Math does also have `sum` and `product` in the form of Sigma and Pi. Of course, not exactly the same thing (since they operate over a set, not discrete elements).

I would venture to say that the reason infix notation is naturally preferred is related to our psychology, the same way most human languages are SVO (Subject Verb Object) or SOV. VSO languages (Lisp like) are less prevalent.

In general my opinion is that when a majority vastly prefers one alternative, there is usually a strong reason for it (even if it may be irrational) and it's foolish to go against the grain.