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Alan Turing was one of the most influential thinkers of the 20th century and played a crucial part in deciphering the Enigma code. The papers in this text are key works for understanding Turing's phenomenal contribution.

Artificial intelligence. --- Computers. --- Enigma cipher system. --- Enigma cipher machine --- Enigma codes --- Enigma cryptographic machine --- Enigma machine (Cryptography) --- Machine ciphers --- World War, 1939-1945 --- ULTRA (Intelligence system) --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- AI (Artificial intelligence) --- Artificial thinking --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Cryptography --- Turing, Alan, --- Turing, Alan Mathison, --- Turing, Alan M. --- Turing, A. M. --- Cognitive science. --- Electronic data processing. --- ADP (Data processing) --- Automatic data processing --- Data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- Science --- Philosophy of mind --- Automation --- Muziektechnologie --- Computerwetenschappen

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The mathematical genius Alan Turing, now well known for his crucial wartime role in breaking the ENIGMA code, was the first to conceive of the fundamental principle of the modern computer-the idea of controlling a computing machine's operations by means of a program of coded instructions, stored in the machine's 'memory'. In 1945 Turing drew up his revolutionary design for an electronic computing machine-his Automatic Computing Engine ('ACE'). A pilot model of the ACE ran its firstprogram in 1950 and the production version, the 'DEUCE', went on to become a cornerstone of the fledgling British

Computers --- Computer engineering --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- History. --- Design and construction --- Turing, Alan Mathison, --- Turing, Alan M. --- Turing, A. M.

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"In the 1930s a series of seminal works published by Alan Turing, Kurt Gödel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics. In the decades since, the theory of computability has moved to the center of discussions in philosophy, computer science, and cognitive science. In this volume, distinguished computer scientists, mathematicians, logicians, and philosophers consider the conceptual foundations of computability in light of our modern understanding. Some chapters focus on the pioneering work by Turing, Gödel, and Church, including the Church-Turing thesis and Gödel's response to Church's and Turing's proposals. Other chapters cover more recent technical developments, including computability over the reals, Gödel's influence on mathematical logic and on recursion theory and the impact of work by Turing and Emil Post on our theoretical understanding of online and interactive computing; and others relate computability and complexity to issues in the philosophy of mind, the philosophy of science, and the philosophy of mathematics."

Computational complexity. --- Mathematics --- Philosophy. --- Logic of mathematics --- Mathematics, Logic of --- Complexity, Computational --- Electronic data processing --- Machine theory --- COMPUTER SCIENCE/General --- MATHEMATICS & STATISTICS/General --- PHILOSOPHY/General --- Computational complexity --- Philosophy --- Computerwetenschappen --- Filosofie

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Church's Thesis (CT) was first published by Alonzo Church in 1935. CT is a proposition that identifies two notions: an intuitive notion of a effectively computable function defined in natural numbers with the notion of a recursive function. Despite of the many efforts of prominent scientists, Church's Thesis has never been falsified. There exists a vast literature concerning the thesis. The aim of the book is to provide one volume summary of the state of research on Church's Thesis. These include the following: different formulations of CT, CT and intuitionism, CT and intensional mathematics,

Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Church, Alonzo,