On Computable Numbers, with an Application to the Entscheidungsproblem (Decision Problem)

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July 1, 2026

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Alan Turing's 1936 paper, "On Computable Numbers, with an Application to the Entscheidungsproblem," introduced the concept of the Turing machine. This theoretical device is an abstract model of computation that can simulate any algorithm's logic. Turing used this machine to explore the limits of computation and to address the Entscheidungsproblem, a question about whether a mathematical proposition can be proven true or false. He proved that no universal algorithm can solve all such problems, demonstrating the existence of undecidable propositions and the famous halting problem. The Turing machine's design, with its infinite tape and finite states, laid the groundwork for modern computer science.1234

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Alan Turing
Early life and career
…1936 Turing’s seminal paper “On Computable Numbers, with an Application to the Entscheidungsproblem [Decision Problem]” was recommended for publication by the American mathematical logician Alonzo Church, who had himself just published a paper that reached the same conclusion as Turing’s, although by a different method. Turing’s method (but not…
Read More
…1936 Turing’s seminal paper “On Computable Numbers, with an Application to the Entscheidungsproblem [Decision Problem]” was recommended for publication by the American mathematical logician Alonzo Church, who had himself just published a paper that reached the same conclusion as Turing’s, although by a different method. Turing’s method (but not…
Read More