In April 1936 Alonzo Church used his lambda calculus, a compact formal system for describing functions in terms of how they take inputs and produce outputs, to prove that no general procedure can decide every question of arithmetic, reaching the same boundary Alan Turing found independently the same year. The lambda calculus did not stay a tool for impossibility proofs: because it is a complete and elegant model of computation built entirely from functions, it became one of the deep roots of computer science, directly shaping functional programming and John McCarthy’s Lisp.