t know what kind of expression he should be making in front of him.
“You and I both know that proof is complete. So is there any need to waste more time?”
“Huh?”
“Competent colleagues will handle the verification. Today, I simply wanted to meet a promising young mathematician.”
Cronen changed his expression and looked at Seo-ha.
“But you, you read my paper, didn’t you? I saw how you used Fourier transforms to suppress the oscillation of the zeta function.”
Seo-ha’s eyes widened.
“Yes! That’s right. Originally, I was completely stuck on how to deal with the diverging tail in the limit interval, but when I applied that transform, all the noise cleared up. It was a brilliant idea!”
Seo-ha’s eyes sparkled like a child’s as he spoke about math.
Cronen’s lips curled into a smile.
“You think so too, huh?”
In proving the Four Color Theorem, Seo-ha had used various theories, and among them, Cronen’s “oscillation-suppression transform” played a crucial role.
Cronen spoke at length with Seo-ha about how he came up with that theory. He also talked about several research topics he was currently working on, almost as if boasting.
It was a delightful conversation.
Seo-ha had never met someone he connected with so well.
“So, what do you plan to do next?”
Cronen had been worried that Seo-ha might, like Perelman, lose all motivation for research after solving a major problem. That was why he had arranged this meeting, but fortunately, his concerns were unfounded.
He could see it in the boy’s face.
The face of a mathematician itching to start new research right away.
“I still have a lot to learn. Taking on something like a Millennium Problem right now would be arrogance.”
Cronen interpreted Seo-ha’s words differently.
‘If I had the time, I could solve it anytime.’
“But still, there must be a problem you want to tackle, right?”
He was curious.
What problem this boy had in mind. If it overlapped with his own, he might need to offer some advice.
“If I had to say... I’m interested in the Riemann Hypothesis.”
“Hmmm.”
A low sound came from Cronen.
‘So he’s more status-driven than he looks?’
The Riemann Hypothesis is, quite literally, a mathematician shredder.
However, solving it would bring honor that no one else in the world could match. Cronen considered it a perfectly understandable choice.
“Why?”
Seo-ha hesitated and then replied in a trailing voice.
“To be honest, I’ve been interested in prime numbers for a long time. So I tried solving Goldbach’s Conjecture on my own. But I came to the conclusion that, in its current form, it’s absolutely unsolvable.”
“What?”
Cronen was taken aback.
[2+2=4, 3+3=6, 3+5=8....]
Like this, “Every even number greater than 2 can be expressed as the sum of two prime numbers.” That’s Goldbach’s Conjecture, simple, yet one of the most difficult problems to prove.
“To prove that, we’d have to rewrite number theory from scratch.”
It would require an entirely new framework, enough to rewrite all the math textbooks.
“So...”
“Ah!”
Cronen exclaimed, as if he finally understood.
“You cheeky brat!
You’re thinking that the Riemann Hypothesis is much easier than Goldbach’s Conjecture, aren’t you? You’re planning to use the Riemann Hypothesis as a hint to ultimately prove Goldbach’s Conjecture.”
The Riemann Hypothesis is deeply related to the distribution of prime numbers.
Therefore, if one could solve this, it would provide an incredibly powerful hint for proving Goldbach’s Conjecture.
The Riemann Hypothesis, which had frustrated more mathematicians than any other in history, was being treated by this boy as little more than a stepping stone toward his real goal.
Seo-ha’s face turned red.
“Well… it’s just that, the Riemann Hypothesis has been studied a lot already…”
Given how many mathematicians had attempted it, there was also a vast amount of accumulated material.
With tens of thousands of papers related to the Riemann Hypothesis, Seo-ha believed there had to be a clue somewhere among them.
“What else?”
“I just… have a feeling I can solve it.”
“A feeling.”
An intuition that only the truly gifted can understand.
Tap, tap.
Cronen tapped the table with his fingers.
“That’s the most essential inspiration in mathematics. But it can also be dangerous.”
“I heard you're also tackling a Millennium Problem, Professor.”
“Why, are you curious?”
Cronen looked at Seo-ha and grinned.
“A little.”
“Promise to come to Princeton, and I’ll tell you. The entire status of the project. Just so you know, we're already pretty close.”
“Then never mind.”
Seo-ha shook his head with a disappointed expression.
For the first time in his life, Cronen had failed to recruit a student.
“Hey, boy!”
As Seo-ha stood up to leave, Cronen stopped him.
“Yes?”
“Listen carefully. If you’re seriously thinking about tackling a Millennium Problem, it’d be wise to form a team later on.
Solving a major problem is like sailing a boat across the vast ocean in search of a single island. But the captain can’t be the one raising the sail and rowing at the same time, right?”
Seo-ha paused for a moment and considered his words. Then he nodded.
“Thank you.”
Seo-ha gave a polite bow and left the meeting room.
‘Teammates…’
It was the second time he had heard someone say that.
As he thought about who would be good, one name came to mind. Though that would be far off in the future.