How did Alan Turing contribute to the study of computability?

Alan Turing made foundational contributions to the study of computability by providing a rigorous, formal definition of what it means for a procedure to be "mechanical" or "effective."1

In 1936, Turing introduced the Turing machine, an idealized mathematical model that encapsulates the logical structure of any computing device. By demonstrating that the class of functions computable by this machine coincides with the class of recursive functions, he helped establish the Church-Turing thesis, which asserts that the informal notion of calculability is fully captured by these formal definitions.2345

Turing’s work was central to addressing the Entscheidungsproblem, a challenge that sought an algorithmic method to determine the provability of mathematical statements. Independently of Alonzo Church, Turing proved that no such universal decision method exists for first-order predicate logic, thereby establishing the existence of undecidable propositions. This work not only defined the limits of mechanical computation but also provided the theoretical blueprint for the modern digital computer.324