 General interest in recursion as a mode of function definition originated in the mid-nineteenth century as part of the broader program of arithmetizing analysis and the ensuing discussions of the foundations of arithmetic itself. In this context, the formulation of recursive definitions for number theoretic functions was closely tied to the isolation of mathematical induction as a mode of reasoning about the natural numbers. It was in this setting in which Grassmann (1861) and Peirce (1881) first gave the familiar recursive definitions of addition and  multiplication:[1] 