#abstract-algebra

[dingdongs-bingbong]

Found this gem in a short process theory paper

[lipshits-continuous]

The ring of Integers: *exists*

Me:

[diesel-multiple-unit]

a thought that’s been floating around my head recently

conservatives like to parade around mathematical truths such as "2 + 2 = 4" as evidence that their social truths are fundamental and cannot be argued against

how long until conservative talking heads and/or annoying traditionalists find out about the esotericism and diversity of study in wider mathematics and start labelling it “degenerate mathematics”?

seriously. i wouldn’t be surprised if counterintuitive notions like “the factorial of one half is equal to half the square root of pi” are somehow a serious insult to a conservative’s idea of mathematics always being concrete and morally correct.

i mean, such an unintuitive idea kinda runs against a conservative philosophy that all truths are either self evident, or delivered by a higher power.

which i think ties into a wider misconception of higher mathematics being about adding things up - which is just not at all what it’s like, at all.

real, actual higher mathematics feels more like writing poetry than doing calculations, and i could make a whole nother post about that.

but all that most people know is times tables and sums. and i fear that if conservatives find out about abstract algebra, they’ll think it’s woke.

[miamaimania]

Mathematics in bloom ➤ A stratifold's beauty unfolds

[straightlightyagami]

you know when you instantly solve a homework problem in your head and then it takes forever to write it because you're like ughh it will take so long...

[informatikerin-freyja]

A bit of a crazy idea here, not entirely sure the formalism is right.

The idea is to axiomatise the idea of an infinite product operation rather than a puny binary product as in normal group theory.

Edit: @locally-normal correctly points out that we need more to make sure the inverses are two-sided inverses. So this definition should require \eta is an involution to fix this.

[transgenderer]

gah its so annoying that modern geometry is so algebraic. im not good at abstract algebra! there's too many layers between me and the objects!

[thecoolnerdblog]

“I love math cause at least everything has a solution” like…. Do you even know math??? Did math tell you this????

I’m pretty sure we have multiple subjects in math for the sole purpose of having no direct answer. Like algebra has a specific way to distinguish the different types of non-answers.

You dont love math enough to know math, girl

[halloiambored]

Pppft - math? Have numbers? Not anymore!

[math-cult-novel]

just saw a post about manipulation and the first thiing that came to my mind was manipulating a set mathematically

the plan is working

[lipshits-continuous]

Fuck you *puts a topology on your algebraic structure such that the relevant algebraic operations are now continuous maps*

[nexus-nebulae]

man i hate that one teacher ruined the whole concept of math for me bc i love physics and string theory and chemistry and all that stuff but every time I'm watching a video about it i hear like. specific algebraic concepts and i immediately lose all interest

[euthymiya]

Remember when math introduced imaginary numbers. wtf was up with that 🥲

[perflupislcup]

Sometimes abstract algebra escapes the ‘Abstract Algebra Box’ in my brain and invades older mathematical knowledge.

[amalgamgooze]

wasting away to the numbers

It's a good thing I studied some math today. Otherwise today would've just been Balatro from sunrise to sundown.

I need to put these numbers away and do something real, something physical.

But the allure of it all!

The allure of getting absurdly high scores in the illegal poker hands of Balatro,

the implications of "group codes" and how they represent this concept of Modern Algebra…

I hate that I've started entertaining myself with a five-dollar Discrete Math and Modern Algebra textbook from Half-Price Books.

How far have I fallen to descend past degeneracy and into insanity?

Numbers…

Those quantitative specters haunt me when I lie down for bed now.

I have to exhaust myself doing math or playing card games until I'm too tired to do literally anything else.

…

I won't be surprised if I wake up tomorrow morning in the shape of a seven.

…

And how did I get so attached to math in the first place, all those years ago?

I was thrashing about, trying to grab hold of any small fragment of reality…

and all I caught was something that's very good at describing the way reality works.

All these years later, I'm at the edge of math,

at the base of a mountain before I reach a plateau of iterations of the fundamentals.

Magmas. Groups. Rings. Tokens. Languages.

And it all bleeds out into the rest of the world.

Letters are tokens in the language of the alphabet just as 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, as well as +, -, *, /, =, are tokens of typical math.

And typically you get to say stuff like 1 + 1 = 2.

But in the world of Modern Algebra, my friend,

we reinvent the wheel to fly through the sky.

0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, that all makes sense.

But 1 + 1 = 0, oh, my friend, welcome to addition modulo two.

If this is far too outlandish and wacky for you, turn back now.

It only gets worse from here.

The worst part is that this crap is at the heart of math.

It's so simple and abstract.

I love it.

In fact, I think I'll…

lie down right here

in all the numbers

and make myself right at home.

Like the immutable, starry heavens above,

the absurdity and outlandishness of math

comforts me

because it doesn't make sense

why

it makes sense.