Theo’s gaze returned to the blackboard.
Admiration and excitement could wait. What mattered was not losing the flow.
Having finished the calculation, Seoha was looking over the faces of his teammates.
Theo guessed he was checking to see whether any further explanation was needed. Seoha nodded as if satisfied, then continued.
“An ontological minimum is meaningless. If there is no path to reach it, then mathematically, it’s a dead solution.”
Sri, startled, stopped typing on his laptop and lifted his head.
“Huh? Then the reason mathematics and engineering haven’t been able to find the optimal solution until now was also…”
Seoha nodded.
“That’s right. The countless counterexamples that appeared in their papers were all for the same reason. Until now, they’ve been clinging to dead solutions. With that approach, they’ll never be able to reach their intended destination in the future either.”
Groans sounded from here and there around the lab.
Theo put a hand to his forehead and looked up at Seoha.
“Don’t tell me you’re going to publish this?”
For a moment, Seoha said nothing.
Directly refuting someone else’s research was not an easy decision for Seoha either.
“Yes.”
It was a brief answer.
But there was no wavering in Seoha’s eyes.
“Will you be okay? I think there’s going to be quite a backlash.”
“That’s right! In engineering, there are a huge number of scholars researching this area. Maybe we should publish after we’ve proved it perfectly first…”
Sujeong cautiously raised her hand.
“This paper will render a significant portion of existing research ineffective. Regardless of whether the proof is right or wrong, it’s saying the goal itself was mistaken.
If it were me, I don’t think I could endure it.”
Theo nodded heavily.
“It’s a statement that turns the direction of an entire academic field.”
Sri hesitated as well, then spoke with difficulty.
“To be honest, I’m worried first. If we submit this as a paper, it means we’re revealing all the results we’ve built up until now.”
Silence settled over the lab.
His words were a realistic concern.
Even at this very moment, hundreds of labs around the world were grappling with similar problems.
Among them, there were probably labs investing far more personnel and capital than Team Apex.
If the direction was presented, speed could be caught up to at any time.
Seoha nodded as if he understood their worries.
“Even so, we have to publish it. There are people who have already poured decades into this. They’ve spent their entire lives running toward the wrong goal.”
Seoha lightly tapped the words “False Minima” still written on one side of the blackboard with his fingertip.
“The longer we keep our mouths shut, the more their passion and time will be wasted.”
Sujeong lowered her gaze.
She had thought Seoha’s decision was cruel, but in truth, she knew as well. What would truly be cruel to them was not saying anything.
“And everyone.”
Seoha paused and made eye contact with each of his teammates.
“Are you perhaps worried our research results might be stolen?
I’m not considering that possibility at all. Even if someone sees this, there’s no way they’ll reach the conclusion faster than we do.
There aren’t many mathematicians as remarkable as all of you, even if you search the whole world.”
“Ahem.”
Theo cleared his throat.
At the unexpected praise, Sri and Sujeong’s faces turned red.
“This research is like walking a rugged mountain path. Since we’re the farthest ahead, let’s leave a sign for those who come after us, saying there’s a cliff in that direction!”
“A sign in front of a cliff, huh.”
Theo murmured in a low voice.
Whenever he saw Seoha like this, Theo felt as if someone were pricking his heart with a needle.
‘This guy…’
A defenseless face.
He was clearly not prepared to fight.
He did not enjoy debate, nor did he seem likely to be skilled at politics.
Even so, if necessary, Seoha was someone who would stand on the blade before anyone else.
Only for truth and axioms.
‘What will happen?’
Once the paper came out, it would take a long time to verify.
There might be ridicule from conferences and reviewers, or deliberate distortions. And Seoha would stand at the center of all that controversy.
Even though he had nothing to gain from it.
Theo slowly exhaled.
‘Then I’ll do it.’
He would take every attack first.
So that Seoha could simply move forward toward the truth.
“Then we’ll have to prepare. Let’s draw up the expected questions. The attacks will probably come in this order. The distinction between existence and reachability…”
Theo’s voice shifted into meeting mode.
Sujeong and Sri nodded, then began participating in the discussion enthusiastically.
‘If Seoha decides the direction, the team supports him with everything they have.’
That was the basic premise of Team Apex.
Theo began organizing a list of questions on one side of the blackboard.
Numbers were attached to the list, and beside them, response arguments were written concisely. Wherever an attack might come, additional marks were added in red pen.
“We absolutely need to attach one more counterexample here.”
Seoha stared blankly at the scene.
‘The people I chose.’
Only now did it become vividly real that he had taken their time, their energy, and even their futures as collateral.
Even so, all of them were following his decision.
Slide.
Seoha’s gaze turned toward the blackboard.
Then, without a word, he walked forward and wrote the next line beside the formula he had written.
Scratch, scratch.
The sound of chalk rang out clearly despite the ongoing meeting.
That sound was like a vow welling up from Seoha’s heart.
‘More accurately, with greater responsibility.’
Seoha steadied his mind.
‘I will solve it.
Because this is a path precious people have chosen to walk with me.’
***
A few days later,
Team Apex’s paper was quietly released.
A single paper uploaded to the archive without any prior notice.
[On Unreachable Solutions in Energy Optimization Problems.]
The first few hours were calm.
But centered around the many scholars who had been interested in Seoha, the paper began spreading rapidly.
And from that night onward, the atmosphere changed.
A certain laboratory at the University of Tokyo, Japan.
“Did you see this?”
“Yeah, it was pretty aggressive. Our professor read it, then ran out with his face bright red.”
“How many years has he been researching this now?”
“Over five years. His budget was cut too, so he must have been under a lot of pressure.”
“That’s rubbing salt in the wound.”
Posts began piling up on public social media, scientist forums, and academic society boards.
[They are blaming the failure of optimization research on the theory.]
[I respect the boldness typical of young researchers, but this is rude.]
The reaction from engineering in particular was immediate and intense.
The statement that decades of accumulated algorithmic research had been aimed at the wrong goal was, in itself, like a challenge issued to the academic world.
In fact, the chief engineer of a major American tech research institute wrote the following on a public forum.
[Their paper is nothing more and nothing less than armchair theory. Reachability only has meaning under ideal conditions. Real systems are always products of compromise.]
There was plenty of other backlash poured out toward them as well.
The dispute spread beyond theory and technology into an emotional fight.
They often took the stance that Team Apex “didn’t understand reality,” as if looking at immature children.
[Theory is trying to lecture the field.]
[An arrogant attitude. We’ve done just fine with this approach until now.]
With more than twenty million registered researchers,
the boards of ResearchGate, the world’s largest scientific community, also exploded.
[It’s interesting that they elevated reachability to part of the definition of a solution. But isn’t this more of a topological issue than an optimization of solutions?]
└Calling existing results dead solutions was a bit much, lol.
└The phrasing is rough, but the counterexample section they presented is hard to ignore. We checked it in our lab, and under those conditions, there really is no path.
If one scrolled just a little farther, the atmosphere became even rougher.
└It’s a trap young researchers often fall into. If you redefine the problem, it looks like innovation, right? The world isn’t that easy.
└I think it’s overconfidence too. It’s dangerous to try to invalidate decades of research with a few counterexamples.
└In a few years, they’ll be kicking themselves under the covers over this.
Yet even amid all that, there were posts appearing as if buried.
[Our lab has repeatedly failed on this problem for the past three years. But only after reading this paper did I understand why we were always blocked at the same point.]
A few quick-witted labs were quietly modifying their code.
Experimental conditions changed, and constraints were added.
Convergence points that had previously been considered obvious were deleted one by one.
The engineering world was clearly splitting.
Into backlash, defense, and a full-scale reexamination carried out in silence.
And as always, in the mathematical world, quiet reflection and verification came before emotion.
At the top of MathOverflow, the most authoritative mathematics community, the following post was pinned as a notice.
[Emotional evaluations of this paper, speculation about intent, and personal attacks will be subject to deletion. Discussion is limited to definitions, propositions, proofs, and counterexamples.]
The content of the paper converged into a single question.
‘Can this definition be accepted?’
Some felt uncomfortable, some nodded, and most mathematicians silently picked up their pens.
└Isn’t the attempt to include reachability as part of the solution too radical?
└But it’s also true that existing definitions failed to explain many failures.
└The repeatedly appearing counterexamples were certainly a problem.
A few days later, the BBC published an interview with a renowned elderly European professor.
“I cannot be certain that everything in this paper is correct. But if it is wrong, then we must prove why it is wrong.”
Team Apex took a step back from this controversy and accelerated their preparations for argumentation.
Theo was the first to arrive in the morning and looked through the emails.
Conference requests, seminar invitations, anonymous questions, or simply emotional insults.
“We should accept this one. Ignore this one for now. Let’s prepare a little more before answering this.”
His judgment was precise and swift.
Sujeong was organizing the counterexample notes. She subdivided conditions that had already been organized once before, drawing clearer lines.
“If we change the boundary condition just a little here, it creates a counterexample the other side could bring up.”
Sri ran simulation logs.
Conditions even harsher than the results published in the paper. They were experiments premised on failure. But in the process, data accumulated.
Dean Whitman also issued a comment.
“It is still too early to conclude whether their hypothesis is correct. But I do know one thing. That paper was clearly an act of consideration. Not an attack.”
And amid all this uproar, there was a boy focused frighteningly only on the difficult problem.
Theo turned his eyes toward one side of the lab.
Seoha was standing in front of the blackboard.
Scratch, scratch.
On one side of the blackboard, the reachability condition and the integer barrier were written separately.
On the other side, the traces of discontinuity that occurred when the two meshed together again were marked densely.
Seoha moved back and forth between them, dismantling the structure one piece at a time as if pulling out threads.
‘Amazing.’
Just how high-dimensional did one’s thinking have to be to make something like that possible?
“Theo! Take a look at this.”
Sri turned his laptop screen around.
The video had already surpassed hundreds of thousands of views.
“Ah, that bastard.”
Alex Howard.
Once a promising star in pure mathematics, now a figure who had shifted toward engineering and become a legend in corporate consulting.
A neat shirt, perfect lighting, a familiar smile.
Behind him, the logo of his company, “Arc Wave,” gleamed.
And below it was written the phrase:
[Mathmatics to Maket]
It was the catchphrase he had long insisted on.
“There’s a paper that’s been a hot topic lately, isn’t there?”
Alex brought a tablet toward the camera.
The paper’s title appeared prominently on the screen.
[On Unreachable Solutions in Energy Optimization Problems.]
“I’m speaking as a mathematician myself, but this paper commits a very typical error. It takes a definition that seems mathematically plausible and overlays it onto an entire real-world problem.”
He tapped the word “Reachability” with his finger.
“Reachability is a constraint, not a definition. The moment you turn this into a definition, we become unable to solve any problem at all.”
The staff’s laughter could be heard.
“This is just my personal opinion, but… perhaps Team Apex couldn’t handle reality. There’s that famous genius there, Yu Seoha, isn’t there?
That friend couldn’t find the answer. Then what happens to the team at a time like that?”
After enjoying the brief silence, he spoke in an exaggerated tone.
“Oh my god! There’s no such thing as a problem Seoha can’t solve. But this one won’t be solved? Ah! Then this must have been a problem with no answer to begin with!
In other words, I think there’s a strong possibility that this is an escape from reality.”
Ngh!
Theo clenched his teeth so hard that a vein stood out at his temple.
Theo knew Alex well.
He never stepped forward for anything that did not make him money.
‘Whatever it is, there must be interests at stake.’
If they stayed silent, Alex would persistently trap them by framing it as running away.
Alex was the sort of person Theo wanted to keep from even hovering anywhere near Seoha.
“I’ve chosen you. I’ll smash you to pieces.”
Theo’s eyes flashed murderously.