Anonymous at Tue, 15 Oct 2024 01:19:49 UTC No. 16432167

>>16432165
start with goup therapy and work from there

Anonymous at Tue, 15 Oct 2024 01:39:45 UTC No. 16432180

>>16432167
no, he should start with oup theory

Anonymous at Tue, 15 Oct 2024 01:56:42 UTC No. 16432195

>>16432165
Australia jews

Anonymous at Tue, 15 Oct 2024 02:55:03 UTC No. 16432263

>>16432165
No. Groups are one of the hardest and most esoteric mathematical concepts and only a handful of people even partially understand them

Anonymous at Tue, 15 Oct 2024 03:27:59 UTC No. 16432298

>>16432263
Ok, I'm gonna try to learn cause the physicists say it's important for understanding how the universe works

Anonymous at Tue, 15 Oct 2024 07:29:10 UTC No. 16432513

>>16432298
is it really tho

Anonymous at Tue, 15 Oct 2024 07:32:22 UTC No. 16432515

>>16432165
Yes. There are like what, 4 axioms if you include closure. And like every second thing in math is a group, from addition to diffeomorphisms. Category theory is the real filter.

Anonymous at Tue, 15 Oct 2024 09:10:48 UTC No. 16432605

>>16432515
Is there a further abstraction beyond categories and groups or is that it

Anonymous at Tue, 15 Oct 2024 09:14:29 UTC No. 16432607

>>16432605
Groups are just as abstract as linear spaces. There's nothing particularly special about them. Category theory is abstract in a sense that it is "metamathematics" just like set theory is. It isn't concerned with mathematical objects themselves, but the relations between them.

Anonymous at Tue, 15 Oct 2024 09:33:53 UTC No. 16432630

>>16432607
ok i see there is higher-category theory and higher topos theory, but that's it right? That's the limit of humans ability to abstract things?

Anonymous at Tue, 15 Oct 2024 09:42:05 UTC No. 16432640

>>16432630
You are very misguided and misunderstand the purpose of abstraction.

Anonymous at Tue, 15 Oct 2024 10:16:20 UTC No. 16432660

>>16432640
are you going to elaborate or just insult me.

Anonymous at Tue, 15 Oct 2024 10:19:59 UTC No. 16432665

>>16432640
there's no singular purpose to abstraction

Anonymous at Tue, 15 Oct 2024 10:27:42 UTC No. 16432669

hold on, we can go deeper, metamathematics!

Anonymous at Tue, 15 Oct 2024 10:31:33 UTC No. 16432675

>>16432165
the hard part of mathematics is proving stuff, understanding things others have proven (given that you have the necessary prerequisite knowledge) is usually very simple. in other words, if an ordinary mind were taught basic proof literacy (e.g. understanding how to capture and frame abstract concepts using something like set theory), they could easily understand the idea of group theory.

Anonymous at Tue, 15 Oct 2024 11:57:38 UTC No. 16432744

bros i'm reading about category theory, these guys are wizards, to dare even think about things like this is an affront to the gods

Anonymous at Wed, 16 Oct 2024 05:23:09 UTC No. 16433953

god this thread really motivates me to finish my category theory textbook

Anonymous at Wed, 16 Oct 2024 05:27:43 UTC No. 16433958

>>16432165
Group theory is quite simple. It is about symmetry.

>>16432607
Nothing about ordinary category theory is more difficult.

>>16432630
Higher category theory is complicated, that is because infinity groupoids are equivalent homotopy theoretically to topological spaces. Hence studying higher category theory is at least as hard as studying topology.

Anonymous at Wed, 16 Oct 2024 05:35:01 UTC No. 16433968

>>16432165
https://github.com/UniMath/SymmetryBook

Anonymous at Wed, 16 Oct 2024 08:58:36 UTC No. 16434094

>>16432165
The Fascination of Groups - Budden