Mathermatical Notation Explained

→ 3 IX 2021

such a weird day today. i finished complete spaces and then moved on to preparing for the math conference i'm going to on sunday. there is a lot of high level stuff so i won't be able to learn everything, of course, but i'm doing my fav thing ever and enjoying it thoroughly. that is, switching from a topic to a topic in the spare of 15 minutes and reading a bit about anything until it stops being ✨super exciting✨

this amounts to a total of 8 hours of math and i am not done yet. love it, absolutely love to waste time like that

concentration: fucking ∞

tomorrow i'm doing an algebra speedrun with bf and two of our friends. this is an experiment aiming at seeing how much information we are able to pack into our heads in one sitting. we haven't studied abstract algebra before. then in a few as i mentioned i am going to a math conference, with bf and our other friend. excited about that too. i fucking love math

omg that's the most beautiful thing I've seen today

Chapter 2 of commutative algebra!

A monoid? Oh, you mean a monad on a one point set in the bicategory of spans of sets?

reverse gaslighting where i pretend to know exactly what you are talking about

“Netflix and chill?”

No, PDF and cry

The beautiful modernism of Oliver Byrne’s, The First Six Books of the Elements of Euclid, 1847

Visualization of the Rubik's cube

fields of mathematics

number theory: The Queen of Mathematics, in that it takes a lot from other fields and provides little in return, and people are weirdly sentimental about it.

combinatorics: Somehow simultaneously the kind of people who get really excited about Martin Gardner puzzles and very serious no-nonsense types who don’t care about understanding why something is true as long as they can prove that it’s true.

algebraic geometry: Here’s an interesting metaphor, and here’s several thousand pages of work fleshing it out.

differential geometry: There’s a lot of really cool stuff built on top of a lot of boring technical details, but they frequently fill entire textbooks or courses full of just the boring stuff, and they seem to think students will find this interesting in itself rather than as a necessary prerequisite to something better. So there’s definitely something wrong with them.

category theory: They don’t really seem to understand that the point of generalizing a result is so that you can apply it to other situations.

differential equations: physicists

real analysis: What if we took the most boring parts of a proof and just spent all our time studying those?

point-set topology: See real analysis, but less relevant to the real world.

complex analysis: Sorcery. I thought it seemed like sorcery because I didn’t know much about it, but then I learned more, and now the stuff I learned just seems like sorcery that I know how to do.

algebraic topology: Some of them are part of a conspiracy with category theorists to take over mathematics. I’m pretty sure that most algebraic topologists aren’t involved in that, but I don’t really know what else they’re up to.

functional analysis: Like real analysis but with category theorists’ generalization fetish.

group theory: Probably masochists? It’s hard to imagine how else someone could be motivated to read a thousand-page paper, let alone write one.

operator algebras: Seems cool but I can’t understand a word of it, so I can’t be sure they’re not just bullshitting the whole thing.

commutative/homological algebra: Diagram chases are of the devil, and these people are his worshipers.

I know one person who started phd without master's but that's in computer science and he already had a research startup running independently. he had a med degree already and his research is about using ML in medicine, so he was granted a "special permission" to start a phd. the guy is a very hard-working genius

now when it comes to math, one of my friends claimed that it is possible to start phd after bsc if someone graduates magna cum laude or something. I never heard of that before and it sounds insane, so I asked my advisor about it and he never heard of that either lol moreover he said that it's a stupid idea unless someone already has a few publications

afaik in the US the undergraduate degree takes 4 years and phd takes 5, it's like a mix of masters and the actual phd, so I guess it evens itself out

okay this might sound stupid to a lot of you but I thought you need a masters degree before you can do a PhD. so weird to me seeing 22 year olds doing a PhD after a bachelors degree. I don't know where I got this idea but I'm having a hard time rearranging my world view around this, even though this is so inconsequential thing to be wrong about xd

me when Čech cohomology

i love math. i hate math. i can do it all day, everyday. i cannot solve a single question. it's my favorite subject. I would rather kms than open the book. it's beautiful and everything makes sense and it's the best. it's fucking useless and nothing is logical and it's the worst. it's the loml. it's my arch nemesis.