A Shortcut to the Stars
Cha Sun-hyuk, Do Sun-joo, and the researchers who were at least in their second year of their doctoral program gathered together.
They were all individuals of strong mental fortitude, rarely seen with serious expressions, but right now, their faces were incredibly tense.
"Alright, let's summarize this first. If you have any questions, ask after I'm finished."
"Yes, Professor."
Cha Sun-hyuk pointed to the equations he had just scribbled on a sheet of A4 paper.
"These equations you're looking at right now—even if you gave a supercomputer a hundred million years, it could never derive them."
Sun-hyuk tapped his pen against the paper, which was densely packed with equations.
"When it comes to the Many-Body Problem, computers have clear limitations. Since computers rely on numerical integration—brute-forcing calculations by mindlessly plugging in numbers—even a tiny intervention from the Z-axis mutual inclination variable causes errors to explode due to chaos. That's why that brilliant Japanese AI smoothed out all the vertical orbital fluctuations, dismissing them as white noise. They blindly believed it was a coplanar system, which ultimately sealed their doom."
Confirming that everyone was nodding, Sun-hyuk continued.
"But the plan Chul-jun laid out is different. He took that three-dimensional noise—the very data the computer gave up on and threw in the trash—and grabbed it by the collar, turning it all into perturbation functions of Hamiltonian mechanics. The orbital fluctuations, which would explode into infinity under a computer's processing power, were perfectly bound and converged using nothing but the Diophantine condition of the KAM Theorem—pure mathematics. It's an absolutely insane blueprint that completely crushes the statistical bias of AI with human intuition and analog analytical mechanics. What do you guys think?"
It was an astounding speech, but neither Do Sun-joo nor the other researchers could bring themselves to nod. They only furrowed their brows.
The first to break the silence was Do Sun-joo, the sole woman in the group.
"...Professor. I understand that this theory is perfect and an absolutely brilliant plan."
"Yeah, go on."
"But this means solving the orbits of the many-body problem using analytical mechanics without a computer. You're saying we have to expand the Poincaré series by hand and even satisfy the Diophantine condition? If we hit even a single Small Denominator Problem along the way, the equations will multiply until they fill a hundred blackboards."
Another researcher chimed in, his brow furrowed.
"He's right. Every time a single orbit deviates, we have to recalculate the infinite series from the very beginning. If our current team tries to tackle this from scratch... without exaggeration, it'll take ten, maybe even twenty years."
The reason for the researchers' despair was clear.
The difficulty of the equations was one thing, but the sheer volume of calculations was enough to shave years off a person's lifespan.
Yet, Cha Sun-hyuk merely curled his lips into a relaxed smile.
"Exactly. Normally, you'd be right. We'd grow old and die before we finished solving these equations."
Sun-hyuk slid the top sheet of paper aside, revealing another sheet underneath.
On it were several geometric constants and determinants that Chul-jun had written on the electronic blackboard earlier.
"But what if Chul-jun could drastically cut down those decades of tedious labor for us?"
Sun-hyuk's index finger tapped the equations.
In truth, they were equations that most of the people in the lab didn't fully comprehend.
Even Sun-hyuk hadn't had the time to analyze them in detail yet; he was merely operating on the hunch of, This might actually work.
Because of this, Do Sun-joo and the other researchers could only tilt their heads in confusion.
"Look, I haven't fully organized it myself yet, but just listen. Out of a near-infinite number of possibilities, what if Chul-jun has already used topology to pinpoint the exact frequency band where the planets lock into perfect harmony? The core resonant frequency band, in other words."
Sun-hyuk tapped the constants firmly with his index finger.
"It means we don't have to grope around in the dark, feeling every single wall of a maze to find the exit. What if Chul-jun flies a helicopter above and draws us a map of the shortest path to the answer? No, it's even more than that. Let's say he just blasted straight through the maze walls to create a straight line. If that's the case, our job isn't to expand infinite series from scratch. We just have to coast along the rails of this coordinate transformation matrix Chul-jun mapped out, categorize the data, and mathematically verify and prove that the values are correct."
Do Sun-joo and the graduate students' eyes widened in unison.
"Then..."
"Yeah. Millions of trials and errors are bypassed. Once Chul-jun sets the guidelines, our only job is to rigorously verify that the direction is correct and package it into formal equations for the paper. Of course, we still need to double-check these formulas, but what do you think? If it works out like this, isn't it worth a shot?"
Sun-hyuk spoke with a grin, but the researchers' expressions only grew stiffer.
A heavy silence ensued before Do Sun-joo shook her head slightly and spoke up cautiously.
"...Professor. I understand that Chul-jun setting the guidelines drastically reduces the amount of calculation. But as for the verification role of packaging it into formal equations... to be completely honest... I might be good at categorizing, but I don't know if I can properly write out the proof for this coordinate transformation. No, actually, I can't. Absolutely, never!"
At Sun-joo's painful confession, the other researchers hung their heads in unison, as if on cue.
"Professor, we only solved analytical mechanics by filling up blackboards with equations back in our undergraduate days. Once we got to grad school, we just preprocessed the data and handed everything over to computer numerical integration. We're people specialized in observing the universe and classifying data, not proving pure mathematics with a pen."
"..."
"This isn't something we can just gloss over with a few lines of equations. To directly refute the Japanese team, we have to write out a flawless proof with absolutely zero mathematical loopholes... Can we really pull off that kind of analog mathematical proof when we haven't touched it in ages? The peer reviewers will tear us to shreds over any error in the equation derivations."
Sun-hyuk's brow furrowed slightly.
It was hard to dismiss the researchers' claims as mere whining.
Understanding the principles by looking at an equation was entirely different from writing a proof with a flawless logical structure from scratch.
For modern astronomers accustomed to observational equipment and simulation programs, building the skeleton of pure mathematics was an incredibly steep cliff, even with the shortcut Chul-jun had carved out.
"Sigh..."
The path was right there. If they just had a little help, an eight-lane highway would open right up.
But they lacked the tools to help.
No matter how absurdly smart Chul-jun was, he couldn't possibly write out all these countless proofs on his own.
Even if they tried to use a computer, it would spit it right back out the moment an irrational number appeared...
Ah, seriously... It feels so close, which makes this so frustrating...
Sun-hyuk stared blankly at the A4 paper covered in equations and let out a deep sigh.
"...So, I don't think it'll be easy. Of course, the concept you've established is an incredible discovery in itself, and it's definitely worthy of a paper on its own, but..."
Chul-jun blinked his round eyes.
Didn't they say everyone here was incredibly good at math?
He thought they would be able to handle a proof of this level...
Chul-jun turned his head and stared at a single coordinate value written in the corner of the electronic blackboard.
The most basic orbital variable coordinate.
Over that simple symbol, a massive waterfall of equations began to cascade and overlap transparently in Chul-jun's mind.
To Chul-jun's eyes, it was merely a natural, beautiful chain reaction, like dominoes falling in perfect sequence.
Tap a single coordinate, and behind the equation representing the stable base orbit, tiny orbital tremors followed in close succession.
And those seemingly irregular tremors soon blossomed into a Fourier series, the sum of countless waves.
The moment the orbital frequencies of the planets and the integer vectors collided, threatening to diverge into infinity, the Diophantine condition Chul-jun had pre-calculated slid in like a solid shield.
The energy on the verge of exploding slipped gracefully through the gap of that inequality, ultimately weaving an eternal, non-collapsing, donut-shaped geometric torus to find perfect stability.
Starting from absolute nothingness to mathematically proving the ultimate resonant state where the universe sustains itself. The time it took for this to blossom completely, without a single error, was barely thirty seconds.
All they have to do is follow the line to the destination and fill in the blanks...
Chul-jun blinked his round eyes repeatedly in confusion, then furrowed his brow.
It was too complex and difficult to explain step-by-step like he did with his friends.
But he couldn't write out all the equations that had to be newly created every time the coordinate values changed by himself.
Imagining it in his head and writing it all down by hand were two completely different things.
Watching Chul-jun's reaction for a moment, Sun-hyuk let out a low sigh and spoke.
"Well, to be honest, this kind of proof work is what the math department kids are good at... We're just good at classification, analysis, and observation..."
Chul-jun nodded slightly.
Thinking back to when he taught his friends, it made sense.
He had momentarily forgotten that not everyone could see the world the way he did.
It was only natural that everyone had different areas of expertise.
To Chul-jun, mathematics, astronomy, and physics all looked like one single entity, but he knew that other people didn't see it that way.
That was why the teachers who were good at math and the teachers who were good at piano felt so different back then.
Suddenly, Chul-jun's eyes went wide.
"Ah! That's right!"
Sun-hyuk flinched at Chul-jun's sudden exclamation.
Chul-jun turned to look at everyone and beamed.
"Then, the teachers who are good at math can just help us, right?"
"...Huh?"
Sun-hyuk blinked blankly.
Gu Byung-ook, the Dean of Natural Sciences, looked out the window with a pleased expression and spoke.
"I see. He came again today?"
The head professor of the mathematics department nodded, looking equally pleased.
"Yes. I heard he arrived a while ago, and he's staying quite long today."
"Haha. That's a relief. Even if it's astronomy he's showing interest in."
"But I am a bit worried. You know how the astronomy department is. If his genius gets contaminated by coding or AI..."
"Hmm. That is indeed a concern. Ah, we must nurture that mathematical talent of his properly..."
Gu Byung-ook could still see the beautiful Fourier transform equation the boy had shown him dancing before his eyes.
There were children who understood calculus at an early age.
But eventually, once they reached high school, other kids would understand it too.
Children with high IQs who were simply fast learners or good at memorization were actually quite common.
But that child was absolutely not one of those common children.
It wasn't just intelligence; it was reasoning, intuition, creativity, insight, geometric imagination, pattern recognition, structural reductionism, convergent thinking...
In short, he was a child from whom an uncountable, almost cheat-like level of genius was expected.
He had seen countless times how gifted children in Korea went through the system only to degenerate into ordinary people.
That was why he was so anxious.
A genius that might appear only once in several centuries could have been born in South Korea, yet here they were, sitting on their hands like they were just casting a fishing line and waiting...
"Sigh, I can't take this. I'll go there myself and—"
As Dean Gu Byung-ook turned around, the head math professor quickly waved his hands.
"You can't, Dean!"
"Why not!"
"His guardian came with him today."
"...Ah."
"I caught a glimpse of him before, and he looks incredibly terrifying."
"..."
"He said so on the phone back then. If we put the kid in a stressful situation one more time, he'd come over in person and flip the entire place upside down..."
Dean Gu Byung-ook squeezed his eyes shut.
They had truly started off on the wrong foot.
"There's nothing we can do. If all else fails, we'll have to lure him by adding astronomy to the gifted program's curriculum..."
"...Excuse me for a moment, Dean."
The head math professor quickly checked his phone.
One of his eyebrows twitched.
It was a message from a research professor in the astronomy department.
He had been receiving reports on what the child did every time he visited, but...
A photo?
It was the first time they had sent a photo, so he tilted his head and opened the image.
What in the world... are these equations?
Adjusting his glasses, the head professor pinched and zoomed in on the photo.
After studying it for a moment, his eyes gradually widened, and his mouth fell slightly open.
"D-Dean..."
Dean Gu Byung-ook furrowed his brows and walked over to him.
"What is it? What's wrong?"
Squinting his eyes as he leaned in to look at the small screen, Dean Gu Byung-ook's eyes also grew progressively wider, his mouth agape.
"Is... Is this..."
"Y-yes. They say the child made this."
Dean Gu Byung-ook without even replying, burst out of the office door and ran.
"Well, Chul-jun. We did what you suggested, but..."
"Yes!"
"To be honest, it's a bit embarrassing for us to admit this... but we are the most minor department in the College of Natural Sciences... no, in the entirety of Seohan University."
Standing beside him, Do Sun-joo whispered in Sun-hyuk's ear.
"We're better off than the philosophy department, Professor."
"At least they don't have to worry about being merged or shut down."
"Ah!"
Listening quietly to their conversation, Chul-jun blinked his round eyes.
Why was such a grand field of study like astronomy considered minor?
"Why?"
"Well, it's complicated to explain..."
Cha Sun-hyuk swallowed hard.
It was incredibly difficult to explain the worldly affairs of adults to such an innocent face.
"Anyway, the mathematics department is one of the top three 'heavenly' departments in the College of Natural Sciences, while we're way down at the bottom..."
After pondering for a moment, Chul-jun nodded.
He seemed to understand roughly what they meant.
It must be like a tier system.
"Ah. I understand."
"You do? So, what I'm saying is, just because we sent a single photo to the head of the math department doesn't mean the Dean would come all the way to this dusty corner... and there's no way the math department would step up to help with an astronomy paper..."
Chul-jun tilted his head.
In the past, just seeing a photo of a Fourier transform music sheet had brought a crowd of math teachers to the small auditorium without even making a proper appointment.
And this time, I found something even cooler and more fun.
Chul-jun twitched his eyebrows and smiled.
"They'll come."
Chul-jun, who had been listening intently toward the door, suddenly turned his head.
"Oh? They're here!"
A moment later, the door to the most remote laboratory in Seohan University's College of Natural Sciences burst open.
"Hello!"
Chul-jun greeted them politely with a bright smile.