Incheon International Airport Arrivals Hall,
“Please look at the camera on your right!”
“Professor, what is the purpose of your visit to Korea?”
“Is it true you came because of the verification of the Four Color Theorem?”
Flashes went off without pause.
Elijah Cronen stood out at a glance, even from afar.
His tall frame, silver hair, ramrod-straight posture, and ice-cold gray eyes made it difficult to guess his age.
A man who had reached the pinnacle of the mathematical world in his mid-forties,
his career, in which he had solved dozens of difficult problems as though collecting trophies, was more than enough to draw praise from people around the world as one of humanity’s greatest minds.
He passed by the reporters with indifferent eyes.
Behind him emerged a young female mathematician.
Chloé Moreau, a topologist from France’s ENS, answered the reporters’ questions briefly despite looking fatigued from jet lag.
“Oui. Something important has happened in the mathematical world here in Korea. I want to see it for myself as soon as possible.”
At another exit appeared Shimura Kenji, a complexity theorist from the University of Tokyo. Japanese media rushed over and surrounded him.
“Professor Shimura! They say world-class mathematicians are gathering in Korea. Are you joining them as well? Can we assume you’re close with Elijah Cronen of Princeton?”
“Professor! There’s a rumor that a thirteen-year-old boy in Korea solved the Four Color Theorem. You’re going to verify that, aren’t you? What do you think of Japan’s promising gifted students?”
Shimura stopped for a moment, looked at the reporters, and sighed.
“What nationality does mathematics have? I am simply here as a fellow researcher to assist with the verification.”
It was an interview with no substance whatsoever, but the Japanese media extracted the headlines they wanted.
[World-Renowned Scholars Gather in Korea, Professor Shimura Kenji Greets Elijah Cronen Warmly]
[University of Tokyo Professor Shimura Kenji Heads to Korea, Will Japanese Mathematician’s Presence Shine in Four Color Theorem Verification?]
[In the End, Japan Takes Charge of the Core Verification]
[A Korean Boy? We’ll Know After Verification Is Complete]
Next, Walter Scott of MIT and Georg Stein of the University of Bonn entered Korea one after another. And several researchers who had been watching the matter with interest also voluntarily boarded flights to Korea.
Young combinatorics scholars from various European countries, doctoral students from the United States, and even independent researchers who had yet to secure formal positions were among them.
The news that Elijah Cronen himself had stepped forward to verify it served as clear proof that this incident was not merely a rumor.
Many believed that simply witnessing the scene where a difficult problem was being handled before their eyes would become an asset for a lifetime of research.
And this atmosphere was soon picked up by the media as well.
[Mathematicians Gathering in Korea—Why?]
-A student at Korea Science Academy is drawing the attention of the global mathematical community.
Recently, claims have emerged that the photograph which became a hot topic on online communities as a “summoning circle” is in fact a new proof of the Four Color Theorem.
The photograph had seemed to be dismissed as a simple incident, but recently the situation has been changing rapidly.
As world-renowned scholars, including Elijah Cronen of Princeton, have entered Korea one after another, not only academia but the general public has begun to stir.
The common reaction among scholars is, “If it were just a rumor, people like that would never come in person.”
Experts say that “the correctness of the proof cannot yet be known,” but assess that the very fact that heavyweight scholars have personally moved shows this incident is not a simple commotion.
If the proof of the Four Color Theorem is confirmed to be true, Yu Seoha (13, first-year student at Korea Science Academy) is expected to be recorded as the first person to solve a difficult problem once considered “impossible to solve without a computer.”
└Barkeep...?
└He really did summon someone, huh.
└Who are those people?
└Just think of it as Nobel Prize winners holding a meetup.
└Korea really has no interest in math. Foreign media are making a bigger fuss. The boy who ranked first at the IMO turned the mathematical world upside down. (link)
└I’m in a master’s program in topology... If this is real, my entire major textbook might get rewritten. We’re scared as hell right now.
└The fact that a thirteen-year-old might change all that is legendary;;
└I’m a grad student too, and the atmosphere right now is no joke. Everyone in our lab has shoved their papers aside and is just watching the news. The mood is that since Cronen came in person, there’s about a 70% chance it’s legit.
└What, what? What are you all talking about without me?
└Yeah, math.
└Oh, I thought it was something else lol
* * *
A luxury hotel near the Sejong Government Complex,
In the hotel lobby, where buyers and officials in business suits usually came and went, people of an entirely different nature had begun staying there two days ago.
Instead of suits, they wore casual jackets and shirts; instead of high-end briefcases, they carried thick leather bags or backpacks.
On a sofa, a middle-aged scholar let his coffee cool while reading a paper, and at a corner table, young researchers peered at laptop screens and continued discussing in low voices.
The front desk employee clicked their tongue inwardly.
‘All of these people are mathematicians...?’
The Korean Mathematical Society provided the verification team with a large conference room at the Korea Institute for Advanced Study (KIAS).
A spacious area with large windows,
a huge whiteboard and electronic blackboard were installed at the front, and cameras and scanners lined the walls.
“All materials will be digitized here.”
A member of the mathematical society guided the verification team.
“The originals in the science academy seminar room will be preserved, and verification will be conducted here. We plan to keep the space open twenty-four hours a day so scholars from each country can discuss freely.”
Cronen nodded. Then he spoke as though it were of little concern.
“I would like to see the site of the proof first.”
Cronen recalled the classroom he had seen in the attached file.
It had been one of the most impressive scenes in his decades-long life as a scholar.
“Pardon?”
The mathematical society staff member, who had spent the entire week organizing the materials, stared blankly.
“Professor, all the data has already been organized. Verification can proceed more efficiently here.”
The staff member objected cautiously.
But when Cronen opened his gray eyes and gazed at him steadily, he had no choice but to lower his head.
“Understood.”
* * *
In front of the main building of Korea Science Academy,
The principal felt sweat gathering in his palms. He fixed his tie one more time and, for no reason, pushed at the stakes of the access-control line to see if they were wobbling.
‘What on earth is happening?’
He had wanted the school to become known, but not to this extent.
A black sedan glided in and stopped in front of him. When the door opened, a middle-aged man in a dark suit stepped out. On his chest was a badge from a government ministry.
“I’m Jeong Minsu, dispatched as a liaison from the Ministry of Education.”
He offered his business card and spoke in a low voice.
“From today on, we will handle all media response, access control, and movement routes. If you need to communicate with the government, please do so through me. Principal, you only need to take good care of the students.”
The principal accepted the business card with a dazed expression, then looked relieved.
“Thank you.”
The new suit he had bought felt awkward.
But once he handed over responsibility, he felt lighter. The situation had long since exceeded the range he could control.
Crackle—
The guard’s radio flickered.
The main gate opened, and a black van, a silver sedan, and a passenger van entered the campus one after another. As the vehicles stopped in a line, attendants got out first. Soon after, the rear door opened, and a man with silver hair stepped out.
‘Elijah Cronen.’
The principal, the faculty, and the academic figures who had come out all held their breath at the same time.
He looked even calmer and sharper than in photographs.
Someone tried to take out a phone, but when a guard glared at them, they hurriedly shoved it back into their pocket.
After him, Japan’s Shimura Kenji, France’s Chloé Moreau, America’s Walter Scott, and Germany’s Georg Stein stepped out of the van one after another.
The principal, watching their reactions, stepped forward first and welcomed them.
“You must be tired from the long journey. Welcome!”
When Cronen gave a brief bow of his head, Jeong Minsu stepped forward.
“We have already secured the route. I will escort you this way.”
At his gesture, the verification team began walking. They passed through the corridor and arrived at the seminar room in question. Sealing stickers and notices reading “Restricted Access” were pasted in layers on the door.
Riiip—
After checking the release documents, a staff member carefully peeled off the tape.
Click—
When he tapped the card key, the door opened.
Cronen was the first to step inside.
The smell of chalk dust and paper, and the metallic air peculiar to a room long kept sealed, flowed outward.
Click.
When the principal turned on the lights, the full view of the seminar room was revealed.
A3 sheets of paper covering the walls on all sides, intricately entangled graphs and symbols, and a massive automata diagram occupying the center of the blackboard.
For a while, the verification team could not speak.
“信じられない (I can’t believe it).”
Shimura murmured in Japanese.
“It’s truly magnificent. I’ve never seen such a wonderful classroom.”
“Jesus Christ.”
Exclamations in various languages burst out, mingling together.
“Hahaha! Incredible. Seeing a site like this after only reading papers reminds me of my younger days.”
Georg burst into laughter, as if delighted.
“Isn’t it? It’s so romantic, isn’t it?”
Chloé slowly walked along the wall with the expression of someone in love. Her fingertips hovered over the edges of the paper, then stopped.
“The numbers recognize one another. One rule embraces another rule.”
They were all top-tier mathematicians.
Verifying papers was an everyday matter for them. But the fact that they had come in person to the living site of a proof, not a pile of papers, excited them.
They imagined the young mathematician who must have fought a lonely battle alone in this room for days.
Stein examined a paper attached to the wall closely.
The symbols were inconsistent, and some lines were slanted, as if written in haste.
“This notation isn’t in any existing textbook.”
Chloé nodded.
“He probably wrote it so only he himself could understand. He clearly had no intention of making this room public.”
“And we have to interpret it.”
Chloé’s hand stopped at one point on the wall.
“He changed methods here. That transition should cause a conflict under the original definition. So he created a new rule. I don’t think I would have done it this way. It’s too risky.”
“A dangerous attempt. Though in the end, it seems he succeeded in avoiding contradiction and closing the system.”
Click.
Click.
The researchers examined various parts of the classroom and collected materials.
Cronen stood in the classroom for a long time.
He was following the flow of logic left behind by the boy. Now that he had come to the site, it became clear. With what determination the boy had chosen this place, and with what line of thought he had begun the proof.
As he moved, the traces seemed to revive like a film, unfolding before his eyes.
A young boy stood before the blackboard and wrote down formulas in a single breath. Before coming here, he must already have completed the overall framework of the logic.
Unfamiliar symbols on the wall caught his eye. Since the existing language could not contain his proof, he had created a new language himself.
‘This isn’t something he did for just a day or two, is it?’
He had skillfully avoided the land mines.
Every rule he created must be a history of failure. He had gathered them together and transformed them into rules.
The faint chalk marks at the edge of the blackboard caught Cronen’s attention. On one side, only erased traces remained, and over them a new arrow had been drawn.
‘So it wasn’t all planned from the beginning.’
He had collided, collapsed, and risen again, building the system. Even so, this structure was astonishingly solid.
A pile of notebooks was visible in the corner.
They were darkened with hand grime, and the corners were frayed here and there. Cronen picked up the notebook on top.
Childlike handwriting, solutions that had yet to escape textbook frameworks, but within them were traces of serious inquiry.
‘It’s like the research journals of mathematicians.’
He sat in a chair and picked up several notebooks.
The dates were kindly written in the notebooks.
As time passed, the handwriting gradually became clearer, and the once unstable development of formulas took on an orderly structure.
The boy’s failures accumulated.
But on top of them, new attempts continued without cease.
He used modular arithmetic to track the cycles of coloring, and he had even attempted to reduce the number of cases by grouping them into isomorphic graphs. As Cronen turned the pages, his finger paused for a moment.
In an attempt to find hints by moving back and forth between the plane and the sphere, he saw a familiar pattern.
‘This is my method, isn’t it?’
This child must have read his paper. And he had immediately tried to apply it to his own research.
By the most recent volume, traces of clear evolution were visible.
His own symbols, signs and conventions never seen in any existing paper, filled the pages.
Cronen closed the notebook and let out a deep breath.
Looking at the notebooks, he could know for certain.
This room had been the boy’s final battlefield.
What he had read was the grand epic of a boy that had continued for seven years, the record of that war.