This book was written by Ernest Nagel, a professor of mathematics and philosophy, and James Newman, the editor of the 4 volume The World of Mathematics. It is aimed at non-mathematicians, but provides a detailed and very understandable walkthrough of Godel’s 1931 paper on the incompleteness of any axiomatic system that is powerful enough to represent the basic structure of arithmetic.
This is a fascinating book. Having labored through the original proof of the incompleteness theorem years ago, I expected that this book would be either too high level to be of any use, or too low level to be easily comprehended. But Nagel and Newman do a splendid job of explaining exactly how Godel’s proof works, without bogging down in too many definitions, lemmas, etc.
If you are interested in the foundations of mathematics, or just want to know more about possibly the most philosophically profound theorem of mathematics, this is the book for you.