A weaker form of Gödel's First Incompleteness Theorem, direct proofs of which in Gödel's manner are lengthy, involved and at some place rather counter-intuitive, has a simple and intuitive proof based on the undecidability of the halting problem - see for example https://en.wikipedia.org/wiki/Halting_problem#Sketch_of_proof
Who first proposed this proof and in what article or book has it been first published?