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A facsimile edition of Alan Turing's influential Princeton thesisBetween inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (1912–1954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world—including Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleene—were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. This book presents a facsimile of the original typescript of Turing's fascinating and influential 1938 Princeton PhD thesis, one of the key documents in the history of mathematics and computer science. The book also features essays by Andrew Appel and Solomon Feferman that explain the still-unfolding significance of the ideas Turing developed at Princeton.A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal—a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms. Turing's point, as Appel writes, is that "mathematical reasoning can be done, and should be done, in mechanizable formal logic." Turing's vision of "constructive systems of logic for practical use" has become reality: in the twenty-first century, automated "formal methods" are now routine.Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science.

Logic, Symbolic and mathematical. --- Turing, Alan, --- Alan Perlis. --- Alan Turing. --- Algorithm. --- Alonzo Church. --- Applicable mathematics. --- Automated theorem proving. --- Axiomatic system. --- Boolean algebra. --- Boolean satisfiability problem. --- C++. --- Calculus of constructions. --- Cantor's diagonal argument. --- Central limit theorem. --- Church–Turing thesis. --- Computability theory. --- Computability. --- Computable function. --- Computable number. --- Computation. --- Computer architecture. --- Computer program. --- Computer science. --- Computer scientist. --- Computer. --- Computing Machinery and Intelligence. --- Computing. --- Coq. --- Cryptography. --- Decision problem. --- Donald Gillies. --- EDVAC. --- ENIAC. --- Enigma machine. --- Entscheidungsproblem. --- Formal system. --- Foundations of mathematics. --- Georges Gonthier. --- Gödel's incompleteness theorems. --- Haskell Curry. --- Howard Aiken. --- Instance (computer science). --- Iteration. --- J. Barkley Rosser. --- John Tukey. --- John von Neumann. --- Kenneth Appel. --- Kepler conjecture. --- Konrad Zuse. --- Lecture. --- Lisp (programming language). --- Logic for Computable Functions. --- Logic in computer science. --- Logic. --- Logical framework. --- Marvin Minsky. --- Mathematica. --- Mathematical analysis. --- Mathematical logic. --- Mathematical proof. --- Mathematician. --- Mathematics. --- Model of computation. --- Monotonic function. --- Natural number. --- Notation. --- Number theory. --- Numerical analysis. --- Oswald Veblen. --- Parameter (computer programming). --- Peano axioms. --- Peter Landin. --- Presburger arithmetic. --- Probability theory. --- Processing (programming language). --- Programming language. --- Proof assistant. --- Quantifier (logic). --- Recursion (computer science). --- Recursion. --- Result. --- Rice's theorem. --- Riemann zeta function. --- Satisfiability modulo theories. --- Scientific notation. --- Simultaneous equations. --- Skewes' number. --- Solomon Feferman. --- Solomon Lefschetz. --- Systems of Logic Based on Ordinals. --- The Unreasonable Effectiveness of Mathematics in the Natural Sciences. --- Theorem. --- Theory of computation. --- Theory. --- Topology. --- Traditional mathematics. --- Turing Award. --- Turing machine. --- Turing's proof. --- Variable (computer science). --- Variable (mathematics).