Nothing in particular, but the same nothing in particular that makes me think that it possibly can. I'm just saying that there's nothing in the known laws of nature that make this impossible from a purely physics based standpoint.

I'd be much more surprised to encounter a ship that could fly me to Alpha Centauri in 3 days than a super-human machine intelligence.

You are forgetting that it is that meat which is doing the building. And physics is subject to the laws of math. If ghat hunk of meat is simple, shouldn't that simplicity stop it from understanding itself.

So uhm, mind explaining what the hell Godel's proof has to do with God?

Look up Godel's ontological proof before getting all ragey on me. Of course, philistines hardly understand the concept of any proof and end up attacking the conclusion. So the point is usually lost on the intended audience.