Mathematicians arguably do not think of the first example as a loop with a mutating variable, but rather as a short-hand notation for f(m) + ... + f(n) - as a m

Mathematicians arguably do not think of the first example as a loop with a mutating variable, but rather as a short-hand notation for f(m) + ... + f(n) - as a macro, if you wish. I agree with the second part.