You’d think of something, ask your friends, and they would be like “Gosh, I don’t know” and then you’d be like “Oh, well, guess that’s a thing I’ll never know” and then everyone just proceeds with their fucking day.

So $$n! \neq m^k$$ for integers $$n, m, k > 1$$ because by Bertrand's postulate there's a prime between $$\lceil n/2 \rceil$$ and $$n$$, right?

But invoking Bertrand's postulate seems like a big rock for this.

When you see $$\cong\mathbb{K}^{nm}$$ and you immediately think "ok, there has to be a matrix somewhere"

(The natural lifting of $$\omega \in \Lambda^1(M)$$ is $$\mathcal{L}_1\omega$$, where $$1: TM \longrightarrow TM$$ is the identity map.)

I spent a ridiculous amount of time trying to find the natural lifting of $$dz-x_1\,dy^1+\dots+x_n\,dy^n$$

Emojo Theatre proudly presents:

The Mathematicians Sup! I wrote so much math that they had to stop naming things after me so the other mathematicians could get some shoutouts too. I revolutionised mathematics and was a pompous twit about telling others I already scooped them. I had to pretend to be a dude so they'd let me in. I really like thinking about rabbit fornication, yo. I really hate beans. Love casual ocean murder, though.

Watch "A Different Way to Solve Quadratic Equations" on YouTube - A Different Way to Solve Quadratic Equations: youtu.be/ZBalWWHYFQc

You have to love how this paper basically forced the fᵤ and fᵥ notation for partial derivatives just by saying

no, I cannot derivate on any given manifold

but you know what I can do? this

*deep fried df(∂u) and df(∂v)*

Oh boy the explanation of what the Thom-Boardman symbols are is rather complicated here. I think it's time to whip out my good ol' friend Gibson...

my notes are very sloppy in general lol you can tell they are /by/ me and /for/ me as I skip everything I remember from last year and carefully explain everything I didn't understand the first time I read it...

whatever gets into the final thesis is going to need a serious revision but I hope I can explain the concepts more clearly by then

I'm not totally into ᵣJᵏ(n,p) as notation because the ᵣ makes it hard to handwrite the symbol and the author of this book keeps getting the ᵣ everywhere else lol because of course latex assumes it's a subindex for whatever you wrote /before/, not /after/

non mathematicians: i hate math because i hate numbers

me, a mathematician: what the frick is a number

Another suggestion is g.co/kgs/fktbUb

This one seems to go deeper and (I assume) is more complete as a reference. It uses techniques from sheaf theory.

Going to make this into a thread in case someone else is interested. I found this book which seems to be an introduction to the subject written *for* a particular course. Also, CC BY-NC-SA (kudos to Jiří Lebl!)

There is a thread on mathoverflow (mathoverflow.net/questions/313) but I ask here anyway in case someone is familiar with the subject

Do you know a book on several complex variables I can use for reference? Basically to check when the rules IRⁿ can be applied to Cⁿ (e.g. Hadamard's lemma apparently holds in Cⁿ)

The proofs being complicated is not a problem as I don't think I will read them; I've been told several complex variables is a tough branch of complex analysis.

I like #blackfriday . I get emails from newsletters I almost forgot to unsubscribe from 