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==The Turing Machine==

==The Turing Machine==

At Princeton, Turing proposed the concept of a "[[Turing machine|Universal Turing Machine]]". Turing had first proposed that the operations needed to calculate any formula could be broken down into a base set of instructions (or primitive [[Recursion|recursive functions]]) that could, in principle, be followed by a machine: the "Turing Machine". Once fully formalized, the calculations needed to derive the instructions themselves were capable of being run by a Turing Machine. The looped logic allowed the conception of a Turing Machine that could create its own instruction and, in principle, run a huge variety of calculations. Turing then used the concept of Universal Turing Machine to prove the insolubility of the [[halting problem]]. After gaining his PhD in June 1938, he returned to Cambridge University.

At Princeton, Turing proposed the concept of a "[[Turing machine|Universal Machine]]". Turing had first proposed that the operations needed to calculate any formula could be broken down into a base set of instructions (or primitive [[Recursion|recursive functions]]) that could, in principle, be followed by a machine: the "Turing Machine". Once fully formalized, the calculations needed to derive the instructions themselves were capable of being run by a Turing Machine. The looped logic allowed the conception of a Turing Machine that could create its own instruction and, in principle, run a huge variety of calculations. Turing then used the concept of Universal Turing Machine to prove the insolubility of the [[halting problem]]. After gaining his PhD in June 1938, he returned to Cambridge University.

==Code breaking==

==Code breaking==