I've seen in college that some functions are not computable. The proof for that was the case of Halt(x,y) function.

The thing is, the proof used a very artificial (IMHO) case which is evaluating the function in it's own program number. In fact the whole idea of the Halt function is quite self-referencial...

I'd like to know if there is a more "normal" function which cannot be computed. Can someone show me a function which is non-computable but does not refer to itself?

I hope I made myself clear... if not, just comment and I'll explain. Thanks!

proofsof uncomputability, is that right? You keep wording your comments as referring to (e.g.) "mundane functions", but I cannot imagine a function more mundane than determining whether a polynomial has integer solutions. $\endgroup$ – Reid Barton Nov 9 '09 at 5:40