Could using a tool like Mathematica hinder true understanding?

Mathematics itself is just a tool people use to simplify things. It is an artificial model of the real world. Numbers don't exist except as pure abstractions . Really inventive ideas start in people's heads and then mathematics can be used as a way of expressing these ideas in a standardized format that anyone else could understand. It is similar to a composer thinking up a song and then writing it down as a musical score. The score itself is just ink and paper. The same is true of a mathematical formula describing the details of some sort of physical process. What sets mathematics apart is that it can refer completely to itself. There are many mathematical functions which might have solutions, but they haven't been discovered yet. It is rather like using mathematics in reverse. First one finds the solution to a formula and then it is up to someone to find the real world phenomenon this formula may pertain to. People who really like math are the sorts who also like solving puzzles.