Chapter 177
Translator: Dreamscribe
On the streets of Göttingen, blanketed in thick dawn fog, while the tent village on the auditorium lawn was still deep in slumber, Seo-ha quietly opened his eyes.
Today was a day with an important appointment. He put on the neatest clothes he owned and slipped out of his hotel room without a sound. In his hand he carried the flowers he had prepared the day before.
When he came down to the lobby, Theo was nodding off, his head bobbing. On the table sat an empty coffee cup, and an open laptop screen, perhaps from a night of working straight through, blinked white.
"Where are you off to?"
Roused by the sense of someone there, he opened his eyes, and when he saw Seo-ha, he rubbed them as he asked.
"I didn't mean to wake you. There's just somewhere I wanted to go quietly, on my own."
"A place in Göttingen you'd go to alone, at this hour."
Theo stretched and rose from his seat.
"I think I know where. I'll drive you."
Seo-ha gave a small nod.
This city, the sacred ground of modern mathematics, was also the final resting place of great scholars. Among them was someone Seo-ha very much wanted to meet.
Theo grabbed the car keys and led the way. The cold dawn air felt good. Old buildings swept past beyond the car window. Seo-ha thought it was as if time in this city had stopped a hundred years ago.
The car came to a stop at the Göttingen municipal cemetery.
Great old trees rose thick and dense, and gravestones cloaked in green moss spoke of the passage of years. It felt less like a cemetery than a quiet park deep in the woods.
"I'll wait here."
"Thank you."
Seo-ha slowly made his way along the fog-laced path.
Max Planck, Otto von Guericke, Max Born. He passed gravestones engraved with the names of great figures he had only ever seen in textbooks. And then, at the very end of the path, he came upon a modest-looking headstone.
DAVID HILBERT
1862 — 1943
A great scholar who had commanded the world of mathematics in the late nineteenth and early twentieth centuries.
Seo-ha came to a quiet stop before the headstone.
There, alongside his name, was carved the belief he had devoted his entire life to proving.
「We must know. We will know.」
A sublime declaration that no problem lay beyond the reach of human reason, and that ignorance would not be tolerated.
Seo-ha's lips parted.
"Professor Hilbert."
At the 1900 International Congress of Mathematicians in Paris, he had laid out twenty-three unsolved problems for humanity to tackle in the twentieth century. The eighth of them was the very problem concerning the distribution of primes, the one that encompassed both the Riemann Hypothesis and the Goldbach Conjecture.
Swish.
Seo-ha ran his hand over the cold headstone. Then he set down before it the flowers he had brought.
Had he been happy in his final years?
Seo-ha guessed that he had not been. His confident declaration had been mercilessly trampled by Kurt Gödel, the mathematician who became a legend at the age of twenty-five.
"I think I understand the despair you must have felt after you encountered Gödel's Incompleteness Theorem. His theory must have shaken to its very roots the belief you'd held your whole life."
Seo-ha recalled Riemann's Demon, the one he had seen at the auditorium.
The bewilderment of the moment when the logic failed to close and instead diverged into imaginary numbers. A mere fragment though it was, it had unmistakably been the other face of incompleteness. The terrible monster that had crushed Hilbert's dream. He had not been able to raise a single objection against Gödel's logic.
"But I, even if only a very little, have seen beyond the wall."
Strength filled Seo-ha's voice.
Gödel is right.
The mathematics humanity possesses is incomplete, and no axiomatic system can prove its own freedom from contradiction. So what is to be done? Must one simply give up?
No. Twist space, expand its dimensions into spacetime, and forge a new language, and the door that was shut will at last be forced open. The geometry Seo-ha had created was the proof of exactly that.
"And so you were not wrong. Because I figured it out, in the end."
Whoooosh-
The dawn wind blew in, and the leaves swayed.
It was as if a sleeping giant were answering Seo-ha's words with a pleased smile. Seo-ha closed his eyes and felt it. A faint smile bloomed at the corners of his mouth.
After stroking the headstone for a long while, Seo-ha stepped back and quietly bowed his head. It was a sincere show of respect and reverence toward a senior mathematician who had borne the weight of his age.
"Rest easy now."
He drew out a single sheet of paper he had carried inside his coat and laid it before the headstone. Then he picked up a small stone and set it on top.
Rustle.
After Seo-ha had gone, Dean Whitman emerged from behind one of the great old trees.
His academic roots were in Göttingen. Whitman, too, had been one of the countless students of mathematics who, in their youth, had stood before this headstone and taken Hilbert's grand declaration to heart.
The Dean carefully removed the stone Seo-ha had placed and unfolded the paper beneath it.
「On the Geometric Structure of Primes and the Zeros of the Zeta Function.」
-Author: Yu Seo-ha
-Affiliation: Department of Mathematics, Massachusetts Institute of Technology
"This is...."
Whitman's wrinkled hand trembled.
He had heard the words Seo-ha spoke before the grave. Gödel's paper, published in 1931, and the Halting Problem that Alan Turing put forward soon after.
The two geniuses had mathematically proven the existence of an absolute wall of logic that humanity could never pass beyond.
For the past century, modern mathematics had done nothing but cautiously expand its territory beneath the colossal barrier they had erected, the one called 'incompleteness'.
But just moments ago, the young Crown Prince from Korea (everyone had read Reporter Nam's article) had quietly made a declaration before this grave. That he would not accept the limit, that he would challenge head-on the iron wall Gödel had raised.
The cover of this paper was both the proof of it and a declaration of war.
"Haha...."
A helpless laugh slipped out. And it soon turned into a roaring fit of laughter.
"Hahahaha!"
In the still cemetery at dawn, the old scholar's delighted laughter rang out.
"Arrogant, and yet dazzlingly beautiful."
Was the Riemann Hypothesis merely the start of it all?
If the new geometry that boy had created took full root in academia, a great upheaval would follow.
He was certain Seo-ha would not stop. If problems once thought impregnable, like the Goldbach Conjecture or the Navier-Stokes Equations, were solved, what would the future hold?
Hilbert may have been frustrated, but he had never once given up. That was why he had asked for this phrase to be carved into his gravestone. As a message to the mathematician who would seek him out in the future.
Whitman carefully laid the paper Seo-ha had left back down before the headstone. And in a small voice, he whispered.
"Did you see, Professor? Your wait was not in vain."
By now it was morning.
The rising sun bathed the cemetery in golden light.
* * *
A few days later, having wrapped up every part of their schedule in Germany, Seo-ha and the team boarded a flight back to the United States.
"Why is Seo-ha so popular with all these older guys?"
Su-jeong asked, slurping coffee up through her straw.
The night before Seo-ha was due to leave, middle-aged scholars had come swarming into the hotel in a great crowd. They had created quite a spectacle, pulling out Seo-ha's old papers or treasured notebooks of their own and asking for his autograph. One professor even gripped Seo-ha's hand tightly, his eyes brimming with tears.
"Because to them, Seo-ha is no different from a rock star. He shattered the limits of the discipline they'd given their whole lives to and showed them a brand-new universe."
Theo answered with a faint smile.
The plane crossed the Atlantic and touched down safely at Boston Logan International Airport. Back at MIT, the team headed straight for the lab without even a moment to unpack. There was an important task left for them to finish.
"Final review's done. No typos, and the typesetting's perfect."
"Good. Then I'm uploading it."
Click.
The instant Theo clicked the mouse, the massive paper, all four hundred pages of it, was sent off to the arXiv server.
* * *
"It's up!"
"For real? Download it, quick!"
Countless scholars who, because the semester was in session, because of projects still in progress, or simply for lack of time and money, had been unable to attend the historic event in person.
For the past ten days, these people had been through hell. They had gathered the scattered fragments of information drifting around the internet, but like blind men groping at an elephant, they could not piece together the whole. Naturally, their curiosity and their thirst had only swelled to a frenzied pitch.
News that the paper had been posted spread through the math community and social media within minutes. And from all over the world, download requests began pouring in all at once.
Five hundred, a thousand, ten thousand, seventy thousand....
The download count, which had been climbing like mad, suddenly stopped. Cornell University's main arXiv server, which had never once gone down since its launch in 1991, could not withstand the unprecedented traffic and crashed.
└The archive crashed! Gimme! I said gimme the file!
└Why does it have to die right when it's my turn...
└Anyone willing to shoot it over by Google Drive or email? Please, I'm getting lightheaded over here!
└Cornell, you jerks! What have you been doing with all those donations instead of beefing up your servers!
└For sale. Yu Seo-ha's Riemann Hypothesis paper PDF, never opened.
└Undergrads, have a heart and download it tomorrow. You won't get it anyway.
└Tomorrow's seminar is 100% going to be about this, and I can't prep because I don't have the paper. Please, someone save me!
When the server went down, the community turned into utter chaos.
It was not Cornell's fault. On any ordinary day, the traffic for math and science papers was as calm as a lake. Who could have guessed that the world's intellectuals would all come rushing in at the same moment, like fans scrambling for idol concert tickets?
The scholars who fought through the competition and managed to download it opened the PDF file with trembling hands. And before they had turned more than a few pages, they fell into utter confusion.
"Is this really possible?"
A structure that rebuilt geometry and number theory from the ground up. They were struck as though hit over the head with an iron hammer.
"Somebody explain this!"
But even when they wanted to ask, there was no one around who knew. And so, quite naturally, their shock and awe transformed into an enormous volume of questions that began raining down on MIT and Apex Lab like a bombardment.
* * *
"Aaaaaargh!"
In Apex Lab, Sri, who had been staring blankly at his laptop screen, clutched his head and screamed.
"How many emails is this...."
"I think the shared inbox has already blown up?"
Beside him, Su-jeong and Cecilia were left shaking their heads in disbelief.
"And they're still coming in."
Ding-
Ding-
The notifications rang without pause. Sri moved to shut his laptop, then stopped his hand. Running from reality would solve nothing.
Messages were flooding Seo-ha's personal social media accounts as well. Most of them were long, detailed questions.
Rrring!
The lab's internal phone line rang without stopping. Ben, worn ragged, screwed his eyes shut and yanked out the cord.
"We need a plan."
It would have been nice if they could simply ignore it all, but they couldn't even do that.
Theo scanned the list of senders.
The Institute for Advanced Study in Princeton, Oxford's Department of Mathematical Physics, the Clay Mathematics Institute....
Perhaps feeling a sense of responsibility, Seo-ha spoke with a grimly determined face.
"I'll try to answer as many as I can. If I pull out the common questions first and organize them...."
The instant he went to place his hands on the keyboard, Theo stopped him.
"No."
"What? But...."
He shook his head.
"The list of questions alone is already in the thousands.
The thing is, this is only the beginning. Even if the whole team did nothing but write answers twenty-four hours a day, it'd take months. This just isn't an amount we can physically handle on our own."
"Then what do we do?"
He's the experienced adult here; it falls to him to step up and handle this.
Theo was running through various scenarios in his head when a familiar voice came from behind him.
"That's a problem I think I can help with."
Dean Whitman said as he walked into the lab.
"Seo-ha, from this moment on, you're going to write a book. You'll lay out the concepts and principles of the geometry you created in language the academic world can understand. It would be best to write it assuming undergraduates will be the ones reading it."
"Undergraduates?"
He tilted his head.
The ones sending in questions are mostly professors and PhDs, so why undergraduates, all of a sudden?
"That alone will make half the questions vanish. The other half, the lab can handle at its own level."
Seo-ha's face darkened.
Because it was obvious that while he sat comfortably writing a book, his handful of teammates would be ground down by months of grueling labor.
"With just five people? I'm sorry, but that's..."
The Dean cut Seo-ha off.
"Who said anything about five people?"
"What?"
"You have reliable allies, don't you? Among themselves, they call it the '512 Brigade', I hear."
The Golden Generation that would one day share in MIT's peak era alongside Seo-ha. This time, only the select few who could understand Seo-ha's paper were summoned.
Years later, whenever they looked back on this time, every one of them would brag about it with a face full of pride.
So, they would ask the others, were you there for the 'Officers' Mobilization Order'?
*****
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