Charles Babbage

“ In the same manner as an exponent expresses one operation on quantity, namely, the multiplication of it by itself a certain number of times, or raising it to the power expressed by that exponent, so the term Function, which has been introduced into modern analysis, is intended to express generally the results of all the various operations that can be performed upon quantity. ”

“ Many of these operations consist of two parts, the direct and the inverse. To extract a root is the inverse, with reference to that of raising any number to a higher power. So the integral is the inverse of the differential calculus; and the same observation applies to finite differences. In all these cases the inverse method is by far the more difficult of the two. ”