 The next important steps in the development of a general theory of recursive function arose as a consequence of the interaction between  Hilbert’s Program and Gödel’s (1931) proof of the Incompleteness Theorems.  Hilbert (1900) had announced the goal of proving the consistency of arithmetic—and ultimately also analysis and set theory— in the face of the set theoretic paradoxes.   His initial plans for carrying out such a proof are described in a series of lectures and addresses in the 1910s–1920s which provide a description of what would come to be called the finitary standpoint—i.e., the fragment of mathematical reasoning pertaining to finite combinatorial objects which was intended to serve as the secure basis for a consistency proof.   The proof itself was to be carried out using the methods of what Hilbert referred to as metamathematics—i.e., the formal study of axioms and derivations which would grow into the subject now known as proof theory.