I am a high school student wanting to major in Mathematics in the future. I started to like Mathematics recently, starting a year ago and I watched some interesting math videos on YouTube for fun (ex: History of Mathematics Prof. Wildberger, Intro to Real Analysis Prof. Su, Linear Algebra MIT, Multivariable Calculus Prof. Shifrin) and I was studying these topics/subjects only from videos. I still have to finish the Linear Algebra videos though.
While watching videos was not very in-depth or rigorous, it was fun for me and that's all it mattered until recently. Recently, I got a local University Library Card so that I could actually access the textbooks instead of taking the information solely from video lectures. So I borrowed Rudin's Principles of Mathematical Analysis, Munkres' Analysis on Manifolds, Lang's Linear Algebra, and Herstein's Topics in Algebra for the subjects I was studying through videos so that I could have some mathematical maturity and problem solving skills that I currently lack.
The problem I have is that I'm used to having the professors on screen solving problems and proving proofs for me :( So it is difficult for me to do the exercises by myself or prove the theorems myself. Even as a novice with not much experience with Mathematics, I just seem so lacking as I can't even do the exercises on the textbooks. I did not expect/plan for this to happen because I falsely assumed that watching the video lectures would further my understanding of concepts in Mathematics and my mathematical maturity.
When I read the textbooks (I haven't got far into any of the texts, just a few chapters), I read every word but I do not do the exercises. When the author goes through proving some result step-by-step, I enjoy it because I usually follow along and it seems very clean and logical and when I read the author's insights or background information, that interests me as well. While reading these books are fun and entertaining, it is only fun because I skip the exercises; I read the exercises, I think about how to solve them, and if I get an idea, I handwave and say that's obvious but I never write it out with paper and pen and when I do, while the idea is there, I cannot formulate it well. And the questions that I don't have an idea of how to tackle, I skip them, too.
So basically I read but skip all the problems which I know is not beneficial for me. After a month or two of almost no progress with solving exercises, I am bothered because I feel like I'm getting nowhere and reading further seems pointless without understanding how to do the questions from previous chapters since it feels like I didn't learn/get the fundamentals right. I get frustrated and sometimes even reading the books do not interest me.
Is there a systematic way to fix this problem? Also, I just keep rationalizing my actions of not doing the exercises by telling myself that I'll have to learn these topics/subjects again when I get into a university so that I can just relax for now and just read the materials/concepts without solving the problems. It feels very wrong not to do the exercises though because then I'm not really learning how to do mathematics, I'm just reciting information and concepts. If anyone has advice, I would appreciate it a lot if you commented. I'm interested to know the methods of doing exercises and formulating solutions without skipping them all. I also want the solutions to the exercises but there is a lack of solutions for these books which isn't helpful to me as well. I'm also curious as to how many exercises I should do from the book. Should I do all of it, most of it, or some of it? Thank you very much. I probably want to make this a community-wiki but I do not know how to.
P.S. Does it matter how much time I spend studying a day if I want to be successful? Is there or should there be a minimum amount of time I'm dedicating per day for studying Mathematics? I know that this is personal and can depend on different people but I was just curious. I would like to spend 2~3 hours doing Mathematics each day but it seems like a lot of people spend more time and are more dedicated. If this P.S. seems pointless/useless, feel free to ignore it as I'm more interested in the main question.