Martin Davis on Computability, Computational Logic, and Mathematical Foundations by E. Omodeo and A. Policriti (eds.)
Computability has been traditionally considered a practical matter in the edifice of mathematics. A theoretical answer, describing what computation and computability more generally are, came only by the 1930s; after those times, computers have become an indispensable part of our lives. Martin Davis, born 1928, is one who witnessed and took part in most of this development, quite literally for the whole of the second part of the 20th century. Eugenio Omodeo and Alberto Policriti had the happy idea of producing a volume dedicated to Davis in the new series Outstanding Contributions to Logic. To begin, let me outline briefly the emergence of computability as a topic in mathematics:
The notion of computation has its roots deep in the primitive act of counting. Such counting on a unary basis of, say, fingers, pebbles, or sticks, will not lead “beyond seven” if it is not accompanied by a symbolic notation for numbers and rules for operating with them.
- Davis, Martin. 1958. Computability & Unsolvability. New York: McGraw-Hill.Google Scholar
- Davis, Martin, editor. 1965. The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions. New York: Raven Press.Google Scholar
- Davis, Martin. 2000. The Universal Computer: The Road from Leibniz to Turing. New York and London: W. W. Norton & Company.Google Scholar
- Hilbert, David and Paul Bernays. 1934. Grundlagen der Mathematik I. Berlin: Springer.Google Scholar
- Péter, Rosza. 1951. Rekursive Funktionen. Budapest: Akademiai Kiado.Google Scholar