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Von Neumann once gave a lecture which Lagrange published one hundred and fifty years before. He'd simply be unaware of Lagrange's Mecanique Analytique.

Could you imagine the embarrassment?

I didn't want that to happen to me. I come out with my paper on Hyper Real Analysis and the entire mathematical community looks at me confused and says 'yeah, we know. We're busy but you can play in the corner if you want.' No. So if and when I came out with my publication I'd have to hit the nail on the head.

And sure, I was nitpicking with that Von Neumann example. Von Neumann influenced all of mathematics and physics and he messed up one time when he was already established. That's not the same as trying to be some crazy kid popping out of the woodworking and blowing their minds. That's what I was trying to do. I was trying to be this half-mad-half-brilliant cookie little motherfucker who comes out of nowhere.

That was the goal. That was the plan. My phone buzzed on my desk. I stared at it. I didn't get texts except from Komachi who was home. I picked the device up.

u did gr8 have you studied for the wld history test yet?! I'm def gonna fail (_) wot you thnk gonna be on it? No tim left so I gotta cram… plz tch me!

It was a text message from Yui. I stared at it. I stared at it for a long ass time. I stared at it for so long a bug crawled from my left eye to my right eye and back again and I blinked slowly and I was still staring at it.

World history has too broad a scope, so cramming won't help you. There won't be any open ended questions. Look up the dates and the terminology and memorise them.

That was honestly the best advice I could give. It was probably too late for her to really get the material. She wouldn't succeed by spending a few days breezing through the wikipedia page for dates and events.

I set my phone on my desk and returned to set theory. I was trying to define a set in which infinity could be an element and the set could be closed. There was hyperreality which already existed and used aleph numbers. Aleph numbers referred to the indexing of well ordered infinite sets and their sizes. Some infinities were larger than others. For example, the infinite element in a set was \aleph_{0}. The element which came after the infinite element was \aleph_{1}. And there were species of calculus it made sense to write \frac{1}{0} = \infity and really mean it. The goal… the goal was to unite these two branches of mathematics under a single type of analysis. Hyper real analysis. It's what I wanted to be famous for inventing. Now if only these bugs would get out of my ears. I wanted to listen to Georg Cantor talk. I didn't want to listen to the worming of insects in my head.

My phone buzzed again on my desk. I stared at it. Two texts in an hour? What the fresh fuck?

...y so mad, hikki?~

('owo)?

Was this how people texted? I decided that I didn't like it very much.

Huh? I'm not mad.

I wrote back. I leaned back in my chair and breezed a hand through my hair.

It looks lik ur mad cos u dont use emoticons

('owo')!

I read her message. In my head I dared her to look me in the eye and tell me Yukinoshita used emoticons. I'd eat my physics textbooks if she did.

What culture is this? Are you Ancient Egyptian? We don't use hieroglyphics here.

Best of luck responding to that. Now… where was I?

My phone buzzed in my hand before I even set it down.

Wots hieroglyphics ('owo')?

Was she fuckin' serious?

That'll be on the test. You should google it.

I wrote.

I laughed. She was seriously going to fail this fucking test and I wasn't sure how to help her. And I wasn't sure that that was my fault. She was a hopeless case in this instance.

Now… aleph numbers. Different sizes of infinity. The Riemann Sphere was an object which at its North pole had the value of positive infinity and at its South pole it had the value negative infinity. It was a quintessential tool to complex analysis because it gave geometric perspective to values of infinity. It allowed for some problems to be motivated geometrically in this way. It sort of worked by folding the complex plane up on itself. Into a sphere of sorts. Of course it wasn't a sphere. It wasn't even a hypersphere of higher dimension than three.

It was really its own shape with its own properties and it was absolutely fundamental to hyper real analysis the same way the unit circle was quintessential to complex analysis.

e^{i \theta} = cos(\theta) + i sin(\theta)

The goal was to discover something similar for hyper real analysis using the hyperbolic sine and cosine. Then to use that invention to make problems current mathematicians struggle with trivial. The same way Newton had done with the Principia Mathematica. But that was a tall order. Newton was seriously the best. It was him or Euler for the question of who was the best mathematician of all time. But Newton won in terms of physics. He made Einstein look like a lil' bitch. Einstein had like, one good year. Where he kind solved like three different problems but not completely. Compared to the way Newton and Euler were gobbling up and inventing unsolved problems Einstein was nothing. I mean- he was the best we had after a long drought. And that was something. But it didn't put him on the level with Euler and Newton. He didn't eat up problems like crazy.

I sighed. And I was also probably a little bitch. I was probably worse than that too. Would I even kind of half solve any of these problems the way Einstein did?

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It was two weeks before the midterms. A straight‐laced male high school student is someone who stops by a family restaurant on the way home just so he can study. I happened to stop by on the day the teachers visited the city education department, which meant school had ended early and club activities were cancelled.

I was doing easy work, just writing out mathematical statements in English over and over. I was like a great Buddhist priest from long ago; you could even say I was like Shinran. Incidentally, Shinran was the person who preached the doctrine of "relying on others to find enlightenment" ‐ he was a great man. Those teachings made a deep impression on me, and so I decided to sponge off somebody too. I thought like a Buddhist so I was totally Shinran.

After some minutes, I finished taking notes and looked around my surroundings as I downed my cocoa. That was when it happened.

"Yukinon, sorry we couldn't go to Saize," said a girl. "We'll have a Milan‐style rice pilaf next time, okay? I also recommend the Hamburg steak with vegetable salsa, though…"

"I don't particularly mind where we go. They all do the same thing," said another girl. "Come to think of it, is Hamburg steak even Italian cooking, I wonder?"

I heard familiar voices.

"Oh!" one voice exclaimed.

"…ah," the other voice said.

"Damn," I groaned.

The two uniform‐clad girls who had walked inside were Yukinoshita Yukino and Yuigahama Yui. To my consternation, I recognised them as my clubmates. (Incidentally, "clubmate" is the word you use to refer to club members in a cultural club, as opposed to "teammate" for a sports club. It was the first time I'd ever tried using the word.)

"Hikki, what are you doing here?" Yuigahama asked.

"Er, uh, the usual…"

"Ooooh, didn't expect to see you here. Me and Yukinon were gonna study here a bit… so, um, wanna join in our study group?" Yuigahama said as she looked back and forth between Yukinoshita's face and mine.

"Yeah, whatever," I said. "Well, I gotta do the same things you do. Mostly."

"…indeed," said Yukinoshita. "Having you here won't change much."

For once, we weren't biting each other's heads off. For a moment, Yuigahama cocked her head slightly, dumbfounded at this development, but she put it out of mind with a "'kay, it's decided!" and rushed over to my table.

We helped ourselves to new drinks at the self‐serve drink bar, and as we were taking them back to our table, Yukinoshita eyed the unmanned counter fixatedly. She held her cup in her right hand and, for some reason, a small coin in her left. After a pause, she said, "Hey, Hikigaya. Where do you put the money?"

"Huh?" I wondered. Was she pulling my leg? Did dearest Yukinoshita‐san really not know how a self‐ serve drink bar works? Just what kind of sheltered upbringing did she have? "Nah, you don't need money. It's just, you know… like a buffet only for beverages?"

"…Japan is quite the bountiful country," Yukinoshita said with a dark smile on her lips, expressing emotions I didn't understand. As she spoke, she gave up her position in line for me. And then she watched me earnestly as I filled my drink. The machine let out a hum as the cola poured into my cup, and Yukinoshita watched it all happen with sparkling eyes.

I was speechless. Just to make certain I wasn't mistaken about what I had just seen, I set my cup under the espresso machine while I was at it. When I pressed the button for cocoa, she let out a quiet, "Oh, so that's how you do it…"

With a shaky hand, Yukinoshita filled her cup with the drink she wanted, and the three of us returned to our seats together. It was about time for our study meeting to begin.

"'mkay, let's start."

At Yuigahama's signal, Yukinoshita promptly put her headphones on. I looked at her sideways, and then inserted my earphones.

Yuigahama looked at us with a horrified look on her face. "Huh?! Why are you listening to music?!"

"You see, you're supposed to listen to music when you're studying," I said. "Blocks out the noise." And the bugs. And the voices.

"Indeed," said Yukinoshita. "The fact that I'm concentrating when I'm blocking out noise is excellent proof of its positive effect on my motivation."

Yuigahama banged her fist on the table. "That's not how it works! Not at study meetings!" she protested.

At Yuigahama's reaction, Yukinoshita put a hand on her chin in a gesture of deep thought. "So what do you propose we do at this meeting?" she asked at length.

"Uhhh, work out what's gonna be on the test, ask questions on what we don't know… 'course, we'll squeeze in some breaks, and afterwards discuss stuff, and then exchange info. And… we'll chat for a bit, I guess?"

"That's just talking the whole time…" I cut in.

It was a study meeting without a single bit of study. Wouldn't you call that a waste of time?

"Studying has always been a solitary activity in and of itself," Yukinoshita said, as if realising something. I thought the same way.

In other words, if you're a loner, studying is well within your capabilities! Yadda yadda. Hey, that's what it says in those manga that advertise home learning courses.

Yuigahama scowled at the idea of studying right from the get‐go, but when she saw how intent Yukinoshita and I were on studying silently, she let out a resigned sigh and got to work.

I pulled out my phone and was breezing a new development into Quantum Programming languages. Information theory and all that.

And in that way, five minutes passed, and then ten, and then an hour.

Looking at the two of them, I saw that Yuigahama had her face scrunched up slightly and she kept stopping her hand. Yukinoshita, on the other hand, went on solving maths problems without so much as a murmur.

Eventually, Yuigahama turned her gaze to me and spoke up as if she couldn't handle the intense concentration anymore. "Er, um… so about this question…" she asked blushingly, as if her pride couldn't handle the embarrassment of asking me of all people a question.

"The Doppler Effect, huh…" I said. "What do you wanna know?"

"Well, what is it?" Yuigahama asked.

"You ever listen to a bus and hear the high pitch of the engine as it passes you? And then the pitch falls once it's going away?"

"Oh yeah. And with trains and stuff!"

"Well it's that. The sound waves get scrunched up as the object approaches you. By the velocity of the bus. And they get drawn out in frequency as the bus travels away from you. The same thing happens with galaxies moving away from us in the universe and the light they are shooting towards us."

"Huh… So as we're approaching…"

"The frequency increases and so does the pitch."

"And as we're moving away?" She wondered.

"The frequency decreases and so does the pitch. The way I remember it… never mind. That won't be helpful."

"Why?" She asked.

"I always remember that light from distant galaxies is turning red and red is lower pitched light. But I have the feeling that won't help you. Hm… Just try and remember the feeling of standing in front of a moving train and whether the noise goes up or down."

"Thanks Hikki…"

"No problem," and it wasn't.

"I thought you weren't Tao whatever?" Yukinoshita accused.

"So I don't want to teach for a living. I want to research. Doesn't mean I can't teach. I just don't want to. My ability to communicate difficult subjects in a simple manner is indicative of my understanding of them."

"Your ego? Again? Even in this?"

"I'm good," I purred at her in that way she hated. She scowled.

Yuigahama closed her textbook and notebook in resignation and slurped her iced tea through her straw. When she held up her glass and looked around, she let out a gasp as if realising something.

My interest piqued, I looked in the same direction, and standing there was a good‐looking girl dressed in a scruffy sailor uniform, who was cute in an unkempt sort of way. "It's my little sister…"

My little sister Komachi was standing in front of the register, smiling cheerfully. Next to her was a boy in a middle school uniform.

"Crap, hang on," I said, standing up from my seat just as they were leaving. But when I got out of the restaurant, the two of them were nowhere to be seen.

Reluctantly, I went back inside, which was when Yuigahama spoke up. "So, uhhh, was that your sister just now?"

"Ugh. Why was she with a boy in a family restaurant…?"

I was so shaken I couldn't get back to studying. There was no way my little sister could be hanging around in a family restaurant with a boy I didn't know.

"She might've been on a date!" Yuigahama suggested.

"That's bull… there's no way…"

"You really think so? Komachi's cute so it's no surprise she'd have a boyfriend, right?"

"Ugh… you might be right. I just wish she would have told me!"

Yukinoshita took off her headphones and glared at me. "Please stop yelling insipid statements. I heard you even with my headphones on just now." It was like she was telling me she was holding a grenade pin in her hand. Make one move and you're dead.

"Er, no. It's just, to think my little sister is with a mysterious, unidentifiable boy…"

"He was a middle schooler no matter how you look at him," Yuigahama said. "I get you're worried about Komachi, but she'll hate you if you pry on her, ya know? Lately, my dad's been all like, 'do you have a boyfriend?' and it's a total drag."

"Hahaha. Your dad's got no clue! In our family, we trust that my little sister doesn't have a boyfriend, so no one's asking her. So seeing all that was a shame, to be honest," I said. "Come to think of it, how come you know my little sister's name?"

I'd never told my little sister's name to anyone. Hell, no one even knew my name, let alone hers.

"Huh?! Uh, um, er, right… your phone? I'm sure I saw it written there…" Yuigahama said, looking away for some reason.

Oh, right, now that she mentioned it, I did hand over my phone to her once. She might've seen it inside a text. "That so? That's good. I thought I had become one of those siscons and let her name slip even without realising just how much I love her…"

"Uh, that really is a siscon reaction, I think…" Yuigahama said, half recoiling from me.

"What? Because I don't want my sister to find my corpse? Quit looking at me like that!"

"Hikki..."

With her knife and fork in hand, Yukinoshita looked at me, utterly speechless with a mixture of horror and disgust in her eyes. She had been unmistakably thinking of stabbing and cutting at my raw flesh right up until I finished speaking. "It's scary that I can't tell whether you're joking when you say that," she remarked. After a pause, she went on, "If you're so curious, why don't you ask her at home?"

Having stated their final words on the matter, Yukinoshita and Yuigahama returned to studying.

But my hand was unmoving because the whole time I got flashbacks of Komachi calling me 'big brother,' followed by, "I'm gonna marry big brother for sure when I grow up!" and the stern disapproval of my father from then on.

And so I didn't ask her anything when I got home. I‐it wasn't like I thought she'd hate me if I pried on her or anything!

Damnit.

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-WG