Teaching Math to a Gallery User
Time flew by like a railgun, and before I knew it, I was six years old.
A-rin had turned four, too.
Since my lecture, I had grown a whopping seven centimeters, reaching 112 centimeters!
My, my, all those stretching exercises really paid off!
For the record, my weight had increased to 19 kilograms, giving me a height-minus-weight index of 93.
And now, it was the sixth month since I submitted my paper to the journal.
Almost every scholar in the mathematical community...
After tearing apart, dissecting, analyzing, and thoroughly enjoying the 148-page paper I submitted...
Finally acknowledged that my proof was correct.
Sitting at the living room desk, I browsed the news on Mom's laptop.
Mathematical Community Virtually Confirms Yoo A-yeon's Proof of the Riemann Hypothesis
A 160-Year-Old Mystery, Finally Solved
6-Year-Old Mathematician Yoo A-yeon Writes a New Page in Mathematical History
Articles about Yoo A-yeon kept pouring in.
Mom's inbox was flooded with dozens of requests every day, practically begging, "Please do an interview with us! Please give a lecture! Pretty please?"
With a fluttering heart, I opened the comment section of one of the articles.
"Hehehehe."
A wide grin spread across my face as I read the comments.
I felt absolutely fantastic.
Finally, everyone recognizes what an incredible genius I am!
All that careful buildup over the last six years was finally paying off.
After reading the news articles, a sudden thought crossed my mind.
Should I check out the gallery too...?
After receiving a smartphone for my fifth birthday, I had only browsed the gallery for exactly two hours.
Then, I voluntarily handed the phone back and hadn't visited the gallery for a whole year.
"But now that my proof of the Riemann Hypothesis is officially confirmed... I'm so curious to see how they're reacting!"
My fingers itched.
The urge to ego-search, which I had sealed away for a year, flared up.
Back then, I had searched under the name Shin Ijun, but there was no need for that anymore.
The name Yoo A-yeon was now incredibly famous!
I, Yoo A-yeon, was even more famous than Detective Kogoro Mouri!
*Clack, clack.*
Typing with my slightly grown fingers, I entered the College Mathematics Gallery.
It's practically official that Yoo A-yeon proved it.
Carl Friedrich Gauss (1777–1855)
Bernhard Riemann (1826–1866)
David Hilbert (1862–1943)
And
Yoo A-yeon (2020–)
Yoo A-yeon, hands down.
It's terrifying to imagine A-yeon sitting in a kindergarten class right now doing spelling tests.
The gallery was buzzing with threads about me.
"Uhehing."
As expected of math majors, they truly understood my greatness!
*Tap, tap.*
Logging into the account I had created a year ago, I sneakily wrote a post, pretending not to be Yoo A-yeon.
If I post a question like this, the gallery users will kindly explain how smart I am. Hehe.
After posting, I browsed other threads for a bit, and the comment notifications started pinging rapidly.
"Huh?"
I rubbed my eyes and looked at the comments again.
"Wait, hold on, how did they know it was me?!"
I panicked for a moment, but then it clicked.
Ah, right. A year ago, I used this fixed nickname to post that I had proved the Riemann Hypothesis.
Thinking about it, any internet sleuth with too much time on their hands could easily deduce that this account belonged to Yoo A-yeon.
"Ugh, this is so embarrassing!"
*Kick, kick!*
Sitting in the chair, my feet still couldn't reach the floor, so I kicked them wildly in the air.
Gotta run!
I was so embarrassed that I was about to close the laptop and leave the gallery for good.
But then, that one question caught my eye.
"Hilbert's Basis Theorem? Hmm..."
Hilbert's Basis Theorem.
An important theorem in commutative algebra, it states that a polynomial ring over a Noetherian ring is also a Noetherian ring.
To put it simply for non-majors, no matter how infinitely many polynomials you have—like x² or x³ + xy—they can ultimately all be generated by a finite set of base polynomials (like x or y).
To use a simpler analogy, even if a dictionary has hundreds of thousands of words, they can all be constructed using just the 26 letters of the alphabet.
It wasn't a question from a professor or a PhD, but a simple plea from an ordinary, struggling undergraduate student.
I found myself drawn to his pitiful request.
Besides...
"Heh. Asking me about college-level math?"
It wasn't a question about my paper, but a genuine inquiry about textbook material.
Which meant he truly respected my expertise.
"Alright, nameless college student, I'll help you out just this once..."
*Clack, clack.*
I typed out a reply.
"Sigh... Seriously, this guy..."
How do you expect to learn multiplication when you don't even know addition? Good grief.
There's always at least one person like this in online communities.
People who cram for exams by memorizing entire proofs, only to forget the most basic definitions.
In martial arts terms, they're the type who dabble in unorthodox techniques without building a solid foundation of internal energy, only to hit a wall in their growth later on.
At least he was polite. The nameless college student left a nice thank-you note.
"Nee-hee-hee."
Well, I got praised, so all's well that ends well!
I should come back often and teach math to these college students. Hehe.
That afternoon.
A-rin was lying face down on the living room floor, humming a tune.
A thick puzzle book lay open in front of her.
When we played together, we usually played two-player or four-player board games.
But when she played by herself, it had become a routine for her to solve solo puzzles.
A-rin didn't seem to mind at all.
Even now, she was biting her pencil, staring intently at the page in deep thought.
*Scoot.*
I closed my laptop and squatted down next to her.
The puzzle page A-rin was working on came into view.
[Puzzle: The following three people either tell only the truth or only lies. Which of them is telling the truth?]
Uncle: "Mare is a liar!"
Mare: "Hmph! Coron is the liar!"
Coron: "Sniff... That's so mean! Both of them are liars!"
It was a logic puzzle where they gave clues to determine who was telling the truth and who was lying.
"Hmm. A liar puzzle."
A-rin looked up.
"Unni, do you want to solve it with me?"
"Shall we?"
*Flop.*
I lay down right next to A-rin.
"A-rin, how far have you gotten with this?"
"Um..."
A-rin tapped the pencil against her lips as she spoke.
"If Uncle tells the truth, then Mare is lying. If Mare is lying, then Coron is telling the truth. But if Coron is telling the truth, then both of the others must be lying..."
"But that doesn't make sense. That would make Uncle both a truth-teller and a liar at the same time."
"Hmm... Then, if we think about it the other way... If Uncle is a liar... then Mare is telling the truth..."
"Right."
"If Mare is telling the truth, then Coron is a liar... and then Coron's statement that both of them are lying becomes a lie... Ugh..."
"For the statement 'both of them are lying' to be false, only one of them needs to be telling the truth."
"...Is that how it works?"
A-rin pondered for a moment.
"Then, Unni, is the answer Uncle: Lie, Mare: Truth, Coron: Lie?"
"Correct."
"Yay!"
A-rin pumped her fist in excitement.
"Now it's Unni's turn to solve one!"
A-rin showed me the puzzle book.
And at that moment...
*Flash!*
What I had read in the gallery this morning suddenly flashed through my mind.
Hilbert's Basis Theorem.
The fact that every ideal of a polynomial ring over the integers is finitely generated.
A mischievous grin spread across my face.
"A-rin."
"Yeah?"
"Unni is going to solve a puzzle, but is it okay if I use a fun little toy to do it?"
"A toy?"
"Yeah. A mathematician's toy."