Chapter 256

Translator: Dreamscribe

Cronen's steps slowed.

The Teaching Assistants looked at him with puzzled expressions. He gave a bitter smile inwardly.

'I suppose I really have been away for a long time.'

A full five years.

That was how long he had shut himself away from the world in an old, isolated research building at the Institute for Advanced Study in Princeton.

Seeing the young Teaching Assistants fail to recognize him immediately made him realize anew just how long he had been absent from academia.

'That Teaching Assistant seems to know who I am, though.'

Otherwise, he would never have been allowed inside so easily.

Knock, knock!

He lightly knocked on the office door. But there was no response.

Creak.

When he opened the door and stepped inside, he saw Seo-ha.

Unlike in the past, he was now a grown man. He was reclined in his chair, fast asleep.

'It feels like only yesterday that I first saw him....'

He could still remember it vividly.

A3 sheets covering every inch of the room, intricately tangled graphs, and an Automata diagram occupying the center of the blackboard.

Even for a man who had been hailed as one of the world's greatest intellects, it was an unforgettable memory.

How shocked he had been when he learned that the person who had filled the blackboard was a thirteen-year-old boy. As Cronen traced the remnants of the proof, he had been unable to contain his admiration for the boy's extraordinary intuition.

Seo-ha had become an adult before he knew it.

Just as he had expected, no, far beyond his expectations, Seo-ha had grown into a remarkable mathematician.

“I'll wait here until Professor Yu wakes up.”

“Understood.”

When Cronen gestured toward a chair as he spoke, the Teaching Assistant withdrew without complaint. Looking around, he found the office surprisingly modest.

'Where's his Fields Medal?'

Professors usually displayed the medals and plaques they had received in their offices. Yet there was nothing of the sort here.

One wall was covered by a blackboard, with unfinished equations layered across it. The bookshelves were packed with mathematics books and tightly arranged binders of papers.

“Hmm.”

The equations on the blackboard were interesting. But they dealt with practical problems in physics. They were not what he had come for.

How much time had passed?

Rustle.

Seo-ha's body stirred, and the blanket draped over him slowly slipped down.

He opened his eyes and stared blankly at Cronen. Seo-ha's eyes widened. He slapped his own cheek once, then blinked.

“Professor Cronen?”

“Have you been well, boy? I suppose I should call you Professor now.”

He looked as though time had passed him by, hardly changed from the past. His characteristic sharpness remained as well.

Seo-ha sprang to his feet and bowed.

“I... It's been a long time, Professor!”

“Yes. You must have been quite tired.”

Cronen spoke with a faint laugh. Seo-ha hurriedly ran a hand through his disheveled hair.

“I'm sorry. There's something I've been struggling with lately. But what brings you here, Professor....”

Seo-ha had recently lost his sense of direction.

What should he research? And was it even right for him to pursue it?

“Curious?”

There was a playful look on Cronen's face.

As if he had an idea of what this was about, Seo-ha nodded.

“I heard from the Dean that you've been attempting one of the Millennium Prize Problems.”

“I was.”

“What?”

Past tense. Did that mean he was no longer working on it?

Seo-ha's expression stiffened. As if to tell him there was nothing to worry about, Cronen shook his head and spoke.

“For the past decade or so, I've devoted myself to the Yang-Mills Mass Gap Hypothesis.”

One of the Millennium Prize Problems, regarded as one of the ultimate challenges spanning quantum mechanics and mathematics.

Seo-ha's mouth fell open. It was a problem he had once resolved to challenge someday as well.

“You completed the proof?”

“Hahaha! I knew that would get your attention.”

Cronen laughed cheerfully and opened his bag.

Click.

A thick stack of papers.

“This is....”

“Read it. Take your time.”

Ellie brought coffee at just the right moment.

Rustle.

The sounds around him faded away. Seo-ha sank into the equations.

Yang-Mills Theory was an attempt to mathematically explain the phenomenon in Quantum Chromodynamics where quarks and gluons never appeared in isolation, the phenomenon known as Color Confinement.

Put simply, it worked like this.

Split an atom, and protons and neutrons emerged. Split those further, and particles called quarks appeared. Yet strangely enough, not once had a single quark ever been observed completely isolated on its own. Quarks always existed in pairs or groups of three.

They were like balls connected by an invisible rubber band.

When they were close together, the band was slack, so no tension could be felt. But when one tried to pull them apart, the band stretched taut and the force pulling them back together grew stronger.

What happened if one kept pulling anyway?

Astonishingly, the instant the band snapped, a new pair of balls appeared on the spot.

Quarks always existed in multiples.

The particles that acted like the rubber bands connecting them were gluons, and Yang-Mills Theory was an attempt to describe that force.

Because Seo-ha had a deep interest in quantum mechanics, he was able to grasp the progression of Cronen's argument faster than almost anyone else could.

He could feel anger in the equations.

Yang-Mills Theory had first arisen as a problem in physics.

As physicists often did, they had pushed ahead without rigorous mathematical proof, insisting, 'The experimental results match, so the hypothesis must be true.'

That was how Lattice Gauge Theory had come about.

Naturally, Cronen had refused to accept even a single line of it. For this seeker who had pursued nothing but the utmost rigor of pure mathematics, such compromise must have been nothing short of an insult.

'Incredible.'

Between every line of equations, it felt as though Cronen were saying this.

'I'll take the incomplete hypothesis you carelessly threw together and finish it with flawless mathematics.'

Relentless arrogance and obsession.

'He used von Neumann Algebra.'

Seo-ha could already envision the argument that was about to unfold.

He reframed the question of whether a mass gap existed into a question of what type the algebra belonged to.

He bound physical reality with the rigidity of an abstract algebraic structure.

'Genius. Elegant and beautiful. But....'

Could this argument really be carried all the way through? There had to be countless obstacles to overcome.

“This is....”

Yu-Riemann Geometry.

Seo-ha looked at Cronen with wide, rabbit-like eyes. Cronen spoke in a low voice.

“I had failed to complete the proof. I knew which path was correct, but I had no means to support it.”

“Ah! So that's why....”

Cronen nodded.

“Exactly. That's why I went into the cave. I thought it would be possible. But even after years, I couldn't solve it. Not until I read your book....”

Cronen had taken the weapon Seo-ha had given to the world, honed it on his own, and used it to dismantle the twisted axes of Yang-Mills space one by one.

A chain law that precisely canceled out the critical points that diverged as Gauge Symmetry broke down through higher-dimensional curvature projections.

What other mathematician could have conceived of something like this?

Seo-ha felt goosebumps rise across his skin.

But true to its status as a Millennium Prize Problem, the Yang-Mills Mass Gap Hypothesis was vicious.

As the pages entered the latter half, cracks began appearing in the tightly woven theory. The once-straight handwriting started wavering here and there. This was also where noticeably larger blank spaces began appearing on the pages.

Yellowed paper, equations stained by spilled coffee. It was easy to imagine just how many long hours Cronen had spent agonizing over them.

'The constraint conditions are conflicting with the Yu-Riemann Matrix.'

The non-Abelian gauge fields were oscillating wildly in every direction. There seemed to be no possible answer.

Then a thought flashed through Seo-ha's mind.

“Could it be....”

If his idea was correct, this might not be a dead end after all. And if it was Professor Elijah Cronen....

His heart pounded.

Seo-ha calmed his thundering chest and rapidly flipped through the pages.

***

Two hours had passed since Seo-ha began reviewing the paper.

Elijah Cronen sat with one leg crossed over the other. Seo-ha's eyes raced across the pages.

'Impressive indeed.'

There was a reason Cronen had secluded himself and devoted himself to the proof alone. Unlike at the beginning, the theory had become excessively abstruse.

There were only a handful of scholars in the world who could even follow it.

Yet Seo-ha had understood the paper in a single sitting.

His expression changed from moment to moment.

'He must be surprised.'

Watching his face was entertaining.

But the important part was the end. As though Seo-ha had realized something, his hands grew more hurried as he turned the pages. And finally, he reached the last page.

Rustle.

“Phew.”

Seo-ha let out a long breath with his eyes closed.

He slowly opened them. His eyes trembled, and his face was flushed. It had been a very long time since another mathematician's paper had sent a thrill through him like this.

“Now do you understand why I came to see you?”

“Yes.”

Cronen had broken through the final obstacle using Seo-ha's 13-Step Hypothesis. More precisely, Step Eight, path convergence in uncountable space.

Unless that was proven first, his theory would remain nothing more than an armchair theory.

“I waited two years. But I heard nothing. What in the world have you been doing?”

“....”

“Are you hesitating? Because you're afraid the world won't be able to keep up? Or are you worried about the disaster you might unleash?”

Seo-ha's head snapped up.

If a new theory of computation were proven, and if someone sufficiently intelligent were to misuse it, a horrifying weapon could be born.

Was that why? He had not been proactive about proving the 13-Step Hypothesis.

Cronen had seen straight through Seo-ha's hesitation.

“There must be a reason someone like you was born.”

“....”

His gray eyes looked steadily at Seo-ha.

“What is it that you ultimately want?”

“I want the truth.”

“Then the fear that must be paid as its price is also yours to bear.”

Seo-ha lowered his head.

“I don't think I'm that remarkable a person.”

“Look at me.”

Seo-ha raised his gaze.

“When Yu Seo-ha was a thirteen-year-old child standing before that classroom blackboard, what did he fear? Nothing. All you wanted to know was whether that equation was true or false.”

Seo-ha's eyes reddened.

The truth was, he had wanted to talk to someone. He had wanted to pour out his worries and finally feel relieved. But perhaps because he could not, he had kept escaping into cryptography, and then into disease research.

“No one can understand the fear you carry. Not even I can.”

“Professor....”

“I realized something this time. I thought I had reached my limit, but once I climbed onto your shoulders, I could finally see the landscape beyond it. I believe this is why God sent you into this world. To become a light in a world of darkness. So....”

A brief silence passed.

“Fulfill the purpose given to you. The world may become better through it, or it may become worse. But none of that can diminish the value of the truth you discover.”

Outside the window, the sun was slowly sinking below the horizon. At last, Seo-ha slowly raised his head.

“...I'll do it.”

A faint smile spread across Cronen's lips.

“I'm counting on you. You need to prove it if I'm going to be remembered as the mathematician who solved a Millennium Prize Problem, don't you think?”

“Hahaha!”

The two continued catching up until late into the night.

*****

For more chapters, join my Patreon: https://patreon.com/dreamscribe

If you enjoy this novel, please review and rate it at Novelupdates. Thanks! 😊

To receive the latest update notifications or report mistakes, join our Discord server linked below.