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Alan M. Turing is born in London, England while his parents were on leave.
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The third question: "Was there some procedure that could determine whether a particular statement was provable, rather than allowing the possibility that some statements were destined to remain in undecidable limbo?" would be
called the Entscheidungsproblem AKA “decision problem" which would be important to Turing years later. -
This is where Turing would begin his academic journey with a strong interest in math and physics.
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Turing's professor Max Newman would explain The Entscheidungsproblem in a question: "Is there “mechanical process” that can be used to determine whether a particular logical statement is provable?" This question would lead to Turing to envision a "Logical Computing Machine"(Isaacson pg.26).
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Turing publishes his proof that the Entscheidungsproblem had no resolution and his concept of a Logical Computing Machine: “It is possible to invent a single machine which can be used to compute any computable sequence". This would be commonly known as the Turing Machine and would be an important foundation for the future of computing (Isaacson pg.25).
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With a growing interest in cryptology, at the Princeton’s physics building, Turing would construct a device that turned letters into binary numbers and multiplied the resulting numerically encoded message by a large secret number, this would become important for Turing in the next couple years (Isaacson pg.41).
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In Bletchley Park, London, Turing is assigned to Hut 8 during the height of the war. This team was tasked to cracking the difficult German enigma code which held encrypted military messages.
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Turing’s team had two operating bombes, which were able to break 178 coded messages (Isaacson pg.41).
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To decipher the most important German messages, Tommy Flowers, who was enlisted by Turing to work on "The Bombe", had produced the first Colossus machine with input from Alan Turing and Max Newman at Hut 11 (Isaacson pg.42).
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The NPL would recruit Turing to create an electric computer. He would come up with a design for the "Automatic Computing Engine which was the first complete specification of an electronic stored-program all-purpose digital computer" (britannica.com).
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With a strong interest in Artificial Intelligence and machine learning and a souring relationship with the National Physical Laboratory, Turing had left and reunited with his former professor Max Newman in Manchester to further his focus on AI.
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This would ask "Can machines think?" and would present the famous "Turing Test". He called this test the "Imitation Game" in which an interrogator sends written questions to a human and a machine in another room and tries to determine from their answers which one is the human (Isaacson pg.61).
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Unfortunately, after disclosing his Homosexuality to the police in relation to the suspect who burglarized his home, Turing was arrested for "gross indecency" and pled guilty to this and was subjected to hormone treatment to "reduce" his sexual urges. This also led him to be stripped of his security clearance despite his major contributions.
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Turing had committed suicide by consuming an apple laced with cyanide after being a victim of major prejudice.
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Alan Turing is finally pardoned after many years after his death and is widely recognized even today for his contributions to computing, AI, and machine learning.