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I had my interview today after school. I sat down at the coffee shop and waited. It was a dainty cafe close to my house. I knew I wouldn't recognize my interviewer when they walked in but they would hopefully recognize me.

I had my notebook before. Notes on hyper reality. A touch of infinity to it. The zero vector was perpendicular to every other vector one could think of. I was trying to find a vector parallel or antiparallel to every vector one could imagine. I thought that had the touch of infinity to it. It was a difficult problem. Let alone prove.

I took a sip of coffee and pulled up the natural logarithm function. Then I pulled up the exponential function, then I plotted the harmonic function. If I could just find the area bounded by these three curves then I could see the far side of forever.

A hyper real unit to compliment the imaginary unit and the ordinary unit would have crazy applications. It would be a whole new branch of mathematics and would trivialize even complex problems. That's what the complex analysis allowed. Even simple counting problems were solved by extending to the complex plane. Complicated problems that would take longer than the age of the universe to solve by brute force made simple. Hyper reality would allow this too. Complex hyperreality, the union of the real numbers, imaginary numbers, and hyperreal numbers would make three dimensional space make sense. I could solve Navier Stokes with that. I might even be able to do the Riemann Zeta Hypothesis or Yang Mills existence and mass gap. Like I said it would trivialize these incredibly complicated problems.

I had my notes on the subject before me. I hadn't gotten very far. My attempts to discover the hyperreal unit and define it were a total loss.

Someone walked in and ordered at the bar. Then they waved at me and sat down across from me. They were a tall, good looking man, I suppose. He was classically handsome. He had brown eyes and black hair. He didn't stand out in a Japanese crowd.

"Hikigaya Hachiman?" He asked.

"That's me," I answered. "And you are?"

"Nakamura Hitochi," he grinned back at me.

I gave him a gentle smile.

"So? Where do we begin?" I wondered.

"Let's start with your proof. I understand it was solving an open problem first explored in the nineteen fifties."

"The sofa couch problem," I clarified. "What, put simply, is the largest two dimensional object one can get around a one by one corridor?"

"That sounds so simple." He chuckled. "I take it that's not the case."

"Well it can slide and rotate at the same time. That's what makes it tricky. Its center follows a non linear path."

He made a note of that. He was scribbling in a little pocket book.

"And what does the sofa couch look like?" He asked me.

"I'm not sure," I answered.

"You don't know? I thought you solved it?"

"I found its area. I didn't find the actual shape. I strongly suspect there are an infinite number of valid sofa couches and rotational paths which all have this given maximum area."

"Fascinating…" he trailed off. "And what pray tell is the maximum area."

"The magnitude of pi zeta of pi plus i pi."

"Zeta?"

"The Riemann Zeta function. It counts the prime numbers. I found its connection to my sofa couch problem fascinating."

"I've heard of the Riemann Zeta Hypothesis," he nodded. He made a note in his book.

"I don't know too much about it myself." I responded. "I'm no expert on prime numbers. But their connection here to the sofa couch problem is most intriguing. There are no coincidences in math."

"You really believe that?" He asked.

"Take the monstrous moonshine conjecture for example. The monster group in group theory found a connection to a totally unrelated part of mathematics. It was considered moonshine that there was a connection but it was there. I think someone won a fields medal for that one."

"Will you win a fields medal?" He asked. "For your sofa couch proof?"

"Unlikely. I didn't do anything truly exceptional." I answered. "I just rigorously applied fourier."

"What do you mean by that?"

"Well any curve can be written as a linear combination of sines and cosines. I took the top of the couch and wrote it as a linear combination of sines and cosines. I took the bottom of the couch and wrote it as a linear combination of sines and cosines. I did the same for the rotational path. I did the same for the rate of rotation. Then I took the first derivative test of the integral of the area between the two curves. It wasn't anything anybody else couldn't do. It was a truly brute force method. I have no doubt cleaner proofs exist."

"Brute force? You called it?"

"That's right."

"Now for the interesting questions. Do you believe mathematics is discovered or invented?"

"Yeah probably." I answered. He laughed. "There are so many coincidences. Aren't there. It's miraculous. For me, mathematics is like a game of chess with god. He trounces you, of course. But you're allowed to play as many times as you want until suddenly he isn't beating you the same way any more. And ahah! Eureka! You have discovered something."

"Interesting. Do you believe in god?"

"I do. Just not a nice one."

"Interesting. Well I think that's enough for my spread on you."

"Sure," I agreed.

"Anything else you would like to say while I have you here?" He asked.

"No, I don't think so…" I trailed off. "No. I'm good."

"Okay. I'll be off. Can I get your email address just in case I have any questions?"

"Sure," I answered and gave it to him.

"Well I'll be off. Sayonara."

"Sayonara." I returned.

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Iroha Isshiki finally cornered me near my home room. I'd been dodging her because she made me uncomfortable but Yukinoshita made it clear she was looking for me. She found me eventually. She leaned in real close. I took a step back away from her. I brushed off my front in an attempt to get rid of something on me when there was nothing.

I just wanted some fucking space from this junior.

"Senpai I wanted to find you. You've haven't been around the service room."

"Well the service club is disbanded," I parried.

"You're friends meet there."

"They sure do but I have no reason to go there."

"Oh. I thought you were avoiding me senpai."

I was but that was neither here nor there.

"Nah. What'd you need?"

"Well I wanted to thank you. You really helped me out."

"It was all Yukinoshita. She blocked all my ideas." I dismissed.

"I heard from her that you helped her win."

"I didn't. Not really."

"Oh. I see. Well I think I see Hayama."

"Hayama? What do you like hi-" I stopped. "What do you think of him."

"Are you coming on to me. I'm sorry but you'll have to try harder than that."

"I wasn't. Obviously," I dismissed once again with a wave of my hand.

"Don't treat me like a pest!"

"Don't act like a pest," I shot back. "I'll treat you how you're acting."

"Don't be like that senpai~!"

"Go talk to Hayama. Leave me be."

"But you're so interesting."

"I'm really not," I denied. "I'm boring."

"I saw your name in the paper."

"What about it?" I demanded.

"Well say what you will but that's not boring."

"Did you bother to see why I was in the paper. I solved a math problem. Boring."

"Hey. I like math. I think it's cool you're solving these things. You're cool senpai."

"Not really…" I stammered back.

"Well it means you're smart. Are you a genius senpai?" She wondered.

"Kinda," I shrugged.

"Well you're probably a prodigy to be solving these things so young."

"Maybe," I granted. "I'd rather be blind to be honest."

"So you see things?"

"I see a lot of things. Not always good things."

"That sounds unfortunate. I'm sorry senpai."

"Look. Anything you think you owe me you don't. Anything you think you know about me you don't. We're strangers. Go bother Hayama."

"Most people wouldn't go out of their way to treat me like a pest or dismiss a favor so readily."

"You don't have anything I want," I denied.

"Are you sure?"

"Pretty sure. Now if you'll excuse me I'm off to my house. I have work to do."

"Math work?"

"More math work."

"Well I think you're interesting. I'll see you around senpai."

"Sure. Whatever."

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-WG