Chapter 83
Afterward, Eun-chae unni and Arin put their heads together and chatted away, sharing the competition schedule.
“Unni-! When is the competition to select the national team?”
“It’s being held next spring. At your age, Arin, I think you can enter all the competitions listed here.”
“Ooh! I definitely wanna enter!”
I quietly watched them from the side.
Until now, Arin had always stuck right by me, simply tagging along whenever I did something with my unnis.
And now she was saying she wanted to enter a competition on her own, one I wasn’t even participating in.
It seemed our Arin was getting ready to venture out into the world little by little.
That sight moved me deeply.
Looking back.
I had raised Arin, soothing and comforting her ever since she was a newborn.
With my short, chubby body not even thirty months old, I had even begged Mom to let me change Arin’s diapers.
So in practice, I had been as much Arin’s caregiver as anyone.
I had raised Arin by mixing her formula, shaking her rattles, hugging her, and playing with her.
And now she had grown this much and was trying to venture out into the world on her own two feet.
My eyes grew just a little misty.
…Ahem. This won’t do.
At this rate, big sis is going to start bawling first!
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Afterward.
The day of the lecture arrived.
After exchanging emails with the school and coordinating the lecture schedule.
Our whole family went to Solsol High School and helped me prepare for my lecture.
Even so, I was no stranger to the stage.
I had competed in a speech contest and given a lecture in front of more than a thousand mathematicians.
Not long ago, I had even received an award in France in front of several hundred mathematicians.
But even so, standing on a stage with everyone’s eyes fixed on me was always nerve-racking.
I cautiously poked my head out from behind the stage and looked over the auditorium.
Murmur-murmur~
Hubbub-hubbub~
Hundreds of older sisters and brothers sat packed into the spacious high school auditorium, all wearing identical school uniforms.
Seeing that, I started getting nervous again. Thump-thump-.
I quickly slipped back behind the stage.
“Phew-.”
Then I took a deep breath.
It’s okay, Yoo A-yeon! You can do this!
Just then.
“A-yeon, you can do it.”
Mom and Dad hugged me tightly from either side.
Being enveloped in their warm embrace put me at ease.
“If I can be big sis’s strength, I’ll hug you too!”
Whoosh-.
Arin spread her arms wide and rushed into my embrace.
With those tiny arms, she squeezed me as hard as she could.
Then.
As oxytocin gently flooded my whole body, my nervousness melted away like snow in the sun.
“Phewww…”
With my family’s hugs, there was nothing in the world I had to fear.
“Yeah! Thanks, everyone. I’ll go give an awesome lecture!”
Pitter-patter-.
I walked onto the stage with a brave expression.
“Wow, look over there. It’s really Yoo A-yeon.”
“Eek, she’s so tiny! So cuuute!”
The high school unnis and oppas in the auditorium erupted into cheers. “Waaaaah-!!!”
“Heheh.”
I curled up the corners of my mouth as I walked.
A normal guest lecturer probably wouldn’t get a reaction like this, but I, Yoo A-yeon, was a hugely popular celebrity famous throughout the entire country.
The reaction was more intense than what most idols got!
This feels sooo good.
I reached the podium, stepped onto the footstool the school had prepared in advance, and hauled myself up.
Then I peeked my head over the podium.
I pulled the microphone right up close to my face.
Tap-tap-.
I gave it a couple of taps to make sure the sound was coming through.
“Hello! Solsol High School unnis and oppas! I’m Yoo A-yeon!”
I introduced myself confidently.
Clap-clap-clap-clap-clap-clap-clap-clap-!
The unnis and oppas responded with thunderous applause.
Far in the back, I spotted Eun-chae unni bragging to the friends around her, saying, “Hey, hey, she’s my friend-!”
I couldn’t help but snicker when I saw her.
✒️✒️✒️
“Ahem-ahem-.”
I cleared my throat.
Then I put the PPT I had prepared with Mom over several days and nights up on the screen.
Actually, a few days earlier.
While preparing this lecture, I had been lost in thought for a long time.
What on earth should I say to the high school unnis and oppas who were at the age when they had to decide on their careers?
Some sort of admissions counseling about which university and department would give them an advantage?
That was obviously out of the question.
After all, I was a preschooler who had never even gone through the regular education system.
For a kid like that to talk about college admissions would be ridiculous.
Then what could Yoo A-yeon, the mathematician who had proved the Riemann Hypothesis, possibly tell high school students?
The answer was obvious: mathematics.
The unnis and oppas were at the point in life when they were closest to mathematics as they prepared for college entrance exams.
That was precisely why there was something I could tell them.
…Of course, it wasn’t some secret trick for solving high school math problems faster.
Still.
I wanted to tell the unnis and oppas some fun stories about mathematics.
I hoped they wouldn’t think of math as nothing more than ‘something invented to torment high schoolers.’
I hoped their perspective on mathematics would become just a little more generous.
That was all I wanted.
The first PPT screen appeared in huge letters on the auditorium’s large screen.
[Math Is Actually Super Fun!!!]
When the title appeared, laughter leaked out here and there.
Okay. The mood isn’t bad.
I pressed the small remote that fit neatly in my hand and flipped through the PPT slides one by one.
Then I brought the microphone close to my face and began speaking slowly and clearly.
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“Unnis and oppas, your heads ache from solving math workbook problems every single day, right?”
In response, sympathetic cries of “Yeees-!” rose from various parts of the audience.
Apparently, the stress caused by mathematics was no joke.
“I think the unnis and oppas might come to hate mathematics because you’re forcing yourselves to study it under the pressure of having to get good test scores. I’m not even a high school student, so I can’t casually talk about that stress. But still…! I think mathematics is incredibly fun in and of itself…!”
I shouted with my eyes squeezed shut.
Maybe it was because my sincerity had gotten through.
The mood among the audience changed just a little.
— Wow, that’s the super-famous Yoo A-yeon. Should I ask for her autograph?
— Holy crap, she’s so freaking adorable... She’s so tiny and cute I wanna bite those chubby cheeks-!
From reactions like those.
— Hmm, should I listen to what she’s saying?
To reactions like this.
“So today, instead of the mathematics used to solve test questions, I’m going to talk casually about how mathematics is actually used in the world we live in.”
I gave them a bashful smile.
“I hope this lecture broadens the unnis’ and oppas’ perspective on mathematics, even just a little!”
✒️✒️✒️
I clicked the remote and moved on to the next slide.
[The Mathematics in Games]
I decided to start with games, something high school students would probably find interesting.
“Unnis and oppas, you like games, right?”
Cries of “Yeees-!” rose from all around in response.
It was a much louder shout than when I had mentioned math problems earlier.
“If any of the unnis and oppas here play gacha games, could you raise your hands?”
Hands shot up here and there in a flurry.
“If you look at the mobile game rankings these days, gacha games are always near the top. You’ve all done a pull or two, right?”
— I do it once a week…!
— I spent all my allowance…!
Laments erupted from all around.
As expected, gacha was scary.
I’d have to ban Arin from playing gacha later.
“Then have you ever thought something like this? Why does that person get the featured character in only fifty pulls, while I can spend two hundred pulls and still not get them!”
— Exactly!
“If the probability is one percent, shouldn’t it obviously appear if you pull a hundred times? You’ve thought that before, right?”
— Yeah!
“But actually, you shouldn’t approach it that way.”
I moved on to the next slide.
There was a chart explaining probability with easy-to-understand bars.
“Listen carefully. Even if the probability is one percent, someone might pull the featured character three times in a hundred pulls. Someone else might pull five hundred times and not get it even once. That’s how cruel probability is.”
A boy in the front row lowered his head dejectedly.
Apparently, he had some bad memories.
“To calculate this properly, you need something called the ‘Poisson distribution.’ It includes the natural constant e that you’ve probably seen often in calculus…”
P(X = k) = (λᵏ · e⁻ˡ) / k!
When a difficult formula appeared on the slide, I could feel the audience tensing up a little.
“Ah, it’s not difficult! I’ll just skip through it like this and tell you the conclusion.”
If this had been Arin, she would have explained the whole derivation from the Poisson limit theorem, but the unnis and oppas’ heads would probably start hurting, so I had to pass on that.
I put a large phrase up on the screen.
[The chance of not getting a 1% item even once in 100 pulls ≈ 36%]
[The chance of not getting a 1% item even once in 200 pulls ≈ 13%]
“Ta-da. If you pull for a one-percent item exactly one hundred times, the chance of not winning even once is a whopping thirty-six percent. In other words, three out of ten people will pull a hundred times, get nothing, and end up empty-handed. Even if they pull two hundred times, one person will still come away with nothing. That’s a pretty high probability, right?”
— Gasp…
— It’s that high?
Sighs erupted throughout the auditorium.
“The probability section in your textbooks is full of problems that twist coin flips and dice rolls into knots, so it can be hard to gain insights like this. But if you step away from solving textbook problems and broaden your perspective a little, you can perform this kind of analysis even in the gacha games you enjoy. Unnis and oppas, you should consider this carefully and protect your allowance before pulling from now on, okay?”
— Yeah…
Downcast answers drifted up from all around.
✒️✒️✒️
“All right, then, the second game topic.”
I clicked to the next slide again.
It showed the titles of popular online games these days, like League of Legends and VALORANT.
“Do you play online games these days? Most of them have ranking systems, right?”
—Yeah!
This time, a booming shout came from the boys.
“The nice thing about a ranking system is that you get matched with opponents who are right at your skill level, so you can play tense, exciting games.”
I paused for a moment.
“But unnis and oppas, do you know where this ranking system actually came from?”
— I don’t know!
A boy in the front row shouted loudly.
Normally, boys are at the point in their lives when they shout the loudest during high school.
Man, they’re bursting with energy.
“It came from chess.”
Perhaps it was an unexpected answer, because everyone looked intrigued.
“Yep. A long time ago, there was a mathematician named Elo, and apparently this mister really loved chess.”
Click-.
When I changed the slide, a black-and-white photograph appeared of a mathematician playing chess.
“Back then, I mean, even just sixty years ago, there was no way to express chess players’ skill as an objective number. So it was hard to know how strong a player was or who they should play against. The organizers just used their gut feelings, going, ‘Hmm, these two seem good, so should we have them play each other?’ If you compare it to today, it was like saying, ‘Platinum and Master both seem good, so let’s match them together!’”
— Whoa!
An incredulous sound came from the audience.
“Right? But once this mister created a system called ‘Elo rating,’ people could see players’ skill as objective numbers, and matching them became much smoother. They also adapted this system for games like League of Legends and VALORANT, turning it into MMR, or matchmaking rating. Of course, the formula isn’t exactly the same, and the way MMR is calculated varies slightly from game to game.”
— Ooooooh!
When familiar gaming terminology came up, the boys reacted with interest.
“And there’s something important the unnis and oppas need to know here.”
I lowered my voice slightly to draw their attention.
“This matchmaking system is actually based on the normal distribution from the probability and statistics you’re studying.”
Click-.
A bell-shaped graph with a bulge in the middle appeared on the screen.
It’s not a boa constrictor that swallowed an elephant.
For reference, textbooks call it the normal distribution.
But in university textbooks, it’s often called the Gaussian distribution, the Gaussian, or simply ‘Gaussian’ with “distribution” left off.
That’s because Carl Friedrich Gauss was the first to establish this probability distribution.
Ah… you again, G A U S S.
I took a moment for some surprise worship.
“On a graph shaped like this bell, the better players are located toward the right tail, while the worse players are located toward the left tail. And people with perfectly average skill are packed into the middle.”
I pointed at both ends of the graph, circling them with a laser pointer.
“So the truly amazing players in the heavenly realm and the truly terrible players in the deep sea take more than ten minutes to get matched because there aren’t many of them. There just aren’t many opponents to pair them with.”
—Ah! That’s why!
A boy slapped his knee.
That boy must be in the deep sea or the heavenly realm, because he really related to that.
“Exactly! On the other hand, the middle tiers are packed with people, so you get matched right away.”
— Ooh…
Exclamations rose from all over the auditorium.
They looked fascinated by the realization that mathematics existed even in the games we played every day.
I chuckled at their reaction and said,
“Heheh, see? Mathematics is actually super fun! Even my four-year-old little sister thinks it’s sooo~ much~ fun!”