An Early History of Recursive Functions and Computability from Godel to Turing

An Early History of Recursive Functions and Computability traces the development of recursive functions from their origins in the late nineteenth century, when recursion was first used as a method of defining simple arithmetic functions, up to the mid-1930's, when the class of general recursive functions was introduced by Godel, formalized by Kleene and used by Church in his thesis. The book explains how the proposal given in Church's 1936 paper, now known as Church's thesis, first arose and concludes with the consideration of another class of functions, the Turing computable functions, that were specially created to be equivalent to the class of effectively calculable functions. The book includes previously unpublished letters between the author and many of the key historical figures.