TITLE: Mathematician (non-logician) seeks reference for Gödel's incompleteness theorems
QUESTION [7 upvotes]: I would like to learn more about the proofs of Gödel's incompleteness theorems. I have read and am rereading Gödel's proof by Nagel, Newman, and Hofstadter. I like it very much, but I would like something a bit more substantial (but not too substantial). More specifically, I am a professor of mathematics, but not a logician. (If it helps, I am a probabilist.) I would like to read something that is aimed more at my level and is preferably self-contained. But this is purely for my own curiosity, so I do not want to learn a whole new field to understand it. Does anyone have any suggestions?

REPLY [3 votes]: It is also possible to proof the incompleteness theorem utilizing computability theory, by reducing it to the halting problem. I think this method is easier to understand, since it just relies on some basic knowledge of the undecidability of the halting problem.
Here is a reference http://www.logicmatters.net/resources/pdfs/PartIII.pdf
As we speak, Scott Aaronson made a wonderful post about this on his blog: http://www.scottaaronson.com/blog/?p=710