The key behind Math is to generalize from very specific rules like the concept of multiplication as n copies of addition to very general rules based on behavior

The key behind Math is to generalize from very specific rules like the concept of multiplication as n copies of addition to very general rules based on behavior. For example, in Ring Theory multiplication and addition are just functions that satisfy specific properties. By focusing on the class of all functions that satisfy these properties, we're able to prove very general theorems that have much wider applications than if we just focused on addition-based multiplication. You see the same pattern in programming. Imagine if you had to have separate addition operators for doubles, floats, ints, and bigints. It's far more useful to have one function that only depends on the behavior of its input, rather than having its input be a very specific type of object.