I'm learning about functional programming,
In functional programming, functions are treated as first-class citizens, meaning that they can be bound to names (including local identifiers), passed as arguments, and returned from other functions, just as any other data type can. This allows programs to be written in a declarative and composable style, where small functions are combined in a modular manner. -Wiki
And.. I started to wonder, how it would be if we tried to adopt this method as foundations to mathematics.
Would it be meaningful to consider mathematics with functions being taken as the fundamental object rather than, say, that of the set or non function types? If it is, what would be the difference between the produced mathematics of that procedure, and that we have when we consider sets as the fundamental objects? What would be the advantages/ disadvantages to this approach?