Mathematics only clicked and became fun for me when I started using Wolfram Mathematica, because I could fairly easily mess around with the formulas I saw in books until I understood the types and arguments and what is an index vs a reference to some unnamed convention of the field.
I so so much agree. Just applying the D (differential operator) twice reveals what are we doing much more than the conventional d2y/dx2 notation.
By and large mathematics education has missed the point of invention of computers. It is only occasionally used to make a point. We should be teaching mathematics with a programming first approach: get your function code to compile, ponder on its signature, write some test cases to really understand what is going on.
