Jiyun did not wait until the students' murmuring died down.
She pulled out a piece of chalk stuck in the lectern and wrote four words large in the center of the blackboard.
[Definition - Theorem - Proof - Critique]
"This semester, we move only in this order. I have no interest in elegant solutions. A proof may collapse even if short, and may be a wasted journey even if long. What matters is logic that absolutely cannot be broken!"
Jiyun wrote "Logic" in large letters.
"You likely think of numbers first when you think of mathematics, but the most important thing in mathematics is proof based on perfect logic. The other three steps I wrote are precisely the process for constructing this flawless logic. So, shall we have a quick test?"
When Professor Kim Jiyun clicked her mouse, a problem appeared on the blackboard.
[In a certain village, there are people with blue eyes and people with brown eyes.
Everyone knows the eye colors of the others, but does not know their own eye color. And there is no way to see one's own eyes directly. The rule is: "If you learn what color your eyes are, you leave the village that night."
One day, a traveler who enters the village says, "There is someone here with blue eyes." What will happen?]
A student in the middle confidently raised his hand.
"Um... Kim Jeonghwan? Good. Speak."
"The person with blue eyes will immediately realize their own eye color and leave the village."
Since everyone knew the eye colors of all the villagers, if there was no one with blue eyes among those one knew, then only oneself could remain.
Most nodded, seemingly having thought the same. But Jiyun shook her head.
"Wrong. Would anyone like to refute it?"
Seoha raised his hand.
"There is an error in that answer.
If there is only one person with blue eyes, upon hearing the traveler's words, he will think, 'Ah! That's me,' and leave immediately. But if there are two or more, it is different. They look at each other and wait, thinking, 'That person will leave.'
If no one leaves on the first day, they only realize on the second day that they had the same thought, and leave at once. If three, on the third day; if four, on the fourth day... It continues in this manner."
Honey practically dripped from Jiyun's eyes as she looked at Seoha.
"Perfect. To keep logic from breaking, you must consider every possible case without omission. What matters is that there are no holes in the logic. In mathematics, proof is the work of filling these gaps. If it wavers even the slightest bit, it is not completed logic."
Tension flowed among the students.
"Of course, the opposite case is also possible. A proof that plugs holes excessively can never be considered a good proof either."
When Jiyun clicked her mouse, a new passage appeared.
"This is an actual report on a past theft incident. Now, let's try removing the parts unnecessary for the proof."
Seoha was beside himself with excitement.
Professor Kim's class was so enjoyable that he felt like dancing.
Seoha's teacher had always been books.
From the moment he first learned to read at around the age of two, there had not been a single day when Seoha put down a book.
Beneath the lamplight, he was always alone.
While reading, Seoha asked questions by himself and found answers on his own. Questions without answers were jotted down on an 'unsolved' list, and he would return to them later and settle them without fail.
While reading, Seoha always set procedures for himself. When encountering a new concept, he first wrote down its definition. Then he underwent a time of careful self-verification to determine whether it was right or wrong.
When Professor Kim Jiyun wrote down the process of 'Definition - Theorem - Proof - Critique,' Seoha could not calm his racing heart. Because this was something he had done as naturally as breathing, routinely, since he was very young.
Thus, it was inevitable that Seoha was strong in logic.
The eyes of the students reading the report were serious.
Perhaps because its nature was different from what they usually read? They thought hard, but the students could hardly grasp what was necessary and what should be deleted.
"Isn't the power outage important too? Because of that, the CCTV stopped..."
"The fact that the woman used a cell phone is a clue, so we can't delete it."
"The time the shop owner opened the door is needed because it's an alibi."
Whispers were heard here and there.
Sujeong, too, seemed to have a headache, furrowing her brows as she chewed over each sentence.
The densely written case summary was a suffocating jumble of various facts.
Time of the incident, time the shop owner opened the door, testimony of a nearby cafe employee, CCTV stopped due to a power outage, explanation about the safe, the existence of someone with past work experience at the shop...
But Seoha did not hesitate in the slightest.
He quickly scanned the passage with his eyes and then raised his hand high.
"Teacher, most of the clues listed in that report are contents unrelated to the conclusion."
Seoha went forward and began erasing sentences one by one.
The students let out small exclamations at Seoha's bold actions. Facts they had thought might be clues were deleted one by one. In the end, only three sentences remained.
[At the time of the crime, the shop owner was out.]
[The shop safe opens only when a password is entered.]
[Only the owner and the man who had worked at the shop knew that number.]
"Excellent!"
Jiyun stood up from her seat with a smile.
"With unnecessary facts removed, the core becomes clearly visible, doesn't it? In reality, the culprit was that employee.
Proof in mathematics is the same. There is no need to use all the conditions given in the problem. Rather, conditions that are not essential obscure our vision, so we must quickly exclude them. What matters is constructing logic without gaps!"
"Now, everyone, applause for Yu Seoha!"
Clap, clap, clap!
Seoha's face turned red.
Then Jiyun approached Seoha and whispered into his ear.
"Seoha, I told you to come visit the research lab anytime, so why didn't you come? In the end, I came all the way here to meet you."
"Gasp!"
Seoha flinched, his body trembling.
It felt like the hair all over his body was standing on end.
After that, the logic game continued.
A student would present logic, and another would tear it down.
And Seoha was the devil of this game.
Every student's logic was shattered by Seoha. Conversely, no one could break Seoha's logic.
"Wow... I've never seen a kid like you before."
Sujeong clicked her tongue, looking worn out.
After the basic logic construction was finished, Jiyun had the students apply this to mathematics.
Seoha's head was spinning.
The problem written on the blackboard was a function proof that looked ordinary.
But approached in Jiyun's way, it revealed an entirely different face.
For Seoha, learning had always been solitary.
Of course, he thought the process itself was sufficiently enjoyable as well, but...
Jiyun was, for such a Seoha, the first 'teacher capable of teaching' he had met in his life.
Seoha was moved by direct learning from someone, an experience he was having for the first time in his life.
Jiyun smiled warmly as she watched Seoha like that.
* * *
Having entered elementary school, Seoeun grew up to be a spirited child. Perhaps because she received plenty of love from her family, there was no timid corner to her actions.
"Teacher! I know!"
Whenever the teacher asked a question, Seoeun raised her hand faster than anyone else.
One Saturday afternoon,
Seoeun was lying prone on the wooden floor. Whether she was playing a fun game, her two legs moved alternately as if dancing.
When Miyeong went to look, she was drawing with crayons.
She had opened a sketchbook like the one her older brother used and was concentrating on studying, writing 'Triangle' and 'Square' in crooked letters. Of course, she thought of it as a shape game.
"The sum of a square's interior angles is 360 degrees, and if you cut it in half, it's a triangle, so 180 degrees. Then a pentagon is three triangles, so 540 degrees?"
Miyeong watched and thought, 'In that strange way, she really takes after her brother.'
"Mom! I'm home!"
A familiar voice from the front gate.
A son who had grown much bigger entered while taking off a large bag. Seoeun, lying on the floor, was startled and opened her eyes wide and round.
"It's Brother!"
Seoeun jumped up and ran over, spreading her arms and hanging onto Seoha's waist. Then Seoha lifted Seoeun up high with both hands. Seoeun laughed gleefully, waving her arms and legs in the air.
"Were you playing the shape game, Seoeun?"
"Yes! A hexagon is four triangles!"
Smiling, Seoha hugged his younger sibling tightly.
"Hurry up and eat."
Miyeong took Seoha's bag and pulled Seoeun away.
Cheolho, who had been watching TV in the room, also came out at some point and welcomed Seoha gladly.
'Ah! Home!'
Coming out of the tension-filled school and arriving home, his chest felt wide open.
Seoha ate two bowls of rice with his mother's doenjang-jjigae and played, taking a walk around the neighborhood with Seoeun.
As evening came, Seoha sat before his familiar desk again.
"Attempt 178."
For mathematicians to obsess over difficult problems was as natural as bees seeking flowers.
However, if someone who cherished Seoha had seen this sight, they would undoubtedly have stopped him. Because clinging to an unsolved problem was an extremely dangerous thing.
Paul Wolfskehl devoted his life to proving Fermat's Last Theorem but could not achieve the desired result. Unable to let go of his obsession until death, he passed away leaving a will bequeathing his entire estate to whoever solved the problem.
Louis de Branges is famously known as a scholar 'possessed by the ghost of the Riemann Hypothesis.' He devoted over thirty years to the problem but ultimately failed to solve it. And he drifted away from academia due to extreme pressure and frustration.
The four-color theorem had also been a difficult problem that countless mathematicians had challenged and failed to solve.
A problem already solved, even if not beautiful.
There was no reason for a boy with a brighter future than anyone to obsess over this problem.
Scratch, scratch.
But giving up was not an option given to Seoha from the start. Because this was the first unsolved problem he had faced in his life.
Until now, Seoha had been struggling with this problem for too long. Thus, he already knew exactly where he was stuck and which paths were dead ends.
So he instinctively tried to avoid all walls.
The deeper the research, the higher the obstacles grew together.
This was the dilemma Seoha faced.
However, on the 178th attempt, he felt something different. Seoha's sharp mathematical intuition told him otherwise.
"Hmm? Must I really avoid this path? I feel like I can handle it later with a different method."
A sudden realization washed over him.
His class with Jiyun came to mind.
'There is no need to use all the given conditions. Rather, conditions that are not essential must be quickly excluded.'
It was knowledge he already knew, but Jiyun's words made Seoha, who had been avoiding conditions out of inertia, realize there was another path.
Scratch, scratch.
Seoha's pencil found a new path.
His hand moved ceaselessly over the formulas filling the paper. In the heavily settled air of the room, Seoha continued his research silently.
Scratch, scratch.
The answer was not yet visible.
But it was distinctly different from the past. If back then it felt like wandering an endless wasteland, now it felt like walking toward an oasis in the desert that must be somewhere.
The massive wall that had blocked Seoha for years began to split before his eyes for the first time.