Chapter 92
After that, I barreled through the material like a runaway locomotive.
A full hour and a half had been allotted for class.
It would be such a waste of time to stop after covering just the definition of a limit, wouldn't it?
I would pack the lecture as densely as possible and mercilessly cram knowledge into the unnis and oppas' heads!
If you've come to the top university in South Korea, you have to put up with this level of Spartan rigor!
Tap-tap-tap-.
I kept moving the footstool this way and that while writing on the blackboard without pause.
The footstool was heavy, so Mom got up from time to time to help me move it.
The unnis and oppas taking the class hurriedly moved their hands and followed along with their notes.
Scratch-scratch-scratch-.
The classroom filled with nothing but the sound of my chalk and the students' pens.
This is absolutely not a boast, but.
The writing I put on the blackboard is actually quite neat and easy to read.
There is a reason for that.
Ever since I was three, it had been part of my daily routine to write formulas on a whiteboard with a marker and ramble on as I explained them to my family.
I've been practicing my handwriting for a full four years!
At this point, shouldn't I be good enough to enter a contest for beautiful blackboard handwriting?
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So, as I bulldozed my way through the material.
Before I knew it.
Tirili-ri-.
The sound announcing the end of class rang from the smartphone with its adorable rabbit case.
At last, the first class was over.
“Phew-.”
Sighs of relief escaped from here and there.
They all had expressions like elite soldiers returning from a fierce battle.
They looked like they hadn't expected the class to be this brutal from the very first day.
But it was still too early to relax.
“All right! To encourage you unnis and oppas to review diligently, I'll give you some homework!”
Rumble-rumble-rumble-.
The entire classroom wore expressions of shock at my declaration.
“Gasp, homework on the first day…?”
Everyone's faces turned pale.
Not the “four colors” kind from the Four Color Theorem, but the kind that means their faces had gone bloodless.
(*Four Color Theorem: Every map drawn on a plane can be colored using just four colors so that no two adjacent regions have the same color.)
It was understandable.
Homework on the very first day of school!
They had probably enrolled while imagining a pink, youthful campus life with cherry blossoms fluttering in the breeze.
“Ah, don't worry too much!”
I quickly waved both hands.
“I understand the importance of having fun just as well as you unnis and oppas do!”
The students' stiff expressions relaxed a little.
How unfair would it be for the unnis and oppas who had come expecting a pink campus youth to have to solve homework on the first day?
I'm not in the business of manufacturing victims.
If anything, I'm a headache manufacturer.
“So, if you don't want to solve this assignment, you don't have to! It's one hundred percent voluntary! You don't even need to submit it!”
“Ooh…!”
“I'll announce the assignments that count toward your grades separately later!”
At that, relieved smiles blossomed all around the classroom.
There was no need to squeeze college students too hard.
Most of them would eventually head down paths unrelated to research, after all.
A murderous schedule was more than enough for the graduate students!
I cleared my throat again and continued speaking softly.
“I won't force you unnis and oppas to study. That's up to each individual. But! There's one thing I can say for certain.”
I emphasized my point by tapping the blackboard sharply with my chalk.
“If you diligently solve the assignments I give you, you'll have a much~ higher chance of getting an A+ than the unnis and oppas who don't do them!”
“……”
At the mention of an A+, the eyes of the grade-starved unnis and oppas lit up.
“So, if you want good grades, it would be a good idea to solve the problems I give you and spend plenty of time thinking about them! The more time you spend thinking, the more skill you build! That's the kind of field mathematics is!”
The little trick was to leave studying up to each individual while dangling a clear carrot in front of them.
Click-click-.
I wrote a simple assignment on the blackboard.
Even in communities that didn't usually discuss mathematics.
The famous problem that sparked flame wars and generated debate fodder whenever people were bored.
[Assignment: Using the definition of limits learned today, prove that 0.99999… = 1.]
0.99999… = 1
A very simple proposition.
When I wrote the assignment, the unnis and oppas' reactions split sharply into three groups.
Some of the unnis and oppas didn't even look at it after hearing that they didn't have to solve it. They were already rummaging through their bags and preparing to leave.
And quite a few of them stared at the blackboard with troubled expressions that seemed to say, “How on earth am I supposed to solve that…?”
They had known since middle school that 0.99999… was equal to 1.
But now they were being told to prove that obvious fact using the definition of limits they had just learned.
Their expressions showed that they had no idea where to begin.
Even so.
A small number of unnis and oppas who had followed the lecture well already looked as if they had gotten the idea, and had begun scribbling something in their notebooks.
I quietly watched the scene from the lectern.
…Hmm.
Even here at Seoul National University, where the finest talents in South Korea had gathered.
A gap this wide had opened up after just a single hour-and-a-half first class.
Even when looking at the same problem.
Some ignored it, some felt overwhelmed, and some had already grasped a clue.
Cruel as it was, this must be reality.
To close that gap, one had to make up the difference through effort.
“All right, that's all for today's class! You all worked very hard!”
I clasped my hands and bowed on top of the footstool.
“Oh, right, and… You remember what I said earlier, right? When class ends, applause—”
Clap-clap-clap-clap-clap-.
Before I could finish speaking, the unnis and oppas sent me a thunderous round of applause.
“Hoo heheh-!”
As expected, receiving applause made all the fatigue from the class vanish in an instant.
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Seo Eun-chae.
There was only one reason she had decided to major in mathematics.
It was the day Yoo A-yeon had visited the high school she attended and given a mathematics lecture.
Seeing Yoo A-yeon explain mathematics with sparkling eyes had made Eun-chae want to learn mathematics seriously herself.
Eun-chae was less the naturally talented type than the hard-working type.
Or perhaps.
It might have been more accurate to say that she possessed a “talent for working hard.”
Just as she had doggedly pursued chess as a hobby for more than ten years.
Whenever she took an interest in a field, she displayed an astonishingly persistent ability to focus.
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During class.
Eun-chae stared intently at the blackboard, lost in deep thought.
[Definition of the limit of a function]
For every ε > 0, there exists some δ > 0 such that,
if 0 < |x − a| < δ, then |f(x) − L| < ε,
we define lim(x→a) f(x) = L.
[Definition of the limit of a sequence]
For every ε > 0, there exists a natural number N such that,
if n ≥ N, then |aₙ − a| < ε,
we define lim aₙ = a.
‘Why did they define it specifically like that?’
She mulled over the strange definition written in Greek letters on the blackboard for a long time.
‘Can this really guarantee logical rigor?’
Eun-chae didn't stop thinking.
She kept thinking, kept questioning, and tried questioning it from other angles as well.
During the lecture, she remembered something Professor Yoo A-yeon had said.
—The more time you spend thinking, the more skill you build! That's the kind of field mathematics is!
It was exactly the same as the way she approached her hobby, chess.
Thinking about how much opening theory to study.
Thinking about strategies for each position.
Thinking about how to increase her win rate in the endgame.
Because the depth of that thinking directly became the difference in skill.
Mathematics was no different.
The sensation of growing stronger only by continuing to think felt strangely familiar and welcome.
Among Eun-chae's classmates in the class of 2027 were students who had come from science high schools or completed advanced study beforehand.
Those students had probably learned epsilon-delta long ago.
But Eun-chae could swear that she was seeing it for the first time today.
In high school mathematics, she had never once thought about ambiguities in the wording of a proof.
When the textbook said something was the case, she had simply accepted it with an “Oh, I see-.”
Rather than worrying about things like that, she had devoted all her attention to learning how to solve various problem types quickly.
Because that was the right answer in high school.
But when Professor Yoo A-yeon pinpointed that ambiguous part today.
A crack that had been invisible until now finally began to stand out clearly.
It was a tiny crack that people would normally ignore and pass by without a thought.
But once she paid attention to it, it kept circling around in her head.
‘Ha… I'm such an idiot. How did I fail to notice this until now?’
Eun-chae quietly asked herself that question.
However, from the perspective of a high school student, it was only natural that she hadn't found that crack.
Even the great mathematicians of Newton's era were said to have done mathematics by relying purely on intuition.
If geniuses from hundreds of years ago had done the same.
There was no way a high school student who had only just graduated could have noticed it.
Even so, Eun-chae learned something for the first time today.
Something she had always believed was obvious.
That it might not actually be obvious at all.
The realization was strangely thrilling.
It felt as if all the common sense she had believed was solid were shaking, while a door to a new world had opened before her.
And, true to her model-student nature.
Eun-chae reread the material she had organized that day again and again.
Mulling over every line.
She tried to solve the assignment Professor Yoo A-yeon had given them.
[Using the definition of limits learned today, prove that 0.99999… = 1.]
‘I understand that 0.99999… and 1 are equal. But how am I supposed to use the definition we learned today…?’
Eun-chae scribbled something in her notebook, erased it, then scribbled again and erased it again.
It felt as if a clue was almost within reach, but not quite.
She wrestled with that ambiguous point for several hours.
It seemed as if she could solve it, yet she couldn't.
And even when it seemed impossible, she felt as if she could almost see something.
“Ugh… This difficulty is freaking insane.”
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Several hours later.
In the end, Eun-chae couldn't come up with a clear answer on her own.
She picked up her notebook and sprang to her feet.
At times like this, asking someone directly was better than struggling alone.
Professor Yoo A-yeon had said she would be holding office hours, after all.
She hurried up the stairs and stood in front of Yoo A-yeon's research lab.
Knock-knock-.
—Yeees-! Come in-!
She opened the door a crack and peeked her face inside.
“Professor Yoo A-yeon~!”