Ackermann function [SEP] named after
Ackermann function
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive.
After Ackermann's publication of his function (which had three nonnegative integer arguments), many authors modified it to suit various purposes, so that today "the Ackermann function" may refer to any of
of his "Was sind und was sollen die Zahlen?" (1888). This work was the first to give a proof that a certain recursive construction defines a unique function.
Primitive recursive arithmetic was first proposed by Thoralf Skolem in 1923.
The current terminology was coined by Rózsa Péter (1934) after Ackermann had proved in 1928 that the function which today is named after him was not primitive recursive, an event which prompted the need to rename what until then were simply called recursive functions.
See also