[kcl]

Your approach will not work. Either continue attempting proofs or give up. It's fine to read the answers after you've tried.

> I've heard many many times that you can only learn math by doing it, which is certainly true

yes

> and is akin to saying that you can only learn a language by...

no. this is you evading the main point.

Taking a graded class with homework can help. So can finding an elementary book on a subject that interests you (topology, combinatorics, algebra, ...). Linear is dry, that may be your issue.

[ravi-delia]

I don't think that's fair. Basic proofs are fairly rote, but if you don't know where to start it can be challenging to replicate them. You sort of begin by learning to translate definitions into algebra, and only branching out from there. Until you get a sense for which tools to reach for when, you could bang your head against that wall for a while without making any real progress (and pick up some terrible habits in the process).