Agree with the rest, but not with "math is just a tool".
Math here is not about answering a question like "what are the coordinates of the point in the middle of those two points here". It is not a tool helping to solve a restricted set of computation problems. Math here is the model for the deterministic handling of a data system and its evolution in time. The silliest glue code is still math: "if button.push('a') thing.do_action('a_action')" translates to "For any x in A_Button_Pushes, action = f('a_action')".
Exactly. Let me also add that math isn't so much a tool as it is a way of thinking. Learning (or should I say understanding) more math helps in all sorts of non-obvious ways. From thinking logically, to seeing intuitive shortcuts, to proofs (used nearly every time a program is debugged), to algorithms, programming is one of the greatest concrete implementations of the math abstract.
Yes, I understand that. What I meant is that math is a tool in the same sense a programming language or methodology is a tool--it's something we ultimately use as a means to an end. If our only goal was math, we would actually be mathematicians ;)
Math here is not about answering a question like "what are the coordinates of the point in the middle of those two points here". It is not a tool helping to solve a restricted set of computation problems. Math here is the model for the deterministic handling of a data system and its evolution in time. The silliest glue code is still math: "if button.push('a') thing.do_action('a_action')" translates to "For any x in A_Button_Pushes, action = f('a_action')".