Seoha had a dream.
A world where no one could understand him. He, too, could not know the thoughts of others. Everything happening around him simply sounded like noisy, buzzing droning.
“···.”
He tried to open his mouth and communicate with the world. But his words scattered without taking form. The people’s expressions contorted.
Bzz-bzz—
The world merely resonated like a giant beehive.
Indistinguishable vibrations. Noise without direction or meaning. Pained by the sound, Seoha covered his ears.
“Huh?”
Then, suddenly, he saw a single line shining in the darkness.
Following it, more numbers and symbols floated up.
The sounds that had tormented him faded away. As if, amidst the static, only a specific frequency could be heard clearly.
Seoha reached his hand toward it.
The numbers and symbols floating in the air drew together and connected.
Perfect logic requires no other interpretation.
Proof invites no misunderstanding.
‘The purest form of communication.’
Humans deluded themselves that they understood one another, but their words were always incomplete.
Unnecessary emotions intervened in conversation, and context twisted. Therefore, memories were always bound to be distorted.
But numbers and symbols were not.
Ducky realized.
To him, the world was merely noise; only numbers and symbols, meaning itself, were the only language he could accept.
“You awake?”
He opened his eyes to find himself in a hotel. Seoha looked around.
A room that was not lavish but clean. Sujeong rose from her chair and drew the curtains.
Swish.
Light flooded in, blinding him.
“How long did I sleep?”
“About nine hours.”
She observed Seoha closely, like a doctor examining a patient.
“I’m fine. More than that, I want to get back to the lecture hall quickly.”
His thirst was not quenched.
He felt he would likely remain this way until the proof was complete.
“Yeah, let’s eat first. The food here is pretty good.”
“Yes. I’ll get ready and head down now.”
As Seoha tried to get up, Sujeong stopped him.
“No! I think it’d be better to eat here.”
“Huh?”
“It’s a bit chaotic outside.”
She made an awkward expression.
The situation had changed while Seoha slept. The hotel lobby had been occupied by mathematicians from all over the world.
Sujeong turned her tablet screen and showed it to Seoha.
[Homeless people lining up at a soup kitchen]
-Suspiciously over-educated, lol. Over 200 tents on the Göttingen lawn, they say. The local McDonald’s has temporarily switched to 24-hour operation.
Usually in Germany, all stores close at two; what the heck is this, lol
└Because money is precious?
└Saw Göttingen trending in real-time and wondered what was up.
└Not too far, should I drop by?
└Just arrived in Frankfurt. Looking for carpool buddies.
└Who are those guys, lol. Aren’t they all old dudes who’ve won major prizes? Andrew Wiles is there too.
└Can’t anyone get a live stream?
└No way. You’ll get kicked out. There’s a sign saying no internal filming.
└What’s going on?
└Our professor’s leaving today too. He was all excited saying an incredibly interesting event is happening?
└What the hell is going on! (Fuming)
“They say the people who returned home before the closing ceremony are all coming back? It’s getting an insane amount of attention.”
“So it seems. This wasn’t in the plans···.”
Sujeong giggled.
“Feeling the pressure?”
“No. I don’t intend to pay attention to anything else until the proof is finished.”
Seoha quickly finished his meal and left the hotel.
‘How long can I hold out?’
Even while he slept, Ducky had not settled beneath his consciousness.
An impulse to the point of being impossible to compromise with. The situation would only grow more difficult. So he had to resolve this before showing people an unsightly side of himself.
Creak—
When the door opened, the buzzing lecture hall fell silent.
Seoha walked with heavy steps to the front of the blackboard, as if he hadn’t seen anything. As he grasped the chalk, Ducky raised its head.
Layers of numbers spread endlessly. Now, integers were space.
Seoha’s consciousness was instantly sucked into that place. And he began writing formulas in one breath.
Andrew stood with his arms crossed, watching the blackboard.
Until yesterday, it had been preparatory work to unfold the logic. From today, the real work would begin.
‘Remarkable concentration, I must say.’
He didn’t look around.
People had filled all the seats and even sat in the aisles, yet he showed no sign of minding at all.
Scratch, scratch.
Seoha’s chalk split the blackboard without hesitation.
Formulas were inscribed, and the core logic unfolded.
“Hmm?”
“T-that is···.”
The scholars filling the lecture hall adjusted their seats, doubting their eyes.
What Seoha had written was Grothendieck’s étale cohomology notation. Yet it was being defined upon Alain Connes’ noncommutative geometric space.
“What in the world···. Those two concepts should never be mixable.”
Bewildered murmurs spread among the professors.
In their common sense, integers were merely a set of points existing discontinuously in Euclidean space. Without continuous faces, they could not contain the oscillations of the zeta function.
‘No, could it be possible?’
Andrew’s mind was spinning faster than ever before. Seoha was creating a manifold that endowed integers with geometric spatial structure. It was an unprecedented spectacle of quantum mechanics’ dynamic laws being transplanted onto the classical soil of integers.
Scratch, scratch.
Seoha’s hand grew faster.
He was lost in a trance. Accepting the rampaging Ducky as it was, his field of vision changed. Walls and ceiling disappeared, and space expanded. What unfolded in their place was infinite numerical space. The endlessly stretching zeros of the zeta function were embedded in multidimensional space, sparkling like stars.
Seoha looked down upon them from an unfathomably distant height.
‘I can grasp them.’
I can see. Everything.
Where to go to find the operator.
Seoha compressed the infinite possibilities that had seemed impossible to resolve into formulas. An innovative idea transferring the role of vector bundles to the noncommutative world through projective modules.
It was a groundbreaking concept never before seen or heard of in the mathematical world, but for Seoha, it was an all too natural inevitability.
However, the professors watching this had a different perspective.
‘What on earth is this? Too many intermediate steps are missing.’
‘Too difficult. His enthusiasm is running ahead of him. To make such a rudimentary mistake···.’
‘Is it acceptable to assume topological continuity as true without a separate proof?’
Distrust spread across their faces.
‘There’s nothing more to see.’
The scholars shook their heads and looked at Andrew, who sat in the front row.
They thought that if it were him, he would have already spotted the errors.
“Hmm?”
He wore a shocked expression. Eyes wide and mouth agape.
He traced Seoha’s formulas one by one. Parts that seemed like excessive leaps at a glance. Logic that seemed riddled with holes, as if skipped without basis. Yet—
‘They are all connected.’
If all of those are assumed to be true, what happens?
Gulp.
He swallowed.
In his youth, he had spent seven years alone to solve Fermat’s Last Theorem. Including preparation time, it was over ten years.
The sensation he had felt then was revived. There are things invisible to the eyes of those who have thought only in certain ways for decades. Andrew unknowingly half-rose from his seat.
Grk—
Those who had been shaking their heads in disbelief began pulling out their notebooks one by one.
Whitman looked at them and snorted.
‘You people aren’t truly acknowledging Seoha.’
Would they have reacted the same if the one standing there were Andrew or Kronen?
Surely they would have first examined whether there was any flaw in their own thinking.
‘But the leaps are too extreme. It’s not like Seoha.’
Just as he thought that Seoha might be feeling the pressure, Theo moved.
Swoosh.
He and his team members moved around handing out prints.
Summaries of fourteen lemmas.
“Please refer to this for the proof of injectivity of the module homomorphism.”
“This is regarding Poincaré duality.”
“The commutator estimate and trace-class convergence.”
“The existence of the spectral gap.”
Seoha’s theory was vicious.
Each derived theorem was complex enough to demand independent proof. Therefore, these became massive barriers obstructing the professors’ understanding.
Team Apex handing out prints with indifferent expressions, as if taking after Seoha.
“Heh heh heh.”
“How long have they been preparing? It wasn’t an impromptu development.”
Theo smiled a wry smile.
They had intended to present it as a paper, but left alone, chaos would ensue, so they had no choice.
The professors scanned the team members’ faces with their eyes.
‘Too young.’
“E-excuse me, did Seoha prepare this as well?”
A professor of Finnish origin carefully raised his hand and asked.
Cecilia opened her eyes wide and answered.
“This wasn’t something he needed to step in for.”
An unusual gleam entered their eyes.
Completing the lemmas meant they perfectly understood Seoha’s final argumentative structure. Had there ever been those capable of such things at that age?
Overshadowed by Seoha, they were no less monstrous themselves.
Scratch, scratch.
The second blackboard was completely filled.
“Seoha, the rest is for tomorrow.”
At Theo’s dissuasion, Seoha’s chalk stopped.
He took a small deep breath and nodded. The lecture hall fell silent for a moment. Once Seoha left and Team Apex also exited the lecture hall, a small commotion broke out.
A space where hundreds of professors sat, yet the atmosphere was strangely one of watching each other’s reactions.
“···Excuse me, Professor Mayer.”
Schmidt from this university, sitting next to him, cleared his throat and spoke furtively.
The summary of lemmas was clutched tightly in his hand.
“It’s about that Lemma 8 from earlier. The trace-class convergence in noncommutative space. Do you really think that holds?”
Mayer hurriedly covered his notebook.
Because in the corner of his notebook, the words “Why on earth?” were written several times.
“Ah! That part! Ahem. Well, theoretically··· it’s not entirely impossible, is it? Though perhaps it needs verification? How far did you understand?”
“M-me? I followed almost all of it. Just got a bit tangled up at the end regarding the projective module part, so I was reviewing it.”
It was a lie.
An awkward silence flowed between the two.
In truth, it wasn’t just them. An awkward atmosphere permeated the entire lecture hall.
‘Am I the only one who doesn’t get it?’
‘Still, I have my pride, so I should at least pretend to know a little···.’
While some professors tightroped between pride and practicality, Andrew and Whitman had their heads together.
“Perhaps it really can be solved.”
“Hmm···.”
“I don’t want to stand there stupidly, unable to understand, at the moment of proof. I want to cheer alongside Seoha.”
Andrew said with a determined expression.
Whitman thought the same.
“Let’s put together a study group. If we fill in each other’s gaps, we should be able to draw up a rough outline by tomorrow.”
Groups split among the professors.
The vanguard was a group led by Andrew and Whitman, consisting of winners of the three major mathematics prizes and authorities from top universities. It was not some childish faction-like gathering. It was merely a natural assembly of those who could help and receive help at the same level, purely.
The second was a group that had not fully digested Seoha’s theory but did not want to give up. This was due more to their fields of specialization than to differences in ability.
Those in topology, partial differential equations, combinatorics, probability theory, mathematical physics, and others without direct connections to the Riemann Hypothesis. They did not fear questions and actively mingled, exchanging knowledge.
The last group contained the most members.
These were mostly young professors and postdocs who realized they could not catch up to Seoha’s theory in a short time. Therefore, they could not dare to criticize or verify the theory.
Instead, to become witnesses of this historic scene, they opened their laptops and digitized Seoha’s blackboard writing. As a bonus, they enjoyed the attention by relaying the situation in real time to the mathematical communities they belonged to.
“Alright, anyone understand the vector bundle transformation part of Lemma 12?”
“Professor Andrew annotated it here. This path is correct!”
The 600-seat auditorium, another lecture hall in the adjacent building, cars in the parking lot, and even inside large tents. Scholars gathered in different zones and held discussions.
Late at night, Andrew came out of the building to receive the delivered late-night snack. He stopped in his tracks as he was returning, cradling the pizza box.
“Ah···.”
He let out an exclamation.
The sight unfolding amid the cold night air was truly a spectacle. Hundreds of tents filling the lawn in front of the auditorium.
Red, blue, and yellow tents of various colors sparkled like jewels under the streetlight. In front of each tent, scholars wielding paper and pen could be seen struggling.
He suddenly thought of the summer math camp he had attended in his distant youth.
“Hahahaha!”
He laughed loudly, seemingly genuinely delighted.