[tinganho]

Note, the origins are stated in Wikipedia:

> Many papers and textbooks refer the definition and proof of undecidability of the halting problem to Turing's 1936 paper. However, this is not correct.[19][24] Turing did not use the terms "halt" or "halting" in any of his published works, including his 1936 paper.[25] A search of the academic literature from 1936 to 1958 showed that the first published material using the term “halting problem” was Rogers (1957). However, Rogers says he had a draft of Davis (1958) available to him,[19] and Martin Davis states in the introduction that "the expert will perhaps find some novelty in the arrangement and treatment of topics",[26] so the terminology must be attributed to Davis.[ https://en.wikipedia.org/wiki/Halting_problem#Origin_of_the_...

[syrak]

The paper in the OP discusses this claim in section 3, and mentions that Kleene came even before that:

> We would note that Kleene seems, however, to have already had the self-referential argument earlier in his classic book from 1952, Introduction to Metamathematics

They also bring up the "symbol-printing problem" present in Turing's 1936 paper, which is trivially equivalent to the halting problem with today's hindsight. That paper has a well nuanced take with a lot of interesting information.