The incompleteness theorem has a computational core.
“The actual notion of computation was isolated soon after, starting with Gödel’s incompleteness theorem.
This theorem showed that axiom systems were limited when reasoning about the computation that deduces their theorems.
Church and Turing independently demonstrated that Hilbert’s Entscheidungsproblem (decision problem) was unsolvable, thus identifying the computational core of the incompleteness theorem.
This work, along with Gödel’s work on general recursive functions, established that there are sets of simple instructions, which, when put together, are able to produce any computation.
The work of Gödel showed that the notion of computation is essentially unique.”