Preparation 2
"Hello, Librarian Yura."
"Ahhh... Welcome~ Gail."
Yura, the librarian mage whose oversized glasses had slipped down her nose while she bowed repeatedly, pushed them back up. Gail greeted her politely as always and passed through the entrance.
"Upper floors again today?"
"Yes."
"I've been hearing a lot of rumors lately."
Gail paused at Yura's casual remark. The magic library had no such thing as silence. There were bizarre books that only conveyed their meaning when read aloud from the reading desks, so the concept of hush didn't fit the magic library at all. That was why a certain level of chit-chat was allowed inside, and in the process, the librarian mages picked up on the gossip. Not to mention the posters plastered all over the Library Arch Bridge leading to the library—no one could miss those.
"It's nothing much."
Gail scratched his chin and tried to move on. The rumors had even spread to the library especially because the Gail fan girls frequented it to catch a glimpse of Gail, who was practically a library regular. It was only natural, and the librarians didn't hate the library diehards that much. Having a popular figure like Gail visit so often kept the Imperial Academy library bustling.
"Hang in there, Gail! I'm always cheering for you."
"Thank you..."
"It's with that friend you met in the library back then, right?"
"Yes, the ranking match. A revenge match, actually."
"You two actually suit each other pretty well."
"...Pardon?"
Gail let out a dumbfounded voice at Yura's overreach. No way did a 7-year-old early enrollee and a 17-year-old like himself suit each other? But Yura tilted her head, looking at Gail strangely instead. Well, once you're in the academy, you see grades, not ages.
"You could become great seniors and juniors!"
"...I hope so."
Every time he saw that arrogant face pulling a "heu~cheop☆" act, his stomach boiled. Was that even possible? Curses bubbled up unbidden; it didn't seem like they'd develop into a good relationship. They'd probably end up as sworn enemies first.
"Don't take it too personally. That kid's actually a loner, that's all."
"Haha, yeah... I suppose."
But Gail, kind-hearted and unable to speak harshly, couldn't even tell Librarian Yura to drop it. Turning away, he thought maybe advice from someone as detached from the world as Yura could be helpful. That thought lingered, but only briefly.
No. Thinking back, he just wanted to flick that bratty kid on the forehead. She'd stared at him with fierce eyes, then grinned wide and flashed a thumbs-up.
"Still, it's a ranking match—you've got to win! I'll be rooting for you, Gail."
"Yes... thank you."
Gail ended the conversation there and entered the library. And trailing behind him was a Black Class freshman.
Luca had been hiding and watching the two talk for a while, but Yura approached as if she'd known he was there all along. Everything that happened in the library fell under the librarian mages' watchful eyes.
"Eavesdropping on others isn't nice, freshman."
"Ugh...! How did you... know?"
"Librarian mages know everything that happens in the library. What brings you here?"
"Well... it's a library, so obviously to borrow books."
Luca brushed her off vaguely. Yura narrowed her eyes amusedly at him. At 13, mental growth was mostly complete. Among academy freshmen, there were ones like Kesera who were total prodigies, but this kid couldn't hide his lies well. That pure, untainted innocence was visible in his eyes—it was downright cute. And... she saw echoes of her own past in his cowering posture.
"Then tell me your full name. We need to make your reading card."
Luca doubted his ears, wondering if the librarian was just being polite. Full names were for noble archmage bloodlines.
"Uh... I'm... I'm not that kind of person."
"The Imperial Academy's principle is to ask without prejudice, no matter who you are. Everyone needs a reading card at first. Even the eldest daughter of the Ascentrius family got one just a few days ago."
"My name's Luca. No family name..."
"Black Class Luca... Got it. Welcome to the academy library. Anyone attending the academy is welcome here~"
Yura beamed at Luca and wrote his name on the reading card. As the name was inscribed, a faint light etched in, infusing a magic circle that made it impossible to lose.
"Um... even Black Class can enter the library?"
"Of course—as long as you don't damage the books, anyone can."
In truth, aside from staff areas or places needing hygiene like special-purpose rooms, White Badges were welcomed everywhere without restrictions. Black Class had some access limits, though. Some academic clubs had rank requirements for joining, and places like party halls required Yellow or Red and above to reserve. Luca had assumed the library was like that and planned to sneak in while the two were talking. Busted now, though.
"Is that really true?"
"Of course, but for dangerous mid- or lower levels, you need a guardian. You never know what might happen down there. Even I can't go to the lower levels."
Yura smiled warmly at Luca and handed him the reading card. Strangely, there were quite a few promising new students this year who seemed like library regulars.
"Here, your reading card. Shall we tour the library together now?"
"Really? That's okay?"
"Don't believe me? I was an academy student before becoming a librarian mage, and I started in Black Class too."
Yura smiled with her eyes and beckoned him. Before he knew it, Luca had forgotten his original reason for coming amid the chat with the librarian. To someone scraping by on alleyway odd jobs, the idea of accessing high-class books in a place like this felt like a dream.
"And you owe Gail an apology, right? Why'd you follow him secretly?"
"Ah... I was curious how White Badge seniors study..."
Instead of pressing, Yura took Luca's hand and dragged him to Gail. Just then, Gail had entered a quiet reading room and was reviewing ballistic triangular calculations to recheck magic trajectories. At the knock, he looked up to see an unfamiliar Black Class freshman there.
"Gail, I caught a stalker for you."
"Sorry."
What? Gail brushed it off. Ever since the Gail fans appeared, he'd had countless stalkers—or fans, depending on how you looked at it—following him. And weirdly, for a upperclassman who rarely mingled with freshmen, this year he kept getting tangled with them. Even the student council was after him.
"I followed because I wanted to see how a White Badge senior studies... Sorry."
"No worries. Ask me anything if you have questions."
Gail treated Luca kindly, just as he did others. Luca felt the unfair grudge in his heart slowly melt away at the senior's friendliness.
Just had dinner and came back early☆ Classes are nothing compared to this time alone in my room. Once I'm in the dorm, I start missing home. If only it were vacation...
"Mom... I miss you☆"
And... tomorrow's the ranking match. That total nobody keeps lingering in my head. I don't care about that lame-ass jerk. Seriously, zero interest☆!
I opened my diary right away and jotted down today's classes and events briefly. Oslo's tricky lecture on replication magic inference came up.
When n is an integer greater than 3, there are no positive integers X, Y, Z satisfying Xⁿ + Yⁿ = Zⁿ.
Transposing Fermat's Last Theorem magically to this world was exactly Oslo's inference. Unlike modern math's exponential systematization, this world's magic was still vague and unstructured after 800 years unproven. Drawing the formula from that magic parchment as a spell actually produced three overlapping circular magic circles inscribed with characters.
Here, does a general solution for magic overlap exist? When you plug in the four elements, does a proper elemental form solution exist? It's a magic circle that looks "super easy." To prove the theorem from my past life, I'd need modular forms, so in this world, develop corresponding new magic.
I'd only been pondering topological magic shapes before, but developing this sparked interest too.
Yeah, this is my calling. Not rolling on the floor thinking about that lame-ass jerk... but developing higher-dimensional magic.
How fantastical and beautiful!
I'd previously test-fired up to elliptical magic shapes. Fermat's proof used reductio ad absurdum: assume a general solution exists and prove no integer solution does.
An intuitive proof method popped up. Mana threads spun from my fingertips, adding strokes to the magic circle.
To create modular magic unlike math formulas, what mana to use? And how to generate it efficiently?
Researching this is the real me.
My mana spilling from the practice room after so long tangled every which way. This is my path.
Did I burn too much mana on the proof yesterday? The next day, my condition was awful. As I groaned trying to get up...
Something damp and hot had pooled around my butt.
"Ah..."
It was stained red. Unexplained vaginal bleeding.