I am interested primarily in physics, and I am generally self-taught in mathematics. However, this implies an inaptitude for rigorous proof. While I am confident that I can grasp the concepts and results well enough, I loath the idea of sitting through just one book on a particular subject, and study it cover to cover. - I do not want to inherit the author's idiosyncrasies, is what I'm saying.
Had I lived in other times, I would not have had a choice, but given the information torrent of our time, I want to shape my education on a mathematical subject through exploration of different means. That being said, having a textbook as a primary exercise and linearity provider (what concept proceeds the other), and multiple others (including the internet in general) to shape my knowledge of the subject, and study results from the definitions I have learned.
There have been many times where I could not see the solution to a simple, nevertheless, problem mainly because I relied on one and only textbook, which did not mention a certain lemma, or some other helpful intuitive result. I wish to abolish that through a more unorthodox approach to learning.
What would your advice be?