Ackermann function: In the 1920s, Wilhelm Ackermann demonstrated a computable function that was not primitive-recursive, settling an important argument in the run-up to the theory of computation. There are several versions of his function, of which the most common is defined over non-negative integers m and n. The function grows very rapidly, even for very small inputs; as an example, ack(4,2) is an integer of about 20,000 digits.