I always feel like `f(a)` invokes the idea that `f` is a value dependent on some `a` where notations like `(f a)` and `f a` are more indicative of the idea that

I always feel like `f(a)` invokes the idea that `f` is a value dependent on some `a` where notations like `(f a)` and `f a` are more indicative of the idea that `f` is a thing which has the operation of application to `a`. This makes sense mathematically as it's taken a long time for people to come around to thinking of functions as things in their own right. Dependent quantities are a more historical notion to my understanding.