In 1936 Turing wrote "On Computable Numbers, with an Application to the Entscheidungsproblem," in which he addresses Hilbert's decidability problem, proves that the Halting Problem is unsolvable, and lays out the modern definition of computability.
Ref: https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/plms/s2-42.1.230
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