I feel as if my understanding of physics require increasingly rigorous mathematical derivations the more advanced the notions get... since I started even high school physics, I lost track of the number of instances where the bulb lighted up in my understanding of physics due to a rigorous mathematical derivation of equations and whatnot, and the density of instances increased as I climbed the ladder of physical notions. But often, in class, the professors often skip over part of what is termed "the algebra", that is, the step-by-step mathematical derivations. When I get lost in my attempts to understand a given physics notion, I often ask about where to find the remainder of "the algebra" because, often, without a rigorous mathematical derivation, I do not understand the physics, or the conditions of applicability. However, I understand that the reverse is also true in other people. So, for you, which one happened more often: that it has been "the math made you understand the physics" or "the physics made you understand the math"?