The nature of "A Programing Language" (APL) is viewed as unambiguous, consistent, and powerful. It is based on the notion of functions as imperative verbs, and is used by a small but growing number of mathematicians and computer programers. Three areas of mathematical activity are addressed: calculation of arithmetic expressions, evaluation of algebraic formulas, and computation of algebraic processes. The uses of APL in each of these areas is illustrated by elementary examples. Because of its design as a language rich in primitive functions, with extensions created by operators and user-defined functions, APL is seen as a powerful tool for mathematical exposition. (MP)