TURING, Alan Mathison (1912-1954). "On computable numbers, with an application to the Entscheidungsproblem." In: Proceedings of the London Mathematical Society . 2nd series, vol. 42, pt. 3 (November 30, 1936): 230-240; 2nd series, vol. 42, pt. 4 (December 23, 1936): 241-265; 2nd series, vol. 43, pt. 7 (December 30, 1937): 544-546.
TURING, Alan Mathison (1912-1954). "On computable numbers, with an application to the Entscheidungsproblem." In: Proceedings of the London Mathematical Society . 2nd series, vol. 42, pt. 3 (November 30, 1936): 230-240; 2nd series, vol. 42, pt. 4 (December 23, 1936): 241-265; 2nd series, vol. 43, pt. 7 (December 30, 1937): 544-546. 3 parts, 4 o . Original grayish-blue printed wrappers (some minor browning along edges and spines, spines chipped and with a few small repairs); cloth box. FIRST EDITION OF ONE OF THE MOST IMPORTANT 20TH-CENTURY COMPUTER PAPERS, which introduced the concept of a "universal machine." Conceived as a way of answering the last of the three questions about mathematics posed by David Hilbert in 1928, is mathematics decidable, Turing's machine was an imaginary computing device designed to replicate the mathematical thought processes and reasoning abilities of a human computer. Hilbert's final question, known as the Entscheidungsproblem, asks whether there exists a definite method, or a "mechanical process," that is guaranteed to produce a correct decision as to whether a mathematical assertion is true. Turing used his universal machine to determine the answer to that question by coming up with the idea of "computable numbers," or numbers defined by some definite rule, and therefore calculable on his imaginary machine. He demonstrated that these computable numbers could create numbers that were not calculable using a definite rule, thus concluding that there could be no "mechanical process" for solving all mathematical questions since an uncomputable number was an an unsolvable problem. Mathematics is therefore undecidable. In addition to answering Hilbert's last question, Turing's paper also showed that a universal machine was possible, making it highly influential in the theory of computation. Origins of Cyberspace , 394.
TURING, Alan Mathison (1912-1954). "On computable numbers, with an application to the Entscheidungsproblem." In: Proceedings of the London Mathematical Society . 2nd series, vol. 42, pt. 3 (November 30, 1936): 230-240; 2nd series, vol. 42, pt. 4 (December 23, 1936): 241-265; 2nd series, vol. 43, pt. 7 (December 30, 1937): 544-546.
TURING, Alan Mathison (1912-1954). "On computable numbers, with an application to the Entscheidungsproblem." In: Proceedings of the London Mathematical Society . 2nd series, vol. 42, pt. 3 (November 30, 1936): 230-240; 2nd series, vol. 42, pt. 4 (December 23, 1936): 241-265; 2nd series, vol. 43, pt. 7 (December 30, 1937): 544-546. 3 parts, 4 o . Original grayish-blue printed wrappers (some minor browning along edges and spines, spines chipped and with a few small repairs); cloth box. FIRST EDITION OF ONE OF THE MOST IMPORTANT 20TH-CENTURY COMPUTER PAPERS, which introduced the concept of a "universal machine." Conceived as a way of answering the last of the three questions about mathematics posed by David Hilbert in 1928, is mathematics decidable, Turing's machine was an imaginary computing device designed to replicate the mathematical thought processes and reasoning abilities of a human computer. Hilbert's final question, known as the Entscheidungsproblem, asks whether there exists a definite method, or a "mechanical process," that is guaranteed to produce a correct decision as to whether a mathematical assertion is true. Turing used his universal machine to determine the answer to that question by coming up with the idea of "computable numbers," or numbers defined by some definite rule, and therefore calculable on his imaginary machine. He demonstrated that these computable numbers could create numbers that were not calculable using a definite rule, thus concluding that there could be no "mechanical process" for solving all mathematical questions since an uncomputable number was an an unsolvable problem. Mathematics is therefore undecidable. In addition to answering Hilbert's last question, Turing's paper also showed that a universal machine was possible, making it highly influential in the theory of computation. Origins of Cyberspace , 394.
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