Positively Prime

One thing that I weirdly like about mathematics as a field is that, as a field concerned with pattern recognition and relationships between abstract concepts, it attracts people undergoing genuine psychosis. I don’t say this in a negative light, nor am I making fun of the condition; I am simply and utterly fascinated as to what the hell they’re talking about. Take this for example:

This is genuine nonsense to me, but I know to the person who created this, this is a work of art. Or this:

What does the animation of a bunch of lines have to do with Keanu Reeves??? I am genuinely curious, please tell me more.

This is just what regular math research does to you actually

can I not express a sign of relief in my exposition, jeezzzz

Something about maths that'll never not amaze me is how sometimes you'll read a certain topic and it'll be kinda out of reach, like you kinda get the idea but the details go over your head. But then a few months later you'll come back to it and somehow it makes so much more sense. Maybe it's cause you've realised something that makes it click or sometimes you'll have learnt other things and it'll put it in a new perspective. And it's honestly one of the best feelings

The cool thing about doing math professionally is that you can work anywhere - on your walks, in the shower, as you fall asleep - just by rotating problems in your head. What's not so cool is that this drives you insane

Shit man, this algebra war is fucked. I just saw a guy clap his hands together and say "the six functors" or some similar shit, and every chain complex around him got put into a short exact sequence, had their long exact sequence taken out and then got their homology calculated. The camera didn't even go onto him, that's how common shit like this is. My ass is casting lagrange's theorem and degree 2 equations. I think I just heard "power word: operad" two groups over. I gotta get the fuck outta here.

Now that this poll is over -- assuming it is over now and I didn't somehow mess up when scheduling this post -- I suppose I should offer some sort of explanation for the options it presents.

Then why did I structure the poll this way? Why the focus on applications and areas traditionally thought of as "applied mathematics"? Why force whole fields of pure mathematics into a ludicrous classification scheme that their practitioners wouldn't recognize or accept, or create artificial splits between what are widely considered one single unified subject, or focus solely on applications for an area famous for its abstraction and generality?

Well, I assumed most of the people who saw the poll would be pure mathematicians, or at least math majors with a particular interest in pure math. Pure mathematicians certainly created most of the "favorite area of math" polls I'd seen before on this site, and I think most mathblr people would self-identify as pure mathematics (if, that is, they even acknowledge applied mathematics as a coequal branch of mathematics at all and don't just assert that all of math can be reduced to analysis and algebra and number theory and topology and geometry and logic).

And, if you are a pure mathematician, and you were puzzled by the way this poll attempted to force your favorite area of mathematics into a classification system that clearly didn't work, if you were a little bit appalled and offended by its attempts to collapse entire areas of mathematics with their own different histories and objectives and traditions into a single 'oh, everything else I guess' mess at the bottom of the list, if you wondered why I didn't just ask about "favorite area of applied mathematics" and leave the pure mathematics out of it ... well, now you have a little bit more insight into how applied mathematicians feel when you ask them if their research area is part of "continuous math" or "discrete math".

Not gonna lie I thought the poll was bait. Like entire 100+ year old research areas were not represented lmao, but still a fun attempt!

She snake on my lemma til I long exact sequence in homology

I think at its heart, calculus is as much abstract algebra and topology as it is analysis

Calculus (the first year uni course) is applied D-module theory

It's kinda cool how Hungarian mathematician Riesz' (known for the Riesz representation theorem and the Riesz representation theorem) first name is 'Frigyes'. That's what I say when I read his results!

Finally some Riesz representation! Frigyes has a brother named Marcel Riesz, and they even proved a theorem together!

Just found a Youtube Channel

Funny that all the real hardcore math in physics comes from classical mechanics, GR is real math but seems well understood at this point, and QM is baby math

I mean depends on the level you’re working at. Finite-dimensional non-relativistic QM is just linear algebra, sure, but as soon as you even want to deal with continua with any kind of rigor you start needing some relatively complex functional analysis. More to the point, QFT is properly formulated in terms of fiber bundles and arguably makes use of more of the formalism of differential geometry than GR does. And then there’s more specialized topics that fall within the general heading of quantum physics: anyon fusion is described by modular tensor categories, the classification of topologically ordered states uses K-theory, etc.

Wait. What is the formulation of QFT in terms of fiber bundles????

Gauge fields with gauge group G are connections on a principle G-bundle over your spacetime manifold, and matter fields are sections of associated bundles

to my best knowledge, a bunch of quantum shitfuckery is in the language of C*-algebras, noncommutative geometry, etc.

besides that, there is plenty of hardcore math in string theory (if string theory counts)

In algebraic QFT all of these C*-algebra applications come back, supposedly. I'm more on the mathematics side, but my operator algebra professor said (paraphrasing/might be wrong) that in QFT one looks at the light cone and then all particles in the light cone. To each particle there is some (typically small) C*-algebra associated (e.g. 2x2 matrices), but since you want to deal with infinitely many of such systems interacting in a certain way you have to take the direct limit of the algebras (in the sense of category theory), which then gives you a hyperfinite bullshit factor of type something blabla.

I think this can be seen as a noncommutative analogue of what kwarrtz is describing, but I am not knowledgable enough in QFT to say anything there

i have crazy garlic fingers from peeling and chopping garlic cloves yesterday this phenomenon is always fascinating to me because it reminds me that i, too, am made of meat, and therefore i am also susceptible to being seasoned