Me: *Removes My Cat From My Lap To Do Something Else.*

everybody cries doing their math hw, those who claim they don't just haven't met that hw yet

this unlocked some ancient pain lol

types of mathematical terminology

descriptive

honeycomb

gradient

quiver

computable

less descriptive

centroid

chaos

end

flag

not descriptive

ring

allegory

surreal

group

you know this person, right?

euclidean

abelianization

grothendieck

cartesian

took some non-english word and hoped for the best

eigen

algebra

shtuka

nullstellensatz

i made up a word!

ergodic

functor

adele

logarithm

idk, just give it a generic name

regular

well

admissible

well-admissible

like, specifically, it’s a vague thing

flasque

lax

fuzzy

pseudo

one symbol and a word

*-algebra

D-module

K-theory

†-compact (although that’s going to usually be written “dagger compact”)

just random letters

rg

cwf

Fσ

erf

well, google, one of them is a giant fuckin red dog

We need books that affect us like a disaster, that grieve us deeply, like being banished into forests far from everyone. A book must be the axe for the frozen sea within us. That is my belief.

Franz Kafka

Mathematics: What do grad students in math do all day?

Mathematics: What do grad students in math do all day? - gist:4158578

“A lot of math grad school is reading books and papers and trying to understand what’s going on. The difficulty is that reading math is not like reading a mystery thriller, and it’s not even like reading a history book or a New York Times article.

The main issue is that, by the time you get to the frontiers of math, the words to describe the concepts don’t really exist yet. Communicating these ideas is a bit like trying to explain a vacuum cleaner to someone who has never seen one, except you’re only allowed to use words that are four letters long or shorter.

What can you say?

“It is a tool that does suck up dust to make what you walk on in a home tidy.”

That’s certainly better than nothing, but it doesn’t tell you everything you might want to know about a vacuum cleaner. Can you use a vacuum cleaner to clean bookshelves? Can you use a vacuum cleaner to clean a cat? Can you use a vacuum cleaner to clean the outdoors?

The authors of the papers and books are trying to communicate what they’ve understood as best they can under these restrictions, and it’s certainly better than nothing, but if you’re going to have to work with vacuum cleaners, you need to know much more.

Fortunately, math has an incredibly powerful tool that helps bridge the gap. Namely, when we come up with concepts, we also come up with very explicit symbols and notation, along with logical rules for manipulating them. It’s a bit like being handed the technical specifications and diagrams for building a vacuum cleaner out of parts.

The upside is that now you (in theory) can know 100% unambiguously what a vacuum cleaner can or cannot do. The downside is that you still have no clue what the pieces are for or why they are arranged the way they are, except for the cryptic sentence, “It is a tool that does suck up dust to make what you walk on in a home tidy.”

OK, so now you’re a grad student, and your advisor gives you an important paper in the field to read: “A Tool that does Suck Dust.” The introduction tells you that “It is a tool that does suck up dust to make what you walk on in a home tidy,” and a bunch of other reasonable but vague things. The bulk of the paper is technical diagrams and descriptions of a vacuum cleaner. Then there are some references: “How to use air flow to suck up dust.” “How to use many a coil of wire to make a fan spin very fast.” “What you get from the hole in the wall that has wire in it.”

So, what do you do? Technically, you sit at your desk and think. But it’s not that simple. First, you’re like, lol, that title almost sounds like it could be sexual innuendo. Then you read the introduction, which pleasantly tells you what things are generally about, but is completely vague about the important details.

Then you get to the technical diagrams and are totally confused, but you work through them piece by piece. You redo many of the calculations on your own just to double check that you’ve really understood what’s going on. Sometimes, the calculations that you redo come up with something stupid, and then you have to figure out what you’ve understood incorrectly, and then reread that part of the technical manual to figure things out. Except sometimes there was a typo in the paper, so that’s what screwed things up for you.

After a while, things finally click, and you finally understand what a vacuum cleaner is. In fact, you actually know much more: You’ve now become one of the experts on vacuum cleaners, or at least on this particular kind of vacuum cleaner, and you know a good fraction of the details on how it works. You’re feeling pretty proud of yourself, even though you’re still a far shot from your advisor: They understand all sorts of other kinds of vacuum cleaners, even Roombas, and, in addition to their work on vacuum cleaners, they’re also working on a related but completely different project about air conditioning systems.

You are filled with joy that you can finally talk on par with your advisor, at least on this topic, but there is a looming dark cloud on the horizon: You still need to write a thesis.

So, you think about new things that you can do with vacuum cleaners. So, first, you’re like: I can use a vacuum cleaner to clean bookshelves! That’d be super-useful! But then you do a Google Scholar search and it turns out that someone else did that like ten years ago.

OK, your next idea: I can use a vacuum cleaner to clean cats! That’d also be super-useful. But, alas, a bit more searching in the literature reveals that someone tried that, too, but they didn’t get good results. You’re a confident young grad student, so you decide that, armed with some additional techniques that you happen to know, you might fix the problems that the other researcher had and get vacuuming cats to work. You spend several months on it, but, alas, it doesn’t get you any further.

OK, so then, after more thinking and doing some research on extension cords, you think it would be feasible to use a vacuum cleaner to clean the outdoors. You look in the literature, and it turns out that nobody’s ever thought of doing that! You proudly tell this idea to your advisor, but they do some back of the envelope calculations that you don’t really understand and tell you that vacuuming the outdoors is unlikely to be very useful. Something about how a vacuum cleaner is too small to handle the outdoors and that we already know about other tools that are much better equipped for cleaning streets and such.

This goes on for several years, and finally you write a thesis about how if you turn a vacuum cleaner upside-down and submerge the top end in water, you can make bubbles!

Your thesis committee is unsure of how this could ever be useful, but it seems pretty cool and bubbles are pretty, so they think that maybe something useful could come out of it eventually. Maybe.

And, indeed, you are lucky! After a hundred years or so, your idea (along with a bunch of other ideas) leads to the development of aquarium air pumps, an essential tool in the rapidly growing field of research on artificial goldfish habitats. Yay!”

in my country having a diagnosis is highly confidential, too. there is no such thing as "the government knowing about your diagnoses" unless you get evaluated for disability documentation (I have no idea how to translate this to english), which is your choice. besides, who knows when the diagnosis will be useful? waiting for a diagnostic appointment takes several months and is very expensive, so taking an opportunity to sort this thing out when it's possible is good. depending on where someone lives, it can be very harmful to say that having a diagnosis somehow creates disadvantages

at my university the support program for people with asd has been introduced two years ago. it took me almost a year to get everything done, a year of unnecessary suffering. treatment for depression with or wihout adhd can be completely different and having it on paper that in your personal circumstances ssri might not work can save so much time. when someone suspects adhd and the situation calls for introducing medication, it's nice to be able to try right away, not wait several months for a diagnosis. those are just some practical examples of how you never know when diagnosis might be useful

and the validation reason, yeah, that too, it's beneficial to have someone work with you through that stuff. moreover, with professional support there comes someone suggesting solutions and forms of help that one might not even thought of. there are shitty doctors, but there are good ones too, and I think we should talk more about how to find the right ones instead of demonizing getting help

By the way. Before you rush to get a professional diagnosis for a Brain Thing you should really weigh your options. Like do you just want to "prove it" or will this actually give you access to treatment you can't have otherwise? Are the treatment options available worth having the government know you're neurodivergent? Because sometimes it's better to keep things off the record because unfortunately we still live in a very deeply ableist society and you might not want to have more real material oppression stacked against you than you have to

imo euclidean geometry kinda sucks, but if we mean geometry in a more general sense then algebraic geometry is the one

I've decided to start a fight

anyways geometry sucks algebra best math

7 XI 2022

I think I found an advisor and a topic for the bsc thesis! or rather they found me

one of the teachers that prepares us for writing our theses approached me and started asking about homology I mentioned during our presentation, he wanted to know what courses I took and how familiar I am with that stuff. I told him that I know a bit about homology only from self-study but I enjoyed everything from algebraic topo so far and I would be happy to write about something from that. "ok then I'll find the right topic for you" was his response. then he suggested I read Groups of Homotopy Spheres by Milnor and Kervaire and write about surgery theory. I was sold the moment I heard that name, it's almost as funny as writing about the hairy ball

so there she is, very high level, very complicated. I barely skimmed the first half of that 34-page paper, it's gonna take a lot of work before I learn the basics necessary to even comprehend what is going on. it feels good to be noticed tho, I'm so happy to start writing asap

other than that my mood hasn't been in a great place, because commutative algebra is super hard and I am struggling to find the right resources to study. the last thing we did was tensor product and I've been procrastinating actually studying it by making pretty notes lol

I found a textbook that seems decent. the theory is very thoroughly explained here and there are plenty of exercises ranging from easy to difficult ones

recently I've been trying a new method of tracking, which is instead of writing to-do lists, I write down what I did each day, here is what it looks like for now:

I find it much less anxiety-inducing than the to-do approach because I know damn well what I need to do and writing down what I actually completed feels much better than crossing things off of the list

this week I hope to study the tensor product, representable functors (yoneda is still not done with me) and probably start the complex analysis homework. if I have time I will study the prerequisites for the Milnor's paper

You think math should relate to the real world? What are you, some kind of physicist? Get the fuck out of here

doing (basic) algebraic topology in this context feels like going to that jungle and saying you know what bring this thing down we are building a city here. everything is a CW complex, everything is euclidean, and compact or paracompact if it must, all of this so that we can forget about sidestepping around topology and do algebra in peace lmao

Measure theory and topology both have this great flavor where you give the most minimal possible definition for the thing you want and then you get all the nice properties, except no, your definition is soft enough to allow crazy nonsense counterexamples hiding behind everything that you have to carefully sidestep around. It's like doing math in a jungle