Translator: Dreamscribe
The moment Seo-ha finished speaking, the studio buzzed with commotion.
A significant number of the people gathered here had ties to the scientific community. They understood exactly what Seo-ha's words meant.
He had just declared that he would rewrite the Minimum Energy Theory, which had been stagnant for decades, right here and now.
Chris was the first to break the silence.
"Can you back that up?"
Seo-ha nodded.
"I've gathered all the materials needed for the proof. I'll show you everything.
Why the conventional approaches were doomed to fail repeatedly, and what conditions, once satisfied, make that failure structurally impossible."
[220,514]
└The nerve on this guy?
└Never thought I'd see something like this live.
└I want to call him a fraud, but it's Yu Seo-ha! I'm scared he might actually prove it.
└Nooo, please! I'm an engineering student! Just let me graduate in peace!
└I'm in the middle of writing my doctoral thesis on energy-related stuff too...
└Wait, so does that mean all the currently accepted theories just become worthless?
The atmosphere was heating up.
Peter shouted at the production crew.
"Bring more boards! No, not those small ones, bring every single one the company has!"
Moments later, the studio doors opened and crew members and staff came running in carrying all sorts of boards.
Large boards on wheels, foldable boards, even a chalkboard ripped from a conference room.
One side of the stage transformed into what looked like a white wall in an instant.
While the cameras were rolling, the PD called over the editor-in-chief, Peter.
"Peter, what were you thinking!"
The PD grabbed at his clothes, face flushed red.
One corner of the studio already looked like a war zone. More boards were being brought in and staff were running around frantically.
He whispered in a low voice.
"What do we do if he starts proving it right now? The ratings won't hold up. I guarantee you, 99% of the viewers won't understand a thing Seo-ha writes."
Ratings, at a time like this.
Peter looked at him with an incredulous expression.
"So?"
"We need commentary. Someone with a sharp tongue who can accurately follow Seo-ha's proof. At the very least, we need someone who can translate what kind of battle he's fighting into plain English."
Peter shrugged as if that were a non-issue.
"He's right there."
The PD's eyes went wide.
"Who?"
Instead of answering, Peter slightly turned his head and pointed toward a figure standing outside the stage lights, in the corner.
"Right there."
The PD's gaze followed.
A man in a black shirt, expressionless face, arms crossed, watching the boards.
"Theodore Langford.
A well-known mathematician in this field. Currently on Yu Seo-ha's team. Great screen presence, and I saw him speak at a conference before; quite the orator."
The instant the editor-in-chief finished speaking, the PD sprinted toward him.
Peter smirked and shook his head.
"Why does nobody understand how important today is?"
Seo-ha had never once bluffed about a proof.
Today would be the day the history of world engineering was rewritten.
The fact that the stage for it had been set by Science, which had served as the cornerstone of the scientific community for decades, gave him immense satisfaction.
* * *
Seo-ha stood before the first board.
The moment the marker touched the surface, equations began flowing out in a steady stream. Seo-ha felt something boiling up inside his chest.
'Ducky, let's go!'
His expression changed in an instant.
Seo-ha plunged into a deep, deep swamp of equations.
Swoosh.
"Right now, Seo-ha is establishing a standard starting point."
Theodore spoke in a calm voice, as if commentating a chess match.
"The Energy Function and State Variables. There's no room for debate here. Anyone in this room would have started the same way."
Seo-ha pulled the next board over.
In his mind, the studio had already vanished.
The lights, the people, the cameras no longer existed.
What stretched out before his eyes was an enormous State Space. A space layered with hundreds, thousands of overlapping axes.
'So this is what it looks like.'
Energies were distributed across varying heights and depths.
An uneven terrain, an imperfect world where Local Minima jittered and pulsed everywhere.
Seo-ha was gazing down upon all of it from a dizzying height above.
"What is Seo-ha doing right now?"
Seo-ha's heart was pounding fiercely.
The speed at which he wrote equations kept accelerating.
Scratch scratch.
「M = {x∣∇V(x)⊤f(x) = 0, ∇²V(x)⪰0}....」
"LaSalle's Invariant Set?"
Theo sprang to his feet in shock.
Peter tilted his head and asked.
"Why are you so surprised? I've heard the name LaSalle before, though I can't quite recall the details."
Theo nodded.
"That's understandable. He never won a Fields Prize or an Abel Prize.
But his contributions are being reevaluated more and more as time goes on. Seo-ha mentioned him once during a previous meeting, but I never expected it to come up here...."
Theo continued urgently.
"LaSalle says this: if energy only decreases, it will eventually be extinguished. But that is mathematically and physically impossible. The point where energy can no longer decrease will inevitably come."
"And LaSalle's Invariant Set captures that moment. But isn't that just an equilibrium point?"
"No."
Theo shook his head firmly.
"LaSalle's Invariance Principle always stops here.
'The set exists.' That was as far as LaSalle could prove. What shape the set takes, how the system behaves within it, and what makes it invariant, no one has ever been able to show."
A brief silence ensued.
But the chat was scrolling at a frenzied pace.
└What? So he just stacked one unsolved problem on top of another?
└ㅋㅋㅋㅋㅋ who's even gonna verify this?
└Is there anyone here who can actually follow this?
└Hmm. Interesting. Quite a creative approach. The question is how he'll steer the proof from here.
└Look at you pretending to know stuff.
└Exactly ㅋㅋㅋ
└Excuse me? You punks, I'm a Yale math professor!
The chat descended into chaos.
Users started clicking on each other's profiles one after another.
└Oh my god, why are there so many professors ㅋㅋㅋㅋ
└MIT, Yale, Harvard, Caltech, Stanford, Columbia, Duke confirmed so far. What is this? A conference?
└Professors having an online get-together ㅋㅋㅋ
└Ahem. Let's keep it down, shall we?
└Colleagues, what a pleasure to see you here. It's been far too long.
On ResearchGate, the world's largest scientific community, users were reviewing Seo-ha's proof in real time.
When word spread, professors from universities around the world had rushed to find the live broadcast.
Scratch scratch.
Before anyone noticed, only a few blank boards remained.
The countless equations Seo-ha had filled in stretched beyond the boundaries of the boards, forming one continuous chain.
"What Seo-ha is doing right now is not a simple application of LaSalle's Invariance Principle."
"Hm? Then what is it?"
Peter stared at Theo as if to ask what on earth he meant.
"LaSalle left a great deal of room in his own theory. It would be no exaggeration to say he merely pointed a direction. Seo-ha is filling in those gaps right now."
"Gaps?"
"Yes. No one has ever been able to find out what actually lies at the end of it."
"Why not?"
"Put simply, because it's extraordinarily difficult.
To make use of LaSalle's theory, you need to determine the Maximal Invariant Set, and computing that is generally impossible."
"...'Generally,' you say. What does that mean? That's rather uncharacteristic word choice for a mathematician."
"Because until now, it has been impossible. But with Seo-ha, you never know.
The Invariant Set doesn't reduce to a single equation. And finding the set isn't the end of it. From there, you still have to extract only the closed portions.
This is the part where even the mathematics community resorts to assumptions. The moment you step into that territory, the gates of hell swing open."
Peter's eyes went wide.
"Th-then right now, Seo-ha is...."
"Exactly. He's thrown those gates wide open."
Seo-ha was drawing upon knowledge from countless fields: Differential Dynamics, Analysis, Differential Geometry, Optimal Control, Numerical Analysis, even Physical Modeling.
A solution where all of these interlocked as one.
Seo-ha saw it clearly.
'Mathematics is most beautiful when it is ready to be used.'
Joseph Pierre LaSalle (1916 - 1983),
A mathematician who had a theory bearing his name.
The Invariant Set came to be called not a theorem but a principle after his death.
'LaSalle, to that conviction of yours....'
Seo-ha quietly drew in a breath.
'...I will offer my answer.'
The marker began to move.
LaSalle never described how to compute the Invariant Set. Nor did he guarantee what geometric structure it held, or whether it was a system that could be sustained in reality.
Seo-ha stepped into a domain no mathematician had ever reached before.
The reason Theo had called this problem hell.
The first was dimensionality.
Position, velocity, oscillation, delay rate: each appeared to be an independent axis, but in reality they pulled at and pushed against one another, tangled together.
Seo-ha sensed it instinctively.
'Ten dimensions.'
And the Invariant Set defined atop those dimensions was a geometry beyond anything a human mind could imagine.
The other problem was Nonlinearity.
'Was this why LaSalle stopped?'
The curve of the Energy Function was smooth, but once differentiated, its gradient raged like violent waves.
Yet even these challenges were easy compared to the final obstacle.
"Time."
Seo-ha overlaid a time axis onto the State Space.
The space folded once.
In that instant, countless possibilities exploded simultaneously inside his mind.
Tens of thousands of timelines surged toward the boundary of the Invariant Set.
'An Invariant Set must be a structure that is closed against every possible future. That is the core of the Minimum Energy Theory.'
Seo-ha gritted his teeth.
If he stopped here, this would remain just another "theory that might be possible."
His brain began thinking at a ferocious pace.
Scratch scratch.
As the symbols defining invariance morphed one by one, the flow across the set revealed itself.
Not a stationary point, but a space where movement itself formed the structure.
'This is it!'
Seo-ha's heart hammered violently, pumping oxygen to his brain.
Theo had forgotten what he was about to say, simply staring at Seo-ha. Under those hands, assumptions once thought impossible were crumbling one by one.
'There is only one person in this world capable of this, and that is Seo-ha.'
Theo clenched his fist.
He had wanted to see Seo-ha like this. The fact that his own contributions to this moment were far from insignificant filled him with pride.
Seo-ha drew a single curve.
A gentle, unbroken surface.
Equations began lining up along it, one by one. Things that should never have been unified by nature.
Energy decrease conditions, the Invariant Set, the time integral terms.
The equations interlocked as though calling to one another.
And each found its exact place and settled in.
As if pulled by gravity, every flow and trajectory tilted toward the surface Seo-ha had drawn.
One hour, two hours.
Every time Seo-ha broke through a new obstacle, Theo commentated for the viewers in real time.
What was happening right now, how impossibly difficult this was, Theo explained it to them until his voice was hoarse.
The atmosphere shifted.
Seo-ha's gaze had settled into something deep and still.
Seo-ha took a deep breath.
'LaSalle, you accomplished something truly remarkable.'
The point where energy could decrease no further.
A set that every trajectory eventually reached, and once entered, could never be escaped. Seo-ha had finally, against all odds, succeeded in finding it.
'This is my tribute to you.'
Swoosh.
LaSalle's invariance condition came alive atop the equations.
And at last, spanning five boards, a single grand structure was completed.
「...All admissible dynamics are confined within this invariant structure. Therefore, under these conditions, both the existence and convergence of the Minimum Energy Solution are simultaneously guaranteed.」
「Q.E.D.」
Cameras alternated, capturing each person in the studio.
Theo and Sri, cheering; Su-jeong, fighting back tears; Peter, smiling with a look of deep satisfaction; and Chris, standing dazed, as if his soul had left him.
Seo-ha kept his eyes closed, still immersed in the afterglow of the proof.
And that very scene became the main page of ResearchGate.
[LIVE: Seo-ha Yu proves both the existence and convergence of the Minimum Energy Structure.]
[320,547]
Chat lines were scrolling upward at a speed impossible to follow with the naked eye.
* * *
"Good lord!"
Thomas, dean of the mechanical engineering department, let out a stunned gasp.
He had been watching the live broadcast from his office with Whitman.
"Don't get ahead of yourself. It's still just a hypothesis for now."
Whitman said in a low voice.
But Thomas, a master of dynamics, was one of the few people in the world capable of recognizing the value of what Seo-ha had accomplished.
"I should get going."
He hurriedly rose from his chair.
"Where are you going?"
"I need to assemble every professor and postdoc we've got. We have to turn that into a patent as fast as possible. It's war from here on out!"
"The verification hasn't even been completed yet?"
Thomas shook his head as if to say, "Come on, really?"
"Then are you saying you doubt Seo-ha, Professor?"
"Of course not."
"I feel the same way. We need to start now. Before every engineer in the world jumps on this. And I sincerely hope the math department will cooperate as well."
He loosened his tie roughly and bolted out of the dean's office.