[joe_the_user]

Godel's theorem and the halting problem began as having difficult and obscure proofs. Today, you can find "one page" proofs of either. And these proofs depend strongly on a variety of computation processes going from obscure to obvious for the average person.

Is it "obvious" you can produce program Y that doesn't halt if program X halts? Do you understand one program can be taken as input string of another? If so, the Halting Problem proof in Sudkamp's Languages and Machines, my undergraduate text in the 90s, can indeed take just a page.