When trying to learn a new topic in mathematics I consistently find myself extremely frustrated because I find that far too often, definitions are given without providing context for why they are chosen as such.
For example, I don't think I have ever come across a text which gives significant preamble to roots of the Normal distribution. It simply appears as:
Definition: A random variable $X$ has a Gaussian distribution with mean $\mu$ and variance $\sigma ^2$ if it's p.d.f is given as:
$$f(x) = \frac{1}{\sqrt{2 \pi \sigma ^ 2}} e^{ - \frac{(x-\mu)^2}{2\sigma^2}} $$
I've never seen this distribution derived, for example, from information-theoretic methods or by the CLT, or by analogy to a diffusion process so that the concept has some significance.
Currently, I'm an undergraduate student and I find that I waste an inordinate amount of time searching for the origins to many concepts to guide my learning. I find myself extremely disgusted by a course's requirement to memorize any formula and it makes it extremely difficult to learn in these kinds of courses.
Am I wrong to approach learning math with such an outlook? Is it possible, in general, to find the kind of resource that I'm looking for? Or, is it recommended that I just painfully memorize my way through undergraduate courses? If so, when does it get better?