I am trying to teach myself mathematics and I can't tell if I'm going about it in an inefficient way. I really admire people who push the frontier and discover new methods and types of math like Newton, Euler, Grassmann, et cetera... I'm not naturally good at math and have had to work hard just to get to where I am now, but I really really adore math and want to be able to discover things myself!
When I'm teaching myself math should I be trying to figure out the subject before I read how to do it? And how bad is it if I'm not good at this??
For example, while learning Linear Algebra I got to eigen values and vectors and I tried to figure out a way to find them without being told how to do it. I was able to come up with a few ideas about how, but I just couldn't figure it out on my own. Same with integrals in Calculus.
So should I be self studying this way? There is so much of mathematics that I am super excited to learn but, it's taking me SO much longer to learn by doing this. But I don't want to just know how to do something. I want to really be able to yield the essence of mathematics! Any help would greatly be appreciated!!
P.S. - This isn't really part of the question, but I recently joined this site and think it is absolutely amazing that you all will sacrifice your time and talent to help others learn! So I just wanted to add that you all are stellar!! Hope adding this doesn't get me in trouble