Korea Institute for Advanced Study, third-floor main conference room,
“I’ll put the materials up now.”
At a gesture from the Korean Mathematical Society coordinator, the light on the recording camera came on. A large scanner then let out a whirring sound.
On the wall screen, the seminar room at the gifted high school was recreated in panorama.
The automata on the blackboard and the A3 sheets covering the walls filled the screen. The image was so clear that even erased chalk marks stood out sharply.
The era when professors gathered in lecture halls with paper and pens to verify theories was already over.
Now every paper was digitized, and if necessary, even virtual experiments could be reproduced with proof assistants and mathematical software.
Kronen lowered the slide and said,
“You’ve checked the materials thoroughly enough, I assume?
We’ll proceed by the book. Interpretation of notation, verification of consistency and completeness, then search for counterexamples.”
Walter Scott wrote the four steps in the center of the whiteboard.
Beside him, Chloe began converting Seoha’s proof into standard notation on the electronic board.
“I think this symbol can be changed to a boundary cycle. The subscripts can be handled as color codes and mappings. I’ll replace the symbol set ‘1, 2, 3, 4’ with the two-bit alphabet (a, b)².”
Georg nodded.
“So the pattern of colors appearing on the boundary is converted into a word of variable length, and then a finite automaton A reads that word to determine whether extension is possible or impossible?
Insane. How did he come up with this?”
Shimura raised his hand.
“But was there a reason the boundary rules had to be exactly thirty-two?”
“It’s in the notes.”
Chloe enlarged the scan and put it on the screen. Seoha’s handwriting appeared clearly.
“The number of equivalence classes of boundary local rules induced by the exceptional group is thirty-two. He minimized it Myhill–Nerode style (* a method of reducing a seemingly large number of cases to the minimum number of patterns that must actually be distinguished).”
Walter laughed.
“He could have just written minimum DFA (Deterministic Finite Automaton * deterministic finite-state automaton), but he went all the way to Myhill–Nerode. Cute.”
Seoha, who had not received a university education, differed considerably from established mathematicians in his notation and method of development. The verification team found that both endearing and astonishing.
Because within it were ideas even experienced researchers would not have easily thought of.
The verification continued for an entire month.
Dozens of mathematicians threw themselves into analyzing Seoha’s theory from multiple angles.
They examined even the most trivial details to see if there might be any holes in the proof. And one by one, lights began to turn on across the checklist.
All the hard-to-read symbols were deciphered and substituted, and in terms of consistency and completeness, it received a verdict of “no errors.”
The final remaining step was to find counterexamples.
Young researchers opened their laptops at the back of the conference room.
They automatically generated small planar graphs, extracted only the boundaries, and passed them through Seoha’s automata.
On the other side, they were turning Seoha’s four-color theorem into an algorithm and applying it to see whether actual coloring was possible.
Every time the two results matched without the slightest discrepancy, a green light appeared on the screen.
As the number of cases increased, tension filled the conference room.
The researcher running the algorithm was holding a coffee cup, but he could not take a single sip, his fingertips trembling.
He thought,
‘What happens today will definitely be talked about among mathematicians for a long time.’
The feeling that he was sharing in a moment of history excited him.
“Matches up to ten faces.”
“Matches up to fourteen faces.”
“No anomalies up to twenty faces.”
Hundreds of thousands of samples were fed in to find a counterexample, but no warning ever sounded.
And at some point, everyone realized it.
This boy’s automata were complete.
* * *
From early morning, the Institute for Advanced Study was in an uproar.
Black vans and broadcast relay vehicles had occupied the road in front of the building, lined up one after another. Journalists from various countries gathered in small groups as well, busily checking camera angles.
Voices in English, Japanese, French, and German could be heard mixed together here and there.
Sim Hyeonu, an MBS reporter, looked around in wonder.
“Wasn’t this supposed to be some kind of math announcement? Is this really something that would become such a scoop?”
The senior reporter clicked his tongue as he looked at him, as if pathetic.
“You think these people came here because of math?”
“Pardon? Then why?”
“Look at the foreign press. Even if a Nobel Prize winner had come out of Korea, they probably wouldn’t have swarmed in like this.”
Reporter Sim nodded. He thought that was probably true as well.
“Then what is it because of?”
“You’ve still got a long way to go if you want to land a scoop.
Obviously it’s because everyone’s making a fuss over a thirteen-year-old kid proving some theorem or other. There was that case in the West too, you know, the one who became a chess grandmaster at thirteen…”
“Ah! Magnus Carlsen? I know him too! Back then, major broadcasters like CNN and BBC all flocked to Norway.”
“It’s like that.”
A podium began to be set up in the open space before the main entrance.
Before long, the scholars entered one after another.
“It’s Elijah Kronen!”
“Professor Walter Scott from MIT is here too.”
“Professor Shimura! Please look this way!”
With world-class mathematicians gathered together, they made a picture just by standing there.
The reporters seated in the front row hurried to focus their cameras.
Flashes went off continuously, and the hands of reporters holding laptops began to move busily.
“Ready?”
Kronen’s voice came in a whisper. An institute staff member nodded at him.
Kronen walked to the front of the podium.
His gray eyes swept briefly over the audience. Dozens of cameras moved with him, flashes bursting one after another.
He lightly adjusted the microphone and began the announcement in a low voice.
“Over the past month, my colleagues and I have verified a new proof of the four-color theorem proposed here in Korea.”
He paused briefly and looked out at the audience.
The reporters held even their breaths as they typed on their laptop keyboards.
“I will state the conclusion first.
We have closely analyzed every step of the proof and conducted nearly one million automated verifications.
As a result, we have found no fatal error so far that would overturn the proof.
We believe this proof possesses sufficient persuasiveness, and we assess it as one of the great advances in the history of mathematics built up by humanity.”
Mathematicians never speak in absolutes.
They habitually add phrases such as “further verification is necessary” or “for now, it remains only a conjecture.”
Because they know all too painfully that a single small crack can bring down even an achievement painstakingly built over decades.
In that sense, the verification team’s wording, “one of the great advances,” was, in effect, the highest praise permitted to mathematicians.
In an instant, the press conference hall stirred.
Reporters raised their hands and shouted over one another.
“Does what you just said mean you are essentially acknowledging the proof?”
“Where is the student? Is he not appearing here today?”
“Is it true that the boy proved it alone? Were there perhaps any helpers around him?”
The last reporter’s question halted Kronen’s steps as he was about to leave the press conference hall.
“Who are you?”
An East Asian man stepped forward and identified his affiliation.
“I’m Abe Shintaro, a reporter from the Sankei Shimbun.
Are we really supposed to believe that a thirteen-year-old boy proved a difficult problem mathematicians have failed to solve for over 150 years? Was there perhaps involvement from other adults in the process?”
Kronen looked straight at the reporter. After a brief silence, he spat out a sentence, sounding displeased.
“Do we look like fools to you?”
“Pardon?”
“A proof is not evaluated simply by whether its conclusion is ‘right or wrong.’
How the logic is developed, which definitions and lemmas are chosen, what manner of notation is used—all of that remains like the researcher’s own unique signature.
In this paper, we saw both the still-unrefined spirit of youth and a fresh leap of insight no one else had conceived. Your question is an absurd insult to mathematicians.”
Everyone in the press conference hall listened to his words with bated breath.
“Are you really saying that boy did it alone?”
The reporter did not back down. Then Kronen threw a question back at him.
“Reporter, did you go to university?”
At the unexpected question, the reporter stammered out an answer.
“Y-yes..? Yes, I did.”
“Then what is the longest you have ever wrestled with a single problem?”
It was a simple question, but he could not easily answer.
“Uh…”
“Ten minutes? Thirty minutes?
I’ll state with certainty that it probably did not exceed an hour at most. Not because you are a deficient person. Because most people are like that.
But did you know that Yu Seoha has pondered this problem for over seven years? If you do not understand what that means, I will explain no further.
The heavens sometimes gather starlight upon a single person.”
The last words were almost inaudible,
but their meaning was conveyed clearly. Relief and pride spread at once across the faces of the domestic broadcast personnel listening to the announcement.
“Ahem!”
The Sankei Shimbun reporter stepped back in embarrassment.
A brief silence passed.
When Kronen stepped down from the podium, a Mathematical Society official hurriedly brought the situation under control.
“That concludes today’s press conference. Additional matters will be announced through the Korean Mathematical Society.”
Though it was a matter in the world of mathematics, far removed from the public’s usual interests, broadcasters starved for topics unusually put out extensive coverage.
[Fields Medal Only a Matter of Time? The World Watches a 13-Year-Old Korean Genius]
[The “Mozart of Mathematics” Is Born in Korea, Headlines Around the World]
[Must Textbooks Be Rewritten? A 13-Year-Old Boy’s Shocking Proof]
[A Boy’s Seven-Year Struggle Finally Topples a 170-Year Problem in Mathematics]
That evening, one broadcasting station overturned its programming schedule and aired an emergency special.
Even math and science YouTubers, usually ignored by the public, rushed to turn on their cameras and hold unplanned joint broadcasts.
But there was someone faster than all of them: U Hyeon, whose mouth had been itching from holding back his bragging about Seoha all this time.
[Frame Series LIVE Sin U Hyeon, I’m Talking About It Today!]
“Guys, before we start Lecture 5 today, I’m going to go off-topic for a bit.”
└What’s he gonna talk about this time lol
└A story about a girl from his Princeton days?
└It’s in the thumbnail. The real genius in Korea he talked about before.
└Whoa lol No way?
“That ‘no way’ is right. I told you, didn’t I? There might be a once-in-a-century genius in Korea too.
I said mathematicians should speak through their achievements, right? I think this is enough for me to talk about it.”
└Goosebumpsㄷㄷㄷ That was Yu Seoha?
└Awesome lololol
└You’re not selling snake oil, right?
“You think I’d sell snake oil with something like this?”
└Tell us the story. Did he come to your academy for consultation?
└No way, is he taking class with us right now?
“The first time I saw Seoha was when he was in first grade of elementary school, and I got the feeling right away. Ah! This kid is really no joke!”
└Seoha lol Acting close lolol
└What was he like?
└Hurry hurry!
└The lectures are already packed, are they going to blow up again like this?
“A seven-year-old kid was working on the four-color theorem.
He was sticking colored paper in a sketchbook and drawing graphs with crayons while doing it, but when I looked closely, it was a highly advanced theorem beyond university level. How do you think I felt seeing that?”
└You already favor kids who study well, so if it was that level lolol
└Wow! He was doing it from back then?
“I was stunned too. I didn’t know he was still doing it.
This kid doesn’t talk until the proof is finished. He’s too taciturn! Even after solving it, he was calm. Seoha knew too. That someday, he would definitely be able to solve it.”
└Then is he your student too, teacher?
└No way, are all of us alumni?
└What did you teach him?
“I didn’t teach him. I only sent him books he needed to read. From the start, he wasn’t a vessel someone at my level could handle. Let’s just say I gave him a little direction.”
└Then is he getting the Fields Medal now?
└Are we finally getting one in Korea?
“Hey, you brats! The Fields Medal is once every four years. This year’s winner has already been announced. So no matter how fast, it’ll be four years from now, right?”
└Wow ㄷㄷ I thought they gave it every year.
└Why are they so stingy with it? Even the Nobel Prize is given every year.
“And the mathematics world is ten times more conservative than you guys think. What did Professor Elijah Kronen say this time too? ‘We have found no fatal error.’ That’s exactly as far as he went.
Once the official paper comes out, bored mathematicians will latch on and verify it again. After doing that for about two years, only then will they barely acknowledge it.”
└That’s insanely harsh ㄷㄷ
└Ugh, I don’t think I could be a mathematician.
└We couldn’t even without that.
“Anyway, Seoha is world-class now.
What else did Professor Kronen say? A great advance in the history of mathematics built up by humanity!
Kya! I know that man a bit, and he is absolutely not someone who says things like that lightly. That’s how impressive Seoha was.”
└He became a celeb in the math world ㄷㄷㄷ
└Somehow I’m not that jealous of that.
└Won’t he show up on variety shows and stuff?
“Now that I’m done bragging, let’s get back to class!”
U Hyeon smiled slightly and picked up a piece of chalk.
But today’s broadcast had an unexpected side effect.
Elementary school parents began seeking out the CSAT instructor.
All of them asked, “My child is also very smart. Can they become like Yu Seoha?” and requested guidance from U Hyeon.