The Paper Factory
The cramped astronomy lab was packed with unexpected guests.
Four mathematics professors sat in front of the electronic whiteboard, scribbling in their respective notebooks, while the head of the mathematics department stood behind them, busily plugging in equations.
"There is absolutely no error in the Fourier series expansion method."
Professor Jeong, who specialized in nonlinear dynamics, swallowed hard and pushed up his glasses. His voice cracked slightly with excitement.
"It's magnificent. To bypass the Small Denominator Problem—where the denominator converges to zero when orbital frequencies overlap in the Many-Body Problem—in this manner!"
"It wasn't bypassed, Professor Jeong."
Professor Choi, an authority on topology, tapped his notebook with a pen and cut Professor Jeong off. The tips of his fingers were trembling slightly.
"Look at this inequality. It's not a bypass; they completely blocked the divergent orbits from the start using the Diophantine condition! They cut out all the exploding orbits, left only the converging ones, and bound them within a perfect topological torus. This is a flawless geometric design!"
"Indeed. I agree."
The head of the mathematics department, who had been staring blankly at the equations behind them, chimed in with a heavy voice.
"Instead of just mindlessly throwing variables at it, they controlled the orbital perturbations with a perturbation function and proved through pure mathematics that it will never collapse. If we can build a formal proof around this framework, it can be considered a perfect analytical solution."
Gasps of sheer astonishment repeatedly escaped the mathematics professors inside the cramped astronomy lab.
Even for men who had dedicated their entire lives to mathematics, they had never witnessed such creative and elegant intuition.
The professors compared their notebooks, exchanging excited opinions for a long while.
Finally, having reached a conclusion, the head of the mathematics department approached Dean Gu Byung-ook.
"Though it hasn't been fully polished into a theorem, the logical direction is absolutely correct. I believe we can proceed, Dean."
Dean Gu Byung-ook, who hadn't been able to tear his eyes away from the electronic whiteboard, slowly turned his head.
Sitting on the sofa with a smug expression, Chul-jun met his gaze, his round eyes curving into crescent moons as he grinned broadly.
Dean Gu Byung-ook nodded and spoke.
"Right, everyone, gather as many capable graduate students as you can."
"Yes, Dean!"
"You all need to roll up your sleeves too."
"Yes, sir!"
Gu Byung-ook frowned slightly and looked at the head of the mathematics department.
"Are the physics professors still not here?"
"They should be here any minute."
Hamiltonian mechanics was, at its core, classical mechanics—the deepest root of physics.
Even if the mathematical proof was flawless, they had to verify whether it violated any actual laws of physics.
They needed to ensure that the basic orbital model and interplanetary interference energy established by Chul-jun did not contradict the gravitational constant, mass, or the law of conservation of momentum in the real universe. Furthermore, if the dynamic equilibrium in phase space was certain, they had to check if it could later be expanded into a universal law.
Just then, the door burst open.
Everyone turned their heads, expecting the physics professors, but...
"Sigh... I told you guys repeatedly not to make things uncomfortable for the kid... Dammit..."
A middle-aged man, looking like a furious bull, suddenly barged in alongside the chair professor of the piano department. He was huffing and puffing, his hands full of various items. Everyone except the astronomy researchers, who had seen him a few times before, flinched.
"Uncle! No, it's not like that this time!" Chul-jun waved his hands quickly with a bright smile.
Cha Seon-hyeok and Do Seon-ju blinked repeatedly in disbelief.
Professors from the mathematics and physics departments, whom they normally wouldn't even dream of sitting at the same table with, were gathered around Chul-jun, engaged in a heated debate.
On top of that, the Dean of the College of Natural Sciences himself was listening intently to the discussion.
"Hey... this has gotten incredibly huge, hasn't it?"
"Y-yeah, it really has."
"What happens to us if that doesn't work out?"
"Hey, don't say things like that! You're the one who said it would work earlier, Professor!"
Cha Seon-hyeok swallowed hard.
To be honest, he hadn't been entirely sure. It was more of a it seems like it should work kind of feeling.
Since they were theories he hadn't delved deeply into himself, he had just pieced them together, and they had looked reasonably plausible. Not fully understanding the equations, that was the extent of Cha Seon-hyeok's impression.
But listening to the professors' conversation, he was slowly beginning to realize how monumental this actually was.
Perturbation functions.
A perturbation function itself was by no means an unsolved cosmic mystery like the Riemann Hypothesis or the Millennium Prize Problems. It was a well-known mathematical tool formulated back in the 18th and 19th centuries by genius mathematicians like Laplace and Lagrange, and it was currently taught to undergraduate physics and astronomy students.
However, while the theory was known, actually applying it was a different story—not because it was an intellectual mystery, but because it was a hellish, endless grind of manual labor.
A perturbation function was not a magic formula where you wrote down a single equation and got an answer. To reduce error, one had to find the first-order perturbation, add the second-order, then the third, the fourth... an infinite series that kept chaining on forever.
Furthermore, solving perturbation functions by hand inevitably led to a notorious obstacle that drove astronomers to despair. When expanding the equations, as the planets' orbital periods fell out of sync, extremely small values would enter the fraction. This caused the denominator to approach zero, making the calculation explode into infinity.
Thus, the moment the Small Denominator Problem occurred, the computer's calculations would explode into infinity.
Because of this, modern astronomy had compromised by using numerical integration via computers instead of expanding perturbation functions by hand.
To put it simply, a perturbation function was like a screwdriver that anyone knew how to use; the small denominator problem was the issue of the screw constantly stripping when you tried to tighten it; and the KAM Theorem was what mathematicians in the 1950s used to prove that, under certain conditions, the screw would never strip.
However, because finding a way to actually satisfy those conditions was incredibly difficult, the theorem was rarely used.
Yet, the logic Chul-jun had just presented took these existing tools—the perturbation function and the KAM Theorem—and applied them to intuitive topology and geometry to find a near-perfect shortcut where the screw would never strip.
Although it wasn't an unsolved millennium problem, mathematicians often said that finding a perfect path was a work of pure art...
Cha Seon-hyeok stared blankly at Chul-jun, who was busy explaining things to the mathematics professors.
"If you expand the perturbation function using this exact determinant, it won't explode midway, and you can solve it cleanly all the way to the end in one go!"
Since the intermediate proof steps were omitted, he didn't know if that was actually true. Yet, the mathematics professors, and even the Dean, were nodding their heads and clapping.
I guess it really works...
Though he didn't fully understand, Cha Seon-hyeok quickly joined in the applause.
Then, someone caught his eye.
Wait. Why on earth is the piano professor here?
Amidst the mathematics and physics professors, a completely out-of-place figure was clapping the most enthusiastically. But the piano professor didn't look like he understood what was going on either.
The next day, at Hanyoung Private Elementary School.
Go Chang-ho smiled warmly at Chul-jun's highly excited explanation.
"Is that so? That happened? It must have been incredibly fun."
"Yes! When the math teachers, astronomy teachers, and physics teachers all gathered together, things I hadn't even thought of started connecting! It was really amazing."
Go Chang-ho knew very well that Seohan University had its eyes on Chul-jun, and he couldn't help but admire their dedication. From what he could gather, it sounded like they had included Chul-jun in some astronomy paper research.
But math and physics for an astronomy paper?
Go Chang-ho didn't know much about the natural sciences, but he understood the general balance of power. So he was quite puzzled.
However, with Chul-jun in the mix, he could somewhat picture the situation. A meticulously designed, university-level, ultra-premium gifted experience program to let a gifted child interested in astronomy naturally experience how crucial the foundations of math and physics are.
The people at Seohan University are really playing on a massive scale just to win over one kid.
Of course, Go Chang-ho knew very well that Chul-jun was exceptionally smart. Even so, how long had it been since the boy first learned about astronomy, and they were already letting him join paper research?
No doubt, a few graduate students acting on a professor's orders had sat Chul-jun in the middle and were chiming in with, "Wow! Our Chul-jun is truly amazing!" He could see the picture clearly in his mind. Well, he could also picture the graduate students getting flustered when Chul-jun showed some genuinely surprising insights.
Go Chang-ho chuckled.
Indeed, the boy was just that desirable.
"I see. Our Chul-jun has been doing something truly incredible with the older brothers and sisters at the university."
"They aren't older brothers and sisters, they're teachers."
Go Chang-ho realized his slip and nodded. To Chul-jun, even the graduate students were all "teachers."
"Ah! Right, right. Teachers."
"Yes! There are elderly grandfather teachers, and uncle-aged teachers too!"
Go Chang-ho nodded with a gentle smile, then paused slightly.
Grandfather teachers?
An older, late-blooming graduate student? A fossil of a postdoc? But "grandfather" was a bit much, wasn't it? Did they have a lot of gray hair?
Go Chang-ho recalled the scruffy beards and exhaustion-worn faces of the senior graduate students who lived like fossils in the labs back in his university days. Perhaps to an eleven-year-old Chul-jun, they really did look like grandfathers. Children's perceptions tended to be a bit exaggerated, after all.
Furthermore, from what he had seen so far, while Chul-jun possessed an incredibly high intellect, his emotional development felt slightly slower than his peers. So he simply nodded in agreement.
"Right, right. Still, you shouldn't bother the university teachers too much. They must all be incredibly busy and tired with their own studies."
"I don't bother them! I just act as a translator so they can understand each other. Well, I just connect them and point out the mistakes in the middle!"
"Haha, I see. So our Chul-jun is the boss over there."
As Go Chang-ho burst into laughter, Chul-jun giggled along.
"So you're heading straight to the university today too?"
"Yes!"
"Alright. See you tomorrow then."
"Yes!"
Watching Chul-jun wave goodbye with a bright smile, Go Chang-ho smiled warmly.
The paper-writing factory of Seohan University's College of Natural Sciences, operating under Chul-jun's direction, was incredibly systematic.
First, the astronomy department thoroughly combed through the raw SDSS data that the Japanese team had discarded as observation errors. They re-extracted only the data with the specific periodicity set by Chul-jun and converted it into the standardized variables he had created.
Then, the mathematics department took that data, applied it to the equations Chul-jun had discovered, and built a solid logical defense so that mathematicians worldwide could find no fault in proving that the perturbation function converged perfectly without diverging to infinity.
Finally, the physics department rigorously verified that the mathematically derived results did not violate actual physical laws.
The ultimate goal was to perfectly define—in the languages of astronomy, mathematics, and physics—the dynamic equilibrium in which planets exchanged energy and coexisted forever.
This was likely the first time in the history of the College of Natural Sciences that research had been conducted in this manner. Yet, it was running remarkably well.
Because the logic Chul-jun had established was so solid, and because this could become a rare, monumental achievement for all departments involved, everyone from the professors to the researchers was absolutely desperate.
Above all, research personally directed by the Dean of the College of Natural Sciences...
The researchers packing the astronomy lab were simultaneously experiencing the pride of being scholars and the agonizing misery of being graduate school slaves.
A few days passed like this.
"How much longer until Chul-jun gets out of school?"
"He should be arriving any minute!"
"Ah, time flies... Finish the proof formulas for the simulation coordinates that just came out first. That way, we can ask him if this was the direction he wanted."
"Yes, Dean!"
The excited replies of the mathematics professors were accompanied by a background chorus of sighs from the math graduate students.
"Astronomy department, speed up the data extraction. Once the proof formulas are finalized, they'll be used up instantly."
"...Yes, sir."
A heavy sigh from the astronomy researchers also settled over the lab.
The verification process, which involved plugging in countless cases through the mathematics professors and computers, was nearing its end.
And though no one had voiced it aloud yet...
It was practically a foregone conclusion that this equation, which had started from an elementary schooler's idea, was flawless.
If this research truly succeeded, it would be a magnificent achievement worthy of drawing the attention of the global natural sciences community. This was why the hollow eyes of the graduate school slaves were sparkling with life.
The lab door swung wide open.
"Hello!"
The director of this magnificent research greeted them with a bright, innocent smile.