Right, if you're a software engineer, the realization that the two theorems are nearly-equivalent really takes the air out of a lot of the existential philosophizing around Gödel's incompleteness.

Gödel's argument basically says that any system of mathematics powerful enough to implement basic arithmetic is a computer. This shouldn't be surprising to software engineers because the equivalency between Boolean logic and arithmetic is easy to show. And if you have a computer, you can build algorithms whose outcome can't be programmatically decided by other algorithms.