I'm an electrical engineering student currently taking quite a few math courses and enjoying it very much. One thing that I have noted in my education is that it is essentially mimetic. I mean that everything I have been taught so far is about copying past great minds. I don't have any particular issue with this, I understand why all of the mathematical tools I'm learning to use are important and I enjoy it.
What I do wonder though, is how to make the leap from learning by copying solved problems to hopefully one day solving unsolved problems. If I meet a problem later on in the world, and I'm unable to manipulate it in a way to use the current tools I have to solve it, how do I go about developing new mathematical tools? Are there any resources that have proved helpful to individuals here? For example, books that provide a certain viewpoint/philosophy or perhaps heuristics or general methods of grappling with a problem that have proven fruitful, maybe stories about how someone conquered a previously unsolved problem on their own. I don't expect to receive precise answers to this questions, but am interested to hear people's thoughts and opinions.