As soon as Seoha finished speaking, the studio began to stir.
Many of those present were people with ties to the scientific community. They understood exactly what Seoha’s words meant.
He had just declared that he would rewrite, then and there, the minimum energy theory that had been at a standstill for decades.
Chris was the first to break the silence.
“Can you take responsibility for that?”
Seoha nodded.
“All the materials needed for the proof are here. I’ll show you everything.
Why the existing methods were bound to fail repeatedly, and under what conditions that failure disappears structurally.”
[220,514]
└What’s with that confidence?
└I never thought I’d see something like this live.
└I want to call him a fraud, but it’s Yu Seoha! I’m scared he might actually prove it.
└Aaaah, no! I’m an engineering student! Please just let me graduate as things are!
└I’m writing my doctoral dissertation on energy-related stuff right now......
└What? Then does that mean all the theories currently in use become scraps of paper?
The atmosphere was heating up.
Peter shouted toward the production crew.
“Bring more boards! No, not those tiny ones—bring every board in the company!”
A moment later, the studio doors opened, and the production crew and staff began running in carrying all kinds of boards.
Large boards on wheels, folding boards, even blackboards taken from conference rooms.
One side of the stage instantly turned into something like a white wall.
While the cameras were rolling, the producer called Peter, the editor-in-chief, over.
“Peter, what were you thinking!”
The producer, his face flushed red, grabbed at Peter’s clothes and tugged him away.
One corner of the studio already looked like a battlefield. More boards were being brought in, and the staff were running around in a frenzy.
He whispered in a low voice.
“What are we supposed to do if he starts proving it right now? The ratings won’t come out. I guarantee you, ninety-nine percent of the viewers won’t understand what Seoha is writing.”
Talking about ratings at such an important moment?
Peter looked at him with an expression of disbelief.
“So?”
“We need commentary. Someone eloquent who can accurately understand the proof Seoha is writing—at the very least, someone who can translate into English what kind of battle he’s fighting.”
Peter shrugged as if to ask what the problem was.
“He’s right over there.”
The producer’s eyes widened.
“Who?”
Instead of answering, Peter slightly turned his head and pointed to someone standing outside the lights at the corner of the stage.
“Over there.”
The producer’s gaze shifted in that direction.
A man in a black shirt, expressionless, arms crossed as he watched the board.
“Theodore Lanford.
He’s a well-known mathematician in this field. He’s on Yu Seoha’s team now, he looks good on camera, and from what I saw at a conference before, he’s quite articulate too.”
The moment the editor-in-chief finished speaking, the producer began running toward him.
Peter chuckled and shook his head.
“Why doesn’t anyone understand how important today is?”
Seoha had never once bluffed when it came to proof.
Today would be the day the history of world engineering was rewritten.
And he was supremely satisfied by the fact that the stage had been prepared by Science, which had served as a cornerstone of the scientific world for the past several decades.
***
Seoha stood before the first board.
The moment the marker touched it, equations began to flow out calmly. Seoha felt something boiling up inside his chest.
‘Ducky, let’s go!’
His expression changed in an instant.
Seoha sank into the deep, deep swamp of equations.
Ssssk.
“Right now, Seoha is taking the standard starting point.”
Theodore spoke in a calm voice, as if he were commentating a chess match.
“The energy function and the state variables. There’s no room for dispute in this part. Anyone here today would have begun in the same way.”
Seoha brought over the next board.
In his mind, the studio had already vanished.
The lights, the people, the cameras—none of them existed anymore.
What unfolded before his eyes was an immense state space. A space where hundreds, thousands of axes overlapped.
‘So this is what it looks like.’
Energies were distributed at various heights and depths.
An uneven terrain, an imperfect world where local minima writhed here and there.
Seoha was looking down at them from a dizzying height.
“What is Seoha doing right now?”
Seoha’s heart was pounding fiercely. The speed at which he wrote equations grew faster and faster.
Scratch, scratch.
「M = {xI▽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 too, but I don’t remember the details.”
Theo nodded.
“I suppose that’s inevitable. He wasn’t a Fields Medal or Abel Prize winner.
But his achievements are being reevaluated more and more as time passes. Seoha mentioned him once in the last meeting, but I never thought it would come up here....”
Theo continued urgently.
“LaSalle says this: if energy only keeps decreasing, then in the end it will disappear. But that is something that cannot happen mathematically or physically. A point where energy no longer decreases must inevitably arrive.”
“So what captures that moment is LaSalle’s invariant set. But isn’t that just an equilibrium point?”
“No.”
Theo firmly shook his head.
“LaSalle’s theorem always stops here.
‘The set exists.’
That was as far as LaSalle could prove. What shape that set has, how the system moves within it, and what makes it invariant—no one has ever been able to show those things.”
A brief silence.
But the chat window was rising at a frantic speed.
└What? Did he just pile another hard problem on top of a hard problem?
└Hahahahaha, who the hell is supposed to verify this?
└Is there anyone who can understand this right now?
└Hmm. Interesting. It’s an extremely creative approach. Though the question is how he’ll pull the theorem forward from here.
└Look at him pretending to know.
└Exactly lololol.
└What did you say? You punks, I’m a professor of mathematics at Yale!
The chat fell into chaos.
Users began clicking on the profiles in the chat window, one after another.
└Good God! Why are there so many professors here hahahahaha
└I’ve confirmed MIT, Yale, Harvard, Caltech, Stanford, Columbia, and Duke. What is this? A conference?
└The professors are having an online meetup lololol.
└Ahem. Let’s keep it down a little.
└Professors. Fancy seeing you here. It’s been far too long.
On ResearchGate, the world’s largest scientific community, users were reviewing Seoha’s proof in real time.
And after hearing the news, professors from various universities had hurriedly come to the live broadcast.
Scratch, scratch.
Before anyone realized it, only a few blank boards remained.
The countless equations Seoha had filled in were extending far past the boundaries of the boards.
“Right now, Seoha is not simply applying LaSalle’s theorem.”
“What? Then what is he doing?”
Peter looked at Theo as if asking what he meant.
“LaSalle left many openings in his theory. It would not be an exaggeration to say he merely indicated a direction. Seoha is now filling in those blank spaces.”
“Blank spaces?”
“Yes. No one has ever figured out what actually exists when you reach the end.”
“Why is that?”
“Simply put, because it is extremely difficult.
To make use of LaSalle’s theory, you have to find the largest invariant set, and finding that is generally impossible.”
“...‘Generally’? What does that mean? That’s a very unmathematic choice of words.”
“Because until now, it has been impossible. But with Seoha, who knows?
An invariant set doesn’t reduce to a single equation. Finding the set isn’t the end of it, either. From there, you must select only the closed parts.
This is an area that even the mathematical community usually passes over as an assumption. The moment you enter it, the gates of hell open.”
Peter’s eyes widened.
“Th-then right now, Seoha is.......”
“That’s right. He has flung the Hell Gate wide open.”
Seoha was mobilizing knowledge from countless fields: dynamical analysis, differential geometry, optimal control, numerical analysis, even physical modeling.
A solution in which all of these interlocked as one.
Seoha saw it clearly.
‘Mathematics is most beautiful when it is ready to be used.’
Joseph Pierre LaSalle (1916–1983),
A mathematician with a theory named after him.
After his death, the invariant set came to be called not a theorem, but a principle.
‘LaSalle, to that conviction of yours...’
Seoha quietly drew in a breath.
‘......I will give my answer.’
The marker began to move.
LaSalle had not said how to obtain the invariant set. He had not guaranteed what geometric structure it possessed, nor whether it was a system that could be maintained in reality.
Seoha stepped into a realm no mathematician had ever reached before.
The reason Theo had described this problem as hell.
The first was dimensionality.
Position, velocity, vibration, delay rate—each appeared to be an independent axis, but in reality, they pulled and pushed at one another, entangled together.
Seoha felt it instinctively.
‘Ten dimensions.’
And the invariant set defined upon those dimensions was not a geometry that human beings could imagine.
Another problem was nonlinearity.
‘Was this why LaSalle stopped?’
The curve of the energy function was smooth, but once differentiated, its slope surged like rough waves.
But even these were easy compared to the final obstacle.
“Time.”
Seoha overlaid the time axis onto the state space.
The space folded once.
Then, countless possibilities burst forth simultaneously inside his mind.
Tens of thousands of timelines rushed toward the boundary of the invariant set.
‘An invariant set is a structure that must be closed with respect to every possible future. This is the core of minimum energy theory.’
Seoha clenched his teeth.
If he stopped here, this would remain yet another “theory that might be possible.”
His brain began thinking furiously.
Scratch, scratch.
As the symbols defining invariance transformed one by one, the flow on top of the set was revealed.
Not a stationary point, but a space where motion itself formed the structure.
“Here!”
Seoha’s heart beat violently, pumping oxygen to his brain.
Theo watched Seoha, at a loss for words. Assumptions once thought impossible were collapsing one by one under his hand.
‘There is only one person in this world who can display this kind of ability: Seoha.’
Theo clenched his fist tightly.
He had wanted to see Seoha like this. And the fact that he had contributed no small part to this gave him pride.
Seoha drew a single curve.
A gentle, unbroken curved surface.
Onto it, equations began to align one by one. Things that, under normal circumstances, could never be bound together as one.
The energy decrease condition, the invariant set, the time integral term,
The equations interlocked as if calling out to one another.
And each found its exact place.
As if drawn by gravity, every flow and trajectory tilted toward the curved surface Seoha had drawn.
One hour, then two.
Each time Seoha broke through an obstacle, Theo explained it to the viewers in real time.
What was happening right now, how difficult this was—Theo explained it to them until his voice was nearly hoarse.
The atmosphere changed.
Seoha’s eyes had sunk into a deep calm.
Seoha took a deep breath.
‘LaSalle, you truly accomplished something extraordinary.’
The point where energy no longer decreases.
The set that every trajectory eventually reaches, and once it enters, can never leave. Seoha had finally succeeded in finding it.
‘This is my tribute to you.’
Ssssk.
LaSalle’s invariance condition operated atop the equations.
And at last, across five boards, one colossal structure was completed.
「...All admissible dynamics cannot escape this invariant structure. Therefore, under these conditions, the existence and convergence of the minimum energy solution are simultaneously guaranteed.」
「O.E.D.」
The cameras alternated between the people in the studio.
Theo and Sri cheering, Sujeong struggling to hold back tears, Peter smiling with satisfaction, and Chris, staring blankly with a dazed expression as if he had lost his mind.
Seoha stood with his eyes closed, immersed in the lingering afterglow of the proof.
And that scene became the main page of ResearchGate just as it was.
[LIVE: Yu Seoha simultaneously proves the existence and convergence of the minimum energy structure.]
[320,547]
The chat was scrolling upward at a speed impossible to follow with the eyes.
***
“Huh!”
Thomas, the dean of mechanical engineering, let out a short exclamation.
He was watching the live broadcast in the dean’s office with Whitman.
“Don’t get too far ahead of yourself. For now, it’s still only a hypothesis.”
Whitman spoke in a low voice.
But Thomas, a master of dynamics, was one of the few people capable of recognizing the value of the proof Seoha had achieved.
“I should get going.”
He hurriedly rose from his chair.
“Where are you going?”
“I have to summon all the professors and postdocs. We need to turn that into patents as quickly as possible. From now on, it’s war!”
“Even though verification isn’t finished?”
Thomas shook his head as if to say he shouldn’t talk like that.
“Then, Professor, do you doubt Seoha?”
“Of course not.”
“I feel the same. We have to start now. Before every engineer in the world jumps in. Please have the mathematics department cooperate as well.”
Roughly loosening his tie, he rushed out of the dean’s office.