I've heard many many times that you can only learn math by doing it, which is certainly true, and is akin to saying that you can only learn a language by attempting to speak it. But to begin to learn to speak well, one must hear tons and tons of speech. Similarly, to begin to learn to write well, one must read tons and tons of writings.
Are there any resources for people who just want to read proofs? Preferably well-commented ones suited for beginners like myself who are trying more to get a feel for proof as an activity rather than trying to learn any particular branch of mathematics through them (at this point).
For a total beginner there is no better choice than Steward and Tall's "The Foundations of Mathematics", an incredibly readable guide which takes you from high-school calculus through a good portion of intro analysis and algebra. Reading this and doing the exercises was enough to get me through my first year of real math classes. There is no praise great enough for this book, and no sufficient recommendation I could give.
With that under your belt, if you'd like a "real textbook" I enjoyed Axler's "Linear Algebra Done Right". It has great exercises and should get you used to proofs done in the textbook style (though considering the high quality it may well not prepare you for the bleak world of lesser options).
https://en.wikipedia.org/wiki/Proofs_from_THE_BOOK
Also, to get you into the right mood, I highly recommend "Fermats Last Theorem", which is light on mathemtics but quite interesting nontheless:
https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem_(book)
and this article:
> 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.
If you try to read math like a novel your brain will just go "zip...zip" and jump over important things. You really have to make math your own.
A very interesting case is
http://www.takayaiwamoto.com/Pythagorean_Theorem/Pythagorean...
because there are so many ways to do it. This book has an insane number of proofs of it
https://www.amazon.com/exec/obidos/ISBN=0873530365/ctksoftwa...
https://www.amazon.com/How-Prove-Structured-Daniel-Velleman-...
How to Prove It: A Structured Approach by Velleman. New edition came out in 2019. It appears to be aimed at your level, and pricewise isn't too bad.
And it actually tries to teach you rather than documenting math knowledge or impressing peers.
I highly recommend it.
So really any math text appropriate to your level will work.