Chapter 99
“Hmm, hmm. Since I’ve memorized all your faces, I’ll skip attendance and start the lecture right away!”
Click-clack-.
I climbed onto the footstool and quickly wrote a summary of the material we’d covered in Monday’s class.
Review is important. Yep.
By the time I had summarized and explained everything at breakneck speed in ten minutes.
“Oh, right, there was an assignment I gave you on Monday, wasn’t there?”
“Yeees-.”
I wrote the assignment on the blackboard.
[Prove 0.99999… = 1]
The fifteen newcomers looked flustered, thinking, “An assignment on the first day?!”
“It’s okay. Like I said last time, it’s voluntary, so you don’t have to turn it in. Instead, I’ll show you how to approach it!”
I carefully explained the solution exactly as I had taught Eun-chae unni.
“The proof using multiplication by ten and subtraction, which you probably learned at school, isn’t logically valid. Using 1/3 is the same. Since we haven’t proved the rules for operations on infinite decimals yet, you can consider every use of arithmetic at this stage a logical leap.”
Everyone’s mouths fell open, just like Eun-chae unni’s group on Monday.
It was the moment the common sense they’d known came crashing down.
I introduced a proof method that chose ε and N carefully, mixed them together like this-this-, and slipped neatly inside the error range.
A few people nodded, as if they had solved my assignment correctly.
Others hurriedly copied down the proof I wrote on the blackboard, looking as though they had never expected it.
And then.
I lowered my voice just a little and said.
“Professor is disappointed in you all.”
I suddenly said something like that out of nowhere.
Then a magnitude-nine Richter-scale earthquake struck everyone’s eyes.
They were probably thinking, Did we do something wrong?
Muu-.
I puffed my cheeks out slightly.
“I held office hours on Monday, but only one person came!”
I shouted with my eyes squeezed shut and my arms thrust down at my sides!
Phew-.
The undergraduate unnis and oppas’ expressions changed to ones of relief.
“Some of you probably solved it because the problem was easy. But judging by the expressions on the unnis and oppas here, it seems quite a few of you couldn’t solve it.”
I clenched my fists and said.
“Undergraduate unnis and oppas, if there’s anything you don’t know, please come ask me! I’ve prepared lots of my favorite snacks too! Don’t feel pressured—come on over!”
The classroom fell silent.
And at the very last moment, I let my true feelings slip out.
“Also… to be honest, I’d like to chat-chat- about math together while we eat snacks…”
Why had I deliberately volunteered to teach when I wasn’t required to lecture?!
Obviously, it was because I wanted to properly teach the scholars who would come after me.
But if only Eun-chae unni came while everyone else stayed away because they were shy, what would that make me?
It was a statement closer to a selfish desire than anything backed by sound logic, but surprisingly, everyone seemed to take it seriously.
“Professor! I’ll definitely come ask questions!”
“Me too!”
“Can I come get your autograph?”
The student unnis and oppas reacted enthusiastically.
I answered with a bright smile.
“Hoo-he-heh-! Of course! As long as you come during the hours I announced, it’s fine! Don’t feel pressured—come by and hang out!”
✒️✒️✒️
3 p.m.
Mom and I were quietly reading papers in the lab as usual.
Whirr-whirr-.
Scritch-scritch-.
Reading papers and thinking is a mathematician’s job, after all.
I was enthusiastically doing just that.
“Hmmmm… If we can reduce the conductor here, I think we might find a better upper bound for the size of the L-function…”
Knock-knock-knock-.
And someone came to visit.
“Yeees-! Come on in-!”
I answered through the door, glad to hear someone arrive.
And the moment I opened the door.
Whoosh-.
About five or six unnis and oppas came streaming in!
“Eeeek-!”
I sprang to my feet with my eyes wide in surprise!
“We came to eat snacks!”
“Professor, I want your autograph!”
“I brought more in case you ran out of snacks! What do you like, Professor? Sweet snacks? Salty snacks?”
“Wow! Your lab is so cute and cozy! Professor, you did the interior design, right?”
Chatter-chatter-.
When I told them to come without feeling pressured.
The undergrads had really come after completely detaching the concept of “pressure” from themselves.
The advertising I slipped into class had an amazing effect!
“Welcome, unnis and oppas!”
“Welcome. Let’s eat snacks together.”
Mom naturally stood up, then spread the snacks the unnis and oppas had brought across the table for lab visitors.
The lab, quiet just moments ago, instantly transformed into a lively snack-party room.
✒️✒️✒️
Munch-munch, nom-nom, chomp-chomp-.
“So, Professor, about those hyperbolic functions you explained today. I’m seeing them for the first time in my life—are they actually used in real life?”
An oppa asked while chewing a snack.
“Yes! You know how, when you hang something like a clothesline, you’ve seen the line sag down?”
“Ah, yes, yes.”
“That’s called a catenary, and when you express its shape as an equation, you use the hyperbolic cosine function!”
“Whoa, that’s fascinating. It really exists!”
“Heh-heh.”
I shrugged.
“But the interesting thing is, it’s completely different from the parabola made by a ball when you throw it.”
“Huh? They look similar, but they’re different?”
“Yes! A thrown ball is affected by gravity. A clothesline is affected by gravity plus the tension in the rope at both ends. So even though they look similar, the functions are completely different!”
“Ooh. I see.”
The undergrad unnis and oppas casually munched their snacks—crunch-crunch—and slurped their drinks—whoosh—while throwing all sorts of questions at me.
…To be honest, it did look a little too informal.
This was a professor’s lab, but it had turned into something like a university club room.
But.
Even so, this was exactly the kind of atmosphere I wanted.
A system where people could freely talk to their professor about whatever they wanted, without feeling pressured.
Personally, I thought this kind of relaxed atmosphere could actually advance scholarship.
Even though I had the title of professor.
That didn’t mean a professor’s ideas were absolutely correct.
Countless times throughout history, a student’s sparkling idea had changed the world.
But the Korean university system concentrates too much authority in professors, making it difficult for fresh ideas that break the mold to emerge, I think.
There are also many cases where graduate students simply follow the research direction designated by their professor.
Of course, the people here today were undergraduates.
But if this atmosphere continued all the way to graduate students.
Wouldn’t they someday make a discovery that astonished academia?
After all, the essence of mathematics lies in freedom.
My mom, currently my only graduate student, still treats me very casually, without regard for hierarchy, and I think that’s a very good thing.
✒️✒️✒️
Before long, another knock sounded.
Knock-knock-.
“Yeees-. Come on in-!”
This time, the graduate-student unnis and oppas taking Functional Analysis came to visit.
“Huh, what? Hello, senior!”
“Huh? Uh, yeah.”
The undergraduate oppa who had been eating snacks greeted them cheerfully.
They seemed to know each other. Maybe they’d gotten close at the freshman orientation camp, or perhaps they were club seniors and juniors?
But the graduate students initially struggled to adjust to the lively atmosphere in our lab and stood there awkwardly for a moment.
“…Uh…?”
“This is Professor Yoo A-yeon’s lab, right?”
Apparently, the sight of snack crumbs flying and undergrads giggling “Hehehe” was rather bewildering.
Then they shook their heads and began quietly taking seats.
“…Can we eat snacks too?”
“Of course! Would you like a drink too?”
Pour-pour-.
✒️✒️✒️
A graduate-student unni picked up snacks and nibbled while asking about the Functional Analysis class from that morning.
“Professor. Why does a theorem that works well in finite dimensions fail in infinite dimensions? For example… that a closed unit ball is compact.”
Oh-ho. She’d already thought over what we’d mentioned in class today and come to ask about it.
“That’s a good question!”
I replied in a very pleased voice.
Pop-.
I pulled out a whiteboard marker with a huff.
I trotted over to the whiteboard.
“Well, in finite-dimensional Euclidean space, a set is compact as long as it’s closed and bounded. That’s thanks to the Heine–Borel theorem.”
Tap-tap-tap-.
I swiftly wrote down the equations.
“But when you move to infinite dimensions, there are infinitely many directions, you know? So you can pick infinitely many points inside the unit ball that stay at least a certain distance apart from one another.”
“Aha-.”
“Then compactness breaks down because you can’t extract a convergent subsequence. That’s why, later on, we introduce something called the ‘weak topology’ to solve this problem.”
“Oh, so that’s why we treat the weak topology as important! I wondered why!”
The graduate-student unni took notes in her notebook with sparkling eyes.
And beside her.
The first-year freshmen unnis and oppas, who had inadvertently gotten a taste of the insanely difficult graduate class beside them.
“…?”
With the mindset of, “The white is the whiteboard, and the black is writing,” they stared at us with blank expressions.
“Is this Korean…?”
“Infinite dimensions…? Compact…?”
The freshman unnis and oppas blinked blankly, snacks still in their mouths.
Gaaah, math newbies are so ridiculously cute!
I have to shower these adorable newbies with affection…!
“Ah, freshman unnis and oppas, it’s okay if you don’t understand yet! This is something you’ll learn much laaater!”
I reassured them with a smile.
“In undergrad, you’ll only study finite dimensions like three-dimensional and four-dimensional space, but later on, you’ll get to see the amazing world of infinite dimensions handled like this-this-, so just watching is more than enough!”
“Yes, ma’am!”
The freshmen unnis and oppas picked up their snacks again with relieved expressions.
Professor, undergraduates, and graduate students.
This scene of everyone chatting about math while eating snacks together.
Even though it had absolutely no formality, I was satisfied just to have removed one barrier to entering the world of learning.
With a pleased smile, I picked up a snack and popped it into my mouth.