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-        The academic community was thus equipped with three mathematically equivalent foundations for computation theory: recursive functions, the lambda calculus, and the Turing Machine. While all three frameworks remain active subjects of study, Turing's formalism is uniquely suggestive of modern computing machines. Because computation theory ultimately defines the physical limits of what machinery can accomplish, the Turing Machine serves as the most appropriate foundation for computer scientists and engineers. This mechanical abstraction was refined into a basis for computation theory and presented as such in foundational textbooks by Stephen Kleene <RT-cite ref="Stephen C. Kleene, Introduction to Metamathematics, North-Holland, 1952"></RT-cite>, Martin Davis <RT-cite ref="Martin Davis, Computability and Unsolvability, McGraw-Hill, 1958"></RT-cite>, and Marvin Minsky <RT-cite ref="Marvin L. Minsky, Computation: Finite and Infinite Machines, Prentice-Hall, 1967"></RT-cite>, leading to the modern standard presentations by authors such as John Hopcroft and Jeffrey Ullman <RT-cite ref="John E. Hopcroft and Jeffrey D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, 1979"></RT-cite>, as well as Harry Lewis and Christos Papadimitriou <RT-cite ref="Harry R. Lewis and Christos H. Papadimitriou, Elements of the Theory of Computation, Prentice-Hall, 1981, ISBN 978-0132624787"></RT-cite>.
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-        For Turing's proof to be known to apply to the
-        Entscheidungsproblem, he had the additional burden of establishing
-        that Hilbert and Ackermann's intuitive concept of an <RT-term-em>algorithm</RT-term-em> was functionally equivalent to a Turing Machine program. Turing
-        addressed this issue in his paper, and with many reviewers
-        over decades acting as a jury, he did so successfully.
+        The academic community was thus equipped with three mathematically equivalent foundations for computation theory: recursive functions, the lambda calculus, and the Turing Machine. While all three frameworks remain active subjects of study, Turing's model is unique in providing practical intuition through direct metaphors for physical machines and programs. This made it the foundation of choice for computation theory textbooks by Stephen Kleene <RT-cite ref="Stephen C. Kleene, Introduction to Metamathematics, North-Holland, 1952"></RT-cite>, Martin Davis <RT-cite ref="Martin Davis, Computability and Unsolvability, McGraw-Hill, 1958"></RT-cite>, and Marvin Minsky <RT-cite ref="Marvin L. Minsky, Computation: Finite and Infinite Machines, Prentice-Hall, 1967"></RT-cite>, leading to the modern standard presentations by authors such as John Hopcroft and Jeffrey Ullman <RT-cite ref="John E. Hopcroft and Jeffrey D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, 1979"></RT-cite>, as well as Harry Lewis and Christos Papadimitriou <RT-cite ref="Harry R. Lewis and Christos H. Papadimitriou, Elements of the Theory of Computation, Prentice-Hall, 1981, ISBN 978-0132624787"></RT-cite>.
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