With the development of modern computing, starting in the 1940s, the substitution of human abilities with technology obtained a new dimension. The focus shifted from the replacement of pure physical power to the substitution of mental faculties. Following the early 1980s personal computers started to attain widespread use in offices and quickly became indispensable tools for office workers. The development of powerful computers combined with progresses in
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b. June 23, 1912, London, England
d. June 7, 1954, Wilmslow, Cheshire
English mathematician and logician who pioneered in the field of computer theory and who contributed important logical analyses of computer processes. 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. 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 propositions. 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 codes of the German "