> I actually think that infix notation has some advantages, especially for associative operations {e.g. if (G, +) is a group and a, b, c \in G, it's much more n

> I actually think that infix notation has some advantages, especially for associative operations {e.g. if (G, +) is a group and a, b, c \in G, it's much more natural to write a + b + c than to choose between the equivalent (+ (+ a b) c) and (+ a (+ b c))}. > But undeniably S-expressions are superior from a teaching point of view as they don't hide the "true" structure. That's exactly what they do though. A group G is not the same as a particular choice of presentation, and an element of g is not a particular tree of generators. Linear transformations aren't matrices, numbers aren't decimal expansions, polygons aren't lines on a chalkboard - and internalizing this is extremely important for beginning math students.