Just to add my own two cents here: while I absolutely agree that numerical simulation is a great approach for understanding physics, the canonical closed-form s

Just to add my own two cents here: while I absolutely agree that numerical simulation is a great approach for understanding physics, the canonical closed-form solutions really are a necessary step for building an intuitive understanding of principles like symmetry and the importance of choosing useful reference frames. These are things that are very well complemented by building numerical models (and I think it would be tough to build those models without that understanding of concepts like that in the first place), but it's important to recognize that it's very difficult to skip directly to the numerical models stage. As I said, I think the parent covered that, but just wanted to try to make it a little more explicit.