Chapter 172
Translator: Dreamscribe
Seo-ha had a dream.
A world where no one understood him. He, too, could not know the thoughts of others. Everything happening around him sounded like nothing more than a loud, droning hum.
"...."
He opened his mouth, trying to communicate with the world. But his words scattered before they could take shape. People's faces twisted.
Hummm- hummm-
The world simply resonated like one enormous beehive.
Indistinguishable vibrations. Noise with neither direction nor meaning. Seo-ha covered his ears, pained by the sound of it.
"Huh?"
Then, all of a sudden, he saw a single line shining in the darkness.
Following it, more numbers and symbols rose up.
The sound that had been tormenting him faded away. As if, amid the static, only a sound of one particular frequency could be heard clearly.
Seo-ha reached out toward it.
The numbers and symbols floating in the air drew one another in and connected.
Perfect logic needed no other interpretation.
A proof invited no misunderstanding.
'The purest form of communication.'
Humans deluded themselves into thinking they understood one another, but their words were always incomplete.
Unnecessary emotions intruded on a conversation, and context got twisted. And so memory was always bound to be distorted.
But numbers and symbols were not like that.
Ducky realized it.
The world was nothing but noise to him; numbers and symbols, which were meaning itself, were the only language he could accept.
"You awake?"
When he opened his eyes, he was inside a hotel. Seo-ha looked around.
A room that was not lavish but clean. Su-jeong rose from her chair and drew the curtains back.
Shhk.
Light poured in, dazzling his eyes.
"How long was I asleep?"
"About nine hours."
She observed Seo-ha closely, like a doctor examining a patient.
"I'm fine. More than that, I'd like to get back to the lecture hall quickly."
The thirst refused to subside.
It seemed he would likely stay in this state until the proof was finished.
"Mm, eat something first. The food here's pretty good."
"Sure. I'll get ready and head down now."
As Seo-ha started to get up, Su-jeong stopped him.
"No! I think it'd be better if we ate up here."
"Sorry?"
"It's a bit chaotic out there."
She made an awkward face.
While Seo-ha had been sleeping, the situation had changed. The hotel lobby had been overrun by mathematicians who had come from all over the world.
Su-jeong turned the tablet screen around and showed it to Seo-ha.
[Homeless people lining up at a soup kitchen]
-suspiciously well-educated ones lol apparently over 200 tents went up on the Göttingen lawn. The local McDonald's has temporarily switched to 24-hour service.
Germany normally has every shop closed by two, so what in the world is going on lol
└Because money is precious?
└Göttingen popped up on the live trending list, so I was wondering what was up.
└It's not far, maybe I should swing by too?
└Just landed in Frankfurt. Looking for ride-share passengers.
└Who even are these guys lol they're all old dudes who've won major awards. Andrew Wiles is here too.
└Can somebody pull a live stream?
└No way. You'll get thrown out. There's a sign saying no filming inside.
└What's going on, though?
└My professor's setting off today too. He was all giddy saying some incredibly exciting event was happening?
└WHAT is going on, I'm asking! (rage)
"Apparently the people who'd gone home before the closing ceremony are all heading back over now? It's getting a ton of attention."
"So it seems. This wasn't part of the plan...."
Su-jeong giggled.
"Feeling the pressure?"
"No. I'm trying not to worry about anything else until the proof is done."
Seo-ha hurriedly finished his meal and left the hotel.
'How long can I hold out?'
Even while he slept, Ducky would not sink back beneath his consciousness.
An impulse too powerful to be bargained with. The situation would only grow harder. And so he had to settle this before he let people see something unsettling in him.
Creeak-
As the door opened, the murmuring lecture hall fell silent.
As though he had seen nothing at all, Seo-ha strode straight up to the blackboard, his footsteps steady. The moment he picked up the chalk, Ducky lifted its head.
Endless layers of numbers, stretching on forever; now the integers were a space.
Seo-ha's consciousness was sucked into that place in an instant. And in one breath, he began writing out the equations.
Andrew Wiles stood watching the blackboard, arms folded.
Up until yesterday, it had all been preparatory work for laying out the logic. From today, the real work would begin in earnest.
'That aside, what extraordinary concentration.'
He never once looked around.
Every seat was filled, with people sitting even in the aisles, yet he showed not the slightest sign of caring.
Scratch, scratch.
Seo-ha's chalk cut across the blackboard without hesitation.
Equations were written down, and the core logic unfolded.
"Hm?"
"Th-that's...."
The scholars filling the hall doubted their own eyes and shifted in their seats.
What Seo-ha had written was Alexander Grothendieck's Étale Cohomology notation. And yet it was being defined over Alain Connes's Noncommutative Geometry space.
"What on earth.... Those two are concepts that should never be able to mix."
A bewildered murmur spread among the professors.
By their common understanding, the integers were nothing more than a set of points existing discretely within Euclidean Space. With no continuous surface, they could not hold the oscillations of the Zeta Function.
'No, wait, is this possible?'
Andrew Wiles's mind was racing faster than ever before. Seo-ha was creating a Manifold that endowed the integers with a geometric spatial structure. It was an unprecedented sight: the dynamic laws of Quantum Mechanics being transplanted onto the classical soil of the integers.
Scratch, scratch.
Seo-ha's hand sped up.
He had fallen into a trance. The moment he accepted the runaway Ducky just as it was, his field of vision changed. The walls and ceiling vanished and the space expanded. What unfolded in their place was an infinite space of numbers. The endlessly extending zeros of the Zeta Function were embedded in a multidimensional space, glittering like stars.
Seo-ha looked down on them from a dizzyingly far distance.
'I can catch it.'
He could see it. All of it.
Where he had to go to find the Operator.
Seo-ha compressed the infinite possibilities, which had seemed utterly impossible to resolve, into equations. A revolutionary idea: using Projective Modules to carry the role of Vector Bundles over into the noncommutative world.
It was a break from convention the likes of which the mathematical world had never heard of or seen, but to Seo-ha it was an utterly self-evident inevitability.
For the professors watching, however, it was a different matter.
'What in the world is this? Far too many of the intermediate steps are missing.'
'He's too young. His ambition has run ahead of him. To make such an elementary mistake.'
'Is it really all right to assume Topological Continuity is true without a separate proof?'
Disbelief spread across their faces.
'There's nothing more to see here.'
The scholars shook their heads and looked at Andrew Wiles, seated in the front row.
Because they figured a man like him would have spotted the error long ago.
"Huh?"
He wore a look of utter astonishment. Eyes wide, mouth hanging open.
He traced back through the equations Seo-ha had written, one by one. The parts that, at a glance, looked like excessive leaps. The holes in the logic that seemed to skip ahead without grounds. And yet-
'It's all connected.'
What would happen if every one of those were assumed to be true?
Gulp.
He swallowed.
In his youth, he had spent seven years alone trying to solve Fermat's Last Theorem. Counting the years of preparation, it had been more than a decade.
The sensation he had felt back then came back to life. There were things that the eyes of people who had thought in only one fixed way for decades could never see. Without realizing it, Andrew Wiles half-rose from his seat.
Nngh-
Those who had been shaking their heads in disbelief began, one by one, to take out their notebooks.
Whitman watched them and let out a small chuckle.
'You people truly don't acknowledge Seo-ha, do you.'
Would they have reacted the same way if the one standing up front had been Andrew Wiles or Cronen?
Surely they would have first looked back to check whether there was any error in their own thinking.
'But the leaps are too great. This isn't like Seo-ha.'
Just as he was thinking that Seo-ha might be feeling the pressure, Theo made his move.
Swish.
He and his teammates moved around, handing out printouts.
Summary sheets for fourteen Lemmas.
"For the proof of the Injectivity of Module Morphisms, please refer to this one."
"This one is on Poincaré Duality."
"Commutator Estimate and Trace Class Convergence over here."
"Existence of the Spectral Gap."
Seo-ha's theory was merciless.
Each and every one of the derived theorems was complex enough to demand its own independent proof. As a result, they became an enormous wall blocking the professors' understanding.
Whether they were growing to resemble Seo-ha or not, Team Apex handed out the printouts with indifferent expressions.
"Heh heh heh."
"How long must they have been preparing this? It wasn't some spur-of-the-moment development."
Theo gave a wry smile.
The plan had been to publish it as a paper, but leaving things as they were seemed bound to cause confusion, so they'd had no choice.
The professors ran their eyes over the team members' faces.
'Far too young.'
"Um... did Seo-ha prepare this too?"
A professor from Finland cautiously raised his hand and asked.
Cecilia narrowed her eyes slightly and answered.
"This wasn't something worth his stepping in for."
A glint of intrigue mingled in their eyes.
For them to have completed the Lemmas meant they fully understood the structure of Seo-ha's final argument. Had there ever been people capable of such a thing at that age?
Overshadowed by Seo-ha though they were, these people too were formidable monsters in their own right.
Scratch, scratch.
The second blackboard was completely filled.
"Seo-ha, the rest tomorrow."
At Theo's restraining word, Seo-ha's chalk came to a stop.
He drew a small, deep breath, then nodded. For a moment the lecture hall went quiet. Once Seo-ha had left and even Team Apex had all filed out of the hall, a small commotion broke out.
A space where hundreds of professors sat, and yet, strangely, the mood was one of everyone watching everyone else's reactions.
"...Er, Professor Meyer."
Schmidt of the University of Bonn, who had been sitting in the next seat, cleared his throat and casually struck up a conversation.
In his hand, the Lemma summary sheet was clutched tight.
"About that Lemma number eight from earlier. The part on Trace Class Convergence in noncommutative space. Do you really think that holds?"
Meyer hastily shut his own notebook.
Because in the corner of the notebook, the words 'Why on earth?' had been written several times over.
"Ah! You mean that part! Ahem, ahem. Well, theoretically.... I suppose the possibility isn't entirely out of the question. Still, wouldn't it need verifying? How far did you follow it yourself?"
"M-me? Oh, I followed pretty much all of it. It's just that on the last bit with the Projective Modules my thinking got a little tangled, so I was going back over it."
It was a lie.
An awkward silence flowed between the two men.
In truth, it was not just the two of them. An awkward mood hung thick over the entire lecture hall.
'Am I the only one who doesn't get it?'
'Still, I've got my reputation to think of. I should at least pretend to know a little....'
While some of the professors walked a tightrope between saving face and getting practical results, Andrew Wiles and Whitman had their heads together.
"This might actually come together."
"Hmm...."
"When the moment of proof comes, I don't want to be standing there like a fool, not understanding a thing. I want to cheer alongside Seo-ha."
Andrew Wiles said with a hardened expression.
Whitman felt the same.
"Let's put together a study group. If we fill in each other's gaps, we should be able to sketch out a rough outline by tomorrow."
The professors split into groups.
The vanguard was a group led by Andrew Wiles and Whitman, gathering the winners of the Three Major Math Prizes and the authorities from the top universities. It was no childish clique. It was simply that those who could give and receive help on the same level had naturally come together.
The second was a group that had not fully digested Seo-ha's theory but had no wish to give up. This had less to do with differences in ability than with reasons tied to their fields of specialty.
These were people with no direct point of contact with the Riemann Hypothesis: Topology, Partial Differential Equations, Combinatorics, Probability Theory, Mathematical Physics, and the like. They were not afraid to ask questions, mingling actively and trading knowledge.
The last group held the largest number of people.
Mostly young professors and postdocs, they realized they could not catch up with Seo-ha's theory in any short span of time. And so they did not dare work up the nerve to criticize or verify the theory.
Instead, to become witnesses to this historic scene, they opened their laptops and transcribed Seo-ha's board work into digital form. Relaying the situation in real time to their respective mathematics communities and basking in the attention was a bonus on top.
"All right, has anyone understood the Vector Bundle transformation part of Lemma twelve?"
"Professor Andrew Wiles annotated it right here. He says this path is the correct one!"
The 600-seat auditorium, another lecture hall in the building next door, the cars in the parking lot, even the inside of a large tent. In every different zone, scholars gathered and held their debates.
Late at night, Andrew Wiles stepped outside the building to collect a delivery of late-night food. Carrying the pizza boxes in his arms on his way back, he stopped in his tracks.
"Ah...."
He let out a single cry.
The scene that unfolded through the cold night air was nothing short of magnificent. Hundreds of tents packed the lawn in front of the auditorium.
Tents of every color, red, blue, and yellow, caught the light of the streetlamps and glittered like jewels. In front of each tent, lights burned, and scholars could be seen wrestling away with paper and pen in hand.
All at once, he was reminded of a summer math camp he had attended in the far-off days of his childhood.
"Hahahaha!"
He laughed out loud, sounding truly delighted.
*****
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