In the streets of Göttingen, where the dawn fog lay thick, while the tent village on the Auditorium lawn was still sunk in deep sleep, Seoha quietly opened his eyes.
Today was an important day. He put on the neatest clothes he owned and silently left his hotel room. In his hand were the flowers he had prepared the day before.
When he came down to the lobby, Theo was nodding off. An empty coffee cup sat on the table, and the screen of an open laptop, as if he had been working all night, blinked white.
“Where are you going?”
Woken by the sound of someone moving, he looked at Seoha, rubbed his eyes, and asked.
“I wasn’t trying to wake you. There’s somewhere I wanted to visit quietly on my own.”
“A place in Göttingen you’d go alone at this hour.”
Theo stretched and rose from his seat.
“I think I know where. I’ll drive you.”
Seoha gave a small nod.
This city, a sacred ground of modern and contemporary mathematics, was also the resting place of great scholars. Among them was someone Seoha had wanted, without fail, to meet.
Theo took the car keys and led the way. The cold dawn air felt pleasant. Old buildings slipped past beyond the car window. Seoha thought that time in this city seemed to have stopped a hundred years ago.
The car stopped at the Göttingen City Cemetery.
Great trees rose thickly, and gravestones covered in green moss spoke of the traces of time. Rather than a cemetery, it felt like a silent park deep in the woods.
“I’ll wait here.”
“Thank you.”
Seoha slowly walked along the misty footpath.
Max Planck, Otto von Guericke, Max Born. He passed gravestones engraved with the names of great figures he had only seen in textbooks. And at last, at the end of the path, he found a single modest-looking stone.
DAVID HILBERT
1862 — 1943
A great scholar who had reigned over the world of mathematics at the end of the nineteenth century and the beginning of the twentieth.
Seoha quietly stopped before the gravestone.
There, along with his name, was engraved the faith he had devoted his entire life to proving.
“We must know. We will know.”
A noble declaration that there was no problem human reason could not solve, and that ignorance would not be tolerated.
Seoha’s lips moved.
“Professor Hilbert.”
At the International Congress of Mathematicians in Paris in 1900, he had presented twenty-three unsolved problems that humanity was to solve in the twentieth century. The eighth among them was the problem concerning the distribution of prime numbers, encompassing both the Riemann Hypothesis and Goldbach’s Conjecture.
Srrk.
Seoha stroked the cold gravestone with his hand. Then he placed the flowers he had prepared before it.
Had he been happy in his final years?
Seoha guessed that he had not. His spirited declaration had been mercilessly trampled by Kurt Gödel, a mathematician who became a legend at the age of twenty-five.
“I think I understand the despair you must have felt after encountering Gödel’s incompleteness theorem. His theory must have shaken the faith you held all your life down to its roots.”
Seoha recalled the demon of Riemann he had seen in the Auditorium.
The bewilderment of logic failing to close and diverging into imaginary numbers. Though it may have been only a fragment, it was certainly the other face of incompleteness. The terrible monster that had frustrated Hilbert’s dream. He could not refute Gödel’s logic.
“But I saw beyond the barrier, if only a little.”
Strength entered Seoha’s voice.
Gödel was right.
The mathematics possessed by humanity was incomplete, and no axiomatic system could prove its own consistency. Then what were they supposed to do? Give up?
No. If one twisted space, expanded dimensions into spacetime, and created a new language, the door that had been closed would inevitably open. The geometry Seoha had created was proof of that.
“So you were not wrong. Because I found it out in the end.”
Whoosh—
The dawn wind blew, and the leaves trembled.
It was as though the sleeping giant were answering Seoha’s words with a pleased smile. Seoha closed his eyes and felt it. A faint smile rose to his lips.
After stroking the gravestone for a long while, Seoha took one step back and quietly bowed his head. It was sincere respect and courtesy toward a senior mathematician who had borne the weight of an age.
“Now rest in peace.”
He took out a sheet of paper he had brought tucked inside his coat and placed it before the gravestone. Then he picked up a small pebble and set it on top.
Srrk.
After Seoha left, Dean Whitman emerged from behind a great tree.
His academic roots lay in Göttingen. Whitman, too, had once been one of the countless young students of mathematics who stood before this gravestone in his youth and took Hilbert’s grand declaration to heart.
The dean carefully moved aside the pebble Seoha had placed there and unfolded the paper beneath it.
“On the Geometric Structure of Prime Numbers and the Zeros of the Zeta Function.”
-Author: Yu Seoha
-Affiliation: Department of Mathematics, Massachusetts Institute of Technology
“This is…”
Whitman’s wrinkled hands trembled.
He had heard what Seoha said before the grave. Gödel’s paper, published in 1931, and Alan Turing’s Halting Problem that followed.
The two geniuses had mathematically proven the existence of an absolute wall of logic that humanity could never reach.
For the past century, modern mathematics had merely expanded its territory cautiously beneath the great barrier of “incompleteness” that they had erected.
But just now, the young crown prince from Korea—everyone had read Reporter Nam’s article—had quietly declared before his grave that he would not accept that limit, and would challenge head-on the iron wall Gödel had built.
The cover of this paper was both evidence of that and a declaration of war.
“Haha…”
A helpless laugh escaped him. And soon, it turned into a broad, roaring laugh.
“Hahahaha!”
The old scholar’s cheerful laughter rang through the silent cemetery at dawn.
“Arrogant, and dazzlingly beautiful.”
Had the Riemann Hypothesis merely been the beginning?
If the new geometry that boy had created fully took root in academia, a great change would occur.
He was certain Seoha would not stop. If seemingly impregnable problems such as Goldbach’s Conjecture or the Navier–Stokes equations were solved, what would happen in the future?
Though Hilbert may have been frustrated, he had never given up. That was why he had asked for this phrase to be engraved on his gravestone. As a message to the mathematicians of the future who would come to find him.
Whitman carefully set the paper Seoha had left back before the gravestone. Then he whispered in a small voice.
“Did you see, Professor? Your waiting was not in vain.”
Before he knew it, morning had come.
The rising sun dyed the cemetery gold.
* * *
A few days later, after completing every item on their schedule in Germany, Seoha and the team boarded a plane bound for the United States.
“Why is Seoha so popular with middle-aged men?”
Sujeong asked while sipping coffee through a straw.
On the night before Seoha left, middle-aged scholars had flooded into the hotel. They created a strange scene, taking out Seoha’s past papers or their own cherished notebooks and asking for his autograph. One professor even clasped Seoha’s hand tightly, his eyes brimming with tears.
“To them, Seoha is no different from a rock star. He shattered the limits of the field they devoted their lives to and showed them a new universe.”
Theo answered with a faint smile.
The plane crossed the Atlantic and landed safely at Boston Logan International Airport. The team returned to MIT and headed straight to the lab without even unpacking. They still had important work to finish.
“The final review is done. No typos, and the typesetting is perfect.”
“Good. Then I’m uploading it.”
Click.
When Theo clicked the mouse, the enormous four-hundred-page paper was transmitted to the arXiv server.
* * *
“It’s up!”
“Seriously? Download it, quick!”
Countless scholars had been unable to visit that historic site because the semester was in progress, because of ongoing projects, or because they lacked the time and money.
They had spent the past ten days in hell. They gathered fragments of information floating around the internet, but like blind men touching an elephant, they could not draw the whole picture. Naturally, their curiosity and thirst had grown to a fever pitch.
The news that the paper had been registered spread through mathematics communities and social media in a matter of minutes. And download requests began pouring in simultaneously from all over the world.
Five hundred, one thousand, ten thousand, seventy thousand…
The download count, which had been climbing at a mad pace, suddenly stopped. The main arXiv server at Cornell University, which had not crashed even once since the service began in 1991, had gone down under unprecedented traffic it could not endure.
└The arXiv crashed! Give it to me! Give it here!
└Why did it have to happen right when it was my turn? ㅠㅠ
└Can someone send it through Google Drive or email? Please, I’m getting dizzy here!
└Cornell, you bastards! What were you doing with all those donations instead of expanding the servers?
└Selling: Yu Seoha’s Riemann Hypothesis paper PDF, never read.
└Undergrads, be human and download it tomorrow. You wouldn’t understand it even if you saw it anyway.
└Tomorrow’s seminar topic is definitely going to be this, but I can’t prepare because I don’t have the paper. Please save me!
Once the server went down, the communities became utter chaos.
It was not Cornell’s fault. The traffic for mathematics and science papers was usually as calm as a lake. Who could have known that intellectuals from all over the world would rush in at the same date and time as if they were trying to buy tickets for an idol concert?
The scholars who succeeded in breaking through the competition and downloading it opened the PDF file with trembling hands. And after turning only a few pages, they fell into extreme confusion.
“Is this really possible?”
A structure that rebuilt geometry and number theory from the ground up. They felt a shock as if they had been struck in the head with a sledgehammer.
“Someone explain this to me!”
Even if they wanted to ask, there was no one around who knew. Naturally, their shock and emotion transformed into an enormous number of questions and began to bombard MIT and Apex Lab.
* * *
“Aaaaaaargh!”
At Apex Lab, Sri, who had been staring blankly at his laptop screen, clutched his head and screamed.
“How many emails are there…?”
“I think the shared inbox already crashed.”
Sujeong and Cecilia, who were beside him, also stuck out their tongues in disbelief.
“They’re still coming in.”
Ding—
Ding—
The notifications rang without pause. Sri was about to close his laptop, then stopped his hand. Running away from reality would not solve anything.
Messages were pouring into Seoha’s personal social media accounts as well. Most of them were long questions.
Ring!
The lab’s internal phone rang nonstop. Ben, looking utterly exhausted, squeezed his eyes shut and pulled out the cord.
“We need a plan.”
It would have been nice if they could ignore them all, but they could not.
Theo skimmed the list of senders.
The Institute for Advanced Study in Princeton, the Mathematical Physics Department at Oxford, the Clay Mathematics Institute…
Perhaps feeling responsible, Seoha spoke with a solemn expression.
“I’ll try to answer as many as I can. If we extract and organize the common questions first…”
Just as he was about to place his hands on the keyboard, Theo stopped him.
“No.”
“Pardon? But…”
Theo shook his head.
“The question list alone is over several thousand.
The problem is that this is only the beginning. Even if the entire team spent twenty-four hours a day doing nothing but answering, it would take months. It’s not a volume we can physically handle at our level.”
“Then what do we do?”
As the experienced adult, he had to step up and deal with it.
Theo was running several scenarios through his head when a familiar voice came from behind him.
“I can help with that problem.”
Dean Whitman said as he walked into the lab.
“Seoha, from now on, you will write a book. You need to organize the concepts and principles of the geometry you created in a language academia can understand. It would be best to write it assuming undergraduates will read it.”
“Undergraduates?”
He tilted his head.
Most of the people asking questions were professors or PhDs, so why suddenly undergraduates?
“Then half the questions will disappear. The lab can handle the remaining half.”
Seoha’s face darkened.
Because it was obvious that while he comfortably wrote a book, the few members of the team would suffer through months of hard labor.
“With only five people? I’m sorry, but that’s…”
The dean cut Seoha off.
“Who said there would only be five?”
“Pardon?”
“You have reliable allies, don’t you? I hear they call themselves the ‘512 Suicide Squad.’”
The second draft order was issued.
In later years, they would become the golden generation that shared MIT’s greatest heyday with Seoha. This time, only a small number of people capable of understanding Seoha’s paper were called in.
When they later reminisced about this time, every one of them would boast with faces full of pride.
So, did you take part in the “officer call-up”?