## Technical Terms and Definitions

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 Alan Turing - People Alan Turing was an English mathematician and logician who pioneered in the field of computer theory and who contributed important logical analyses of computer processes. The son of a British member of the Indian Civil Service, Turing studied at Sherborne School and at King's College, Cambridge. Many mathematicians in the first decades of the 20th century had attempted to eliminate all possible error from mathematics by establishing a formal, or purely algorithmic, procedure for establishing truth. The mathematician Kurt Gödel threw up an obstacle to this effort with his incompleteness theorem; Gödel showed that any useful mathematical axiom system is incomplete in the sense that there must exist propositions whose truth can never be determined (undecidable propositions within the system). Turing was motivated by Gödel's work to seek an algorithmic method of determining whether any given propositions were undecidable, with the ultimate goal of eliminating them from mathematics. Instead, he proved in his seminal paper "On Computable Numbers, with an Application to the Entscheidungsproblem [Decision Problem]" (1936) that there cannot exist any such universal method of determination and, hence, that mathematics will always contain undecidable (as opposed to unknown) propositions. To illustrate this point, Turing posited a simple device that possessed the fundamental properties of a modern computing system: a finite program, a large data-storage capacity, and a step-by-step mode of mathematical operation. This Turing machine, as it was later called, is frequently used as a point of reference in basic discussions of automata theory and was also the theoretical basis for the digital computers that came into being in the 1940s. Turing's work, along with that of Gödel, put to rest the hopes of David Hilbert and his school that all mathematical propositions could be expressed as a set of axioms and derived theorems. Turing continued his mathematical studies at Princeton University, completing a Ph.D. (1938) under the direction of the American mathematician Alonzo Church. He then returned to England and accepted a renewed fellowship at King's College. During World War II he served with the Government Code and Cypher School, at Bletchley, Buckinghamshire, where he played a significant role in breaking the German "Enigma" codes. In 1945 he joined the staff of the National Physical Laboratory in London to lead the design, construction, and use of a large electronic digital computer that was named the Automatic Computing Engine (ACE). In 1948 he became deputy director of the Computing Laboratory at the University of Manchester, where the Manchester Automatic Digital Machine (MADAM, as it was referred to in the press), the computer with the largest memory capacity in the world at that time, was being built. His efforts in the construction of early computers and the development of early programming techniques were of prime importance. He also championed the theory that computers eventually could be constructed that would be capable of human thought, and he proposed a simple test, now known as the Turing test, to assess this capability. Turing's papers on the subject are widely acknowledged as the foundation of research in artificial intelligence.