This continues to be true when you study more abstract math. e.g. "group" is an interface, and "a group" is any type with an operation that implements the 3 required properties/methods. Likewise with vector space, ring, metric space, category, etc. Math is full of interfaces as a "design pattern".

(Interfaces in math are more like type classes and not inheritance in programming. e.g. the same set/type can be a group in more than one way.)