My formal goal is to be able to rigorously understand the mathematical basis for modern statistical learning methods (ML, deep learning). I am told by math people that this involves: linear algebra, multivariable calc, probability theory, statistics. My current strategy is to go through classic textbooks, one subject at a time, and do most the problems (e.g. Axler's linear algebra, Casella-Berger for stats). Is there a more efficient strategy than this? I have heard of Ravi Vakil's advice to learn about things you don't really understand, then backfill knowledge gaps, but I'm not sure what that would look like in practice, and his advice seems to be for very advanced math students.
I took computer science and math classes in college, but didn't have or gain mathematical maturity. Since then I read Pinter's abstract algebra and Abbott's analysis text and did most the problems. This took a really long time and a lot of willpower, hence the question.
I am a full time student in a nontechnical field that I think can benefit from AI. So I can't read math full time, and ultimately want to apply AI, but I also want to do it properly and enjoy math for its own sake.