I was inclined to write something similar myself as I agree in general. Mathematics is much more about the thinking than the doing, programming is more about the doing.

However, I do think that programming can be an excellent complement and aid when understanding certain concepts. Sometimes, writing a numerical simulation of a hard to grasp concept can make things fall into place. In particular in probability theory it can be quite helpful to generate a lot of random samples to validate and clarify some counterintuitive concepts.