I studied theoretical physics for BS, and the 5 years since I have a range of exposure to theoretical mathematics in analysis and combinatorics. Recently I looked into the notes on using Green's function to solve a particle in a 2D well. I cannot help notice how little Green's function is discussed - without justifying its validity in solving problems such as a 2D well. I remember that at the time, I knew how to solve the problem but not understood it enough to apply to it to another scenario. I find similar discomfort in computer science. I learnt search trees, sorting algorithms with great ease through proofs in applied mathematics. Recently I was taking a class on mathematics in computer science, and I was surprised that those simple theorems were casted in so complicated language and description that I was very sure if I had not taken applied combinatorics in the math department, I would be twice confused and spend more than twice the time explaining the theorems to myself. I couldn't quench the little noise in the back of my head that whenever I am introduced to something in physics or computer science, it says "sure I trust the professor ... but I don't know why I should be convinced otherwise." Is this common among physicists and computer scientists here in the forum who have similar experiences?