Translator: Dreamscribe
Theo's gaze returned to the chalkboard.
Admiration and excitent could wait. What mattered was not losing the thread.
Having finished his calculations, Seo-ha was scanning the faces of his teammates.
Theo guessed he was checking to see if anyone needed further explanation. Seo-ha gave a satisfied nod and continued.
"An existential minimum is aningless. If there's no reachable path, it's a mathematically Dead Solution."
Sri looked up in surprise, his fingers freezing mid-keystroke on his laptop.
"Wait, so the reason math and engineering haven't been able to find the optimal solution all this ti is also...."
Seo-ha nodded.
"Exactly. All the countless counterexamples that appeared in their papers were for the sa reason. They've been clinging to Dead Solutions this whole ti. They'll never reach their goal that way, no matter how long they keep at it."
Nngh...
Pained groans escaped from all corners of the lab.
Theo pressed a hand to his forehead and looked up at Seo-ha.
"Don't tell you're going to publish this?"
Seo-ha was silent for a mont.
Directly refuting soone else's research was not an easy decision, even for him.
"Yes."
It was a short answer.
But there was no wavering in Seo-ha's eyes.
"Are you sure about this? There's going to be a lot of pushback."
"He's right! There are tons of scholars in engineering working on related research. Maybe we should publish after we've completely finished the proof...."
Su-jeong raised her hand cautiously.
"This paper would invalidate a significant number of existing studies. Setting aside whether the proof is right or wrong, we'd be saying their goal itself was misguided.
If it were , I don't think I could take it."
Theo gave a heavy nod.
"We'd be redirecting the entire field."
Sri hesitated too, then spoke up with difficulty.
"Honestly, my first feeling is worry. If we publish this as a paper, we'd essentially be revealing everything we've built up until now."
Silence settled over the lab.
His concern was a practical one.
At this very mont, hundreds of labs around the world were grappling with similar problems.
Among them, there were surely labs investing far more manpower and capital than Team Apex.
If only the direction were shown, others could always catch up in speed.
Seo-ha nodded as if he understood their concerns.
"We still have to publish. There are people who've poured decades into this. They've spent their entire lives chasing the wrong goal."
Seo-ha lightly tapped the words "False Minima" still written on one side of the chalkboard with his fingertip.
"Every day we stay silent is another day their passion and ti goes to waste."
Su-jeong lowered her gaze.
She had thought Seo-ha's decision was cruel, but in truth, she already knew. The truly cruel thing would be to say nothing.
"And everyone."
Seo-ha paused and t each of his teammates' eyes, one by one.
"Surely you're not worried about having our research stolen?
I'm not considering that possibility at all. Even if soone sees this, there's no way they'd reach the conclusion faster than us.
You'd be hard-pressed to find mathematicians as talented as all of you, even if you searched the whole world."
"Ahem."
Theo cleared his throat.
Caught off guard by the praise, Sri and Su-jeong turned red.
"This research is like walking a treacherous mountain path. Since we're the ones leading the way, let's leave a marker for those who co after us, warning them there's a cliff ahead!"
"A marker before a cliff."
Theo murmured in a low voice.
Whenever Theo saw Seo-ha like this, he felt a sharp ache, as if soone were pricking his heart with a needle.
'This kid....'
That unguarded face.
He was clearly not ready for a fight.
He didn't enjoy debate, and he didn't seem cut out for politics.
And yet, if it was necessary, Seo-ha was the kind of person who would be the first to stand on the blade's edge.
For truth and the common good alone.
'What's going to happen?'
Once the paper ca out, verification would take a long ti.
There might be snide remarks from conferences and reviewers, or deliberate misrepresentation. And Seo-ha would be standing at the center of all that controversy.
Even though he had nothing to gain from it.
Theo let out a slow breath.
'Then I'll do it.'
He would take every attack head-on.
So that Seo-ha could simply keep moving forward, toward the truth and nothing else.
"Then let's get ready. Let's compile a list of expected questions. The attacks will probably co in roughly this order. The distinction between existence and Reachability is...."
Theo's voice shifted into a eting tone.
Su-jeong and Sri nodded and began joining the discussion with passion.
'Once Seo-ha sets the direction, the team supports him with everything they have.'
That was Team Apex's foundational principle.
Theo began organizing a list of questions on one side of the chalkboard.
Numbers were assigned to each item, with concise counterargunts written beside them. Red pen marks were added at every point where an attack might co.
"We definitely need to attach one more counterexample here."
Seo-ha watched the scene in silence.
'The people I chose.'
Only now did it hit him with full clarity that he was holding their ti, their energy, and even their futures as collateral.
And yet, every one of them was following his decision.
Swish.
Seo-ha's gaze turned to the chalkboard.
And without a word, he walked over and began writing the next line beside his equations.
Scratch scratch.
The sound of chalk rang out clearly through the lab, even in the middle of the eting.
That sound was like a vow rising from the depths of Seo-ha's heart.
'More precisely, with greater responsibility.'
Seo-ha steeled himself.
'I will solve this, no matter what.
Because these precious people have chosen to walk this path with .'
* * *
A few days later,
Team Apex's paper was quietly released.
A single paper uploaded to the arXiv without any prior announcent.
[On Unreachable Solutions in Energy Optimization Problems.]
The first few hours were calm.
But the paper began spreading rapidly, driven by the many scholars who had been keeping an eye on Seo-ha.
And from that night onward, the atmosphere shifted.
A lab at the University of Tokyo, Japan.
"Did you see this?"
"Yeah, it's pretty aggressive, isn't it? Our professor's face went bright red after reading it, and he stord out."
"How many years has he been working on this?"
"Over five. The budget's been shrinking too, so the pressure must've been intense."
"Talk about rubbing salt in the wound."
Posts began piling up across public social dia, scientist forums, and conference boards.
[They're blaming theory for the failures of optimization research.]
[I respect the boldness typical of young researchers, but this is disrespectful.]
The reaction from the engineering side was imdiate and fierce.
The statent that decades of accumulated algorithm research had been aid at the wrong goal was, in and of itself, a gauntlet thrown at the entire field.
In fact, a lead engineer at a major Arican tech research lab posted this on a public forum:
[Their paper is nothing more and nothing less than armchair theorizing. Reachability is only aningful under ideal conditions. Real systems are always the product of compromise.]
Beyond that, there was an outpouring of pushback directed at them.
The debate spilled past the boundaries of theory and technicality into an emotional brawl.
They took the stance that the team "didn't understand reality", as if looking at naive children.
[Theorists trying to lecture the field.]
[An arrogant attitude. We've been doing just fine this way.]
ResearchGate, the world's largest science community with over 20 million registered researchers, also exploded.
[Elevating Reachability to part of the definition of a solution is interesting. But isn't this more of a topological issue than solution optimization?]
└Calling existing results "Dead Solutions" was a bit much lol
└The wording is rough, sure, but the counterexample section they presented is hard to ignore. We checked in our lab, and there really is no path under those conditions.
Scrolling down just a little, the tone grew harsher.
└This is a trap young researchers commonly fall into. Redefine the problem and it looks like innovation, right? The world isn't that easy.
└I agree it's overconfidence. Trying to invalidate decades of research with a handful of counterexamples is dangerous.
└Give it a few years and they'll be cringing at this in bed lmao
Yet even amid all of this, there were posts that surfaced as if buried under the noise.
[Our lab has been repeating failures on this problem for the past three years. But after reading the paper, I finally understood why we always hit a wall at the sa point.]
A few sharp-eyed labs were quietly modifying their code.
Experintal conditions were changed and new constraints were added.
Convergence points that had previously been taken for granted were deleted, one by one.
The engineering world was clearly splitting apart.
Into pushback and defensiveness, and a full-scale reassessnt carried out in silence.
And as always, the mathematics community prioritized quiet reflection and verification over emotion.
At the top of MathOverflow, the most authoritative mathematics community, a notice was pinned.
[Emotional evaluations, speculation about intent, and ad hominem comnts regarding this paper are subject to deletion. Discussion is limited to definitions, propositions, proofs, and counterexamples.]
The content of the paper boiled down to a single question.
'Can this definition be accepted?'
So were uncomfortable, so nodded, and most mathematicians simply picked up their pens in silence.
└Isn't attempting to include Reachability as part of the definition of a solution too radical?
└But it's also true that the existing definition failed to explain many of its shortcomings.
└The recurring counterexamples were definitely a problem.
A few days later, BBC ran an interview with a distinguished, elderly European professor.
"I cannot say with certainty that everything in this paper is correct. But if it is wrong, then we must prove why it is wrong."
Team Apex had stepped back from the controversy and was doubling down on preparing their argunts.
Theo was the first to arrive at the lab each morning, scanning through emails.
Conference requests, seminar invitations, anonymous inquiries, or just emotionally charged insults.
"We need to accept this one. This one we ignore for now. This one we respond to after a bit more preparation."
His judgnt was precise and swift.
Su-jeong was organizing her counterexample notes. She further subdivided conditions that had already been compiled once, drawing clearer lines.
"If we change the boundary conditions just slightly here, it creates a counterexample the other side could use against us."
Sri was running simulation logs.
Conditions harsher than those published in the paper. Experints premised on failure. But through that process, data accumulated.
Dean Whitman also weighed in with a comnt.
"Whether their hypothesis is correct is sothing I can't say just yet. But one thing I do know. That paper was clearly an act of consideration. Not an attack."
And then there was the boy who, amid all this uproar, remained terrifyingly focused on the unsolved problem alone.
Theo glanced toward one side of the lab.
Seo-ha was standing before the chalkboard.
Scratch scratch.
On one side of the board, the Reachability conditions and the Integer Barrier were written out separately.
On the other side, traces of the discontinuities that erged when the two interlocked again were densely marked.
Seo-ha moved between the two sides, dismantling the structure piece by piece, as if pulling out stitches.
'Incredible.'
Just how high-dinsional did one's thinking have to be to make sothing 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 guy."
Alex Howard.
Once a rising star in pure mathematics, now a legend of corporate consulting after pivoting to engineering.
A crisp shirt, perfect lighting, a practiced smile.
Behind him, the logo of his company, Arc Wave, glinted.
And beneath it, a tagline.
[Mathematics to Market]
It was the catchphrase he had always championed.
"There's a paper that's been making waves lately, right?"
Alex brought his tablet up to the cara.
The paper's title appeared large on the screen.
[On Unreachable Solutions in Energy Optimization Problems.]
"Speaking as a mathematician myself, this paper commits a very classic error. It takes a mathematically plausible definition and drapes it over the entirety of real-world problems."
He tapped at the word "Reachability" a couple of tis with his finger.
"Reachability is a constraint, not a definition. The mont you turn it into a definition, we can't solve anything anymore."
Laughter from his staff could be heard.
"This is just my personal take, but.... is it possible that Team Apex simply couldn't handle reality? There's this famous genius there, Yu Seo-ha.
He couldn't find the answer. So what happens to a team when that occurs?"
He savored a mont of silence, then spoke in an exaggerated tone.
"Oh my God! There's no problem Seo-ha can't solve. But wait, this one won't crack? Oh! This must have been an unsolvable problem from the start!
In other words, I think there's a strong possibility this is just escapism."
Crack!
Theo had been clenching his teeth so hard that veins stood out on his temples.
Theo knew Alex well.
He never got involved in anything that wouldn't make him money.
'Whatever it is, there's a vested interest at play.'
If they stayed silent, Alex would fra it as running away and relentlessly tighten the noose.
Alex Howard was the kind of person Theo wanted to keep far away from Seo-ha.
"I've chosen you. I'm going to crush you."
A murderous glint flashed in Theo's eyes.
*****
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