Rough job interview

I have a great idea for a weeder question for developer hires!

1) Is it possible to reconstruct the source code of an executable by running the executable's object code through a compiler?

If the developer passes the test, then you can ask a followup:

2) Assume that it is possible. Discuss the implications on the fields of mathematics and computer science. (Possible topics of discussion: Kolmogorov complexity, the halting problem, etc.)