How do I best learn Gödel's incompleteness theorem?

Question

I'm a math beginner. I am a self-learner. A while ago, I finished reading “How to Prove It: A Structured Approach, 2nd Edition” by Daniel J. Velleman.

Now, I want to learn Gödel's incompleteness theorem to avoid making the same mistakes made in the past by others.

Where do I find the best learning material for Gödel's incompleteness theorem?

Answer 1

You can see Gödel's Incompleteness Theorems.

Two good books are :

• Torkel Franzén, Gödel's theorem : An incomplete guide to its use and abuse (2005)

• Peter Smith, An Introduction to Gödel's Theorems (2nd ed - 2013).

And you can see also this post for other references.

Answer 2

I learned Gödel's Incompleteness Theorem in high school in the 1980's from two books,

The Lady or the Tiger by Raymond Smullyan http://www.amazon.com/THE-LADY-OR-TIGER/dp/0394514661 and

Gödel, Escher, and Bach by Douglas Hofstadter http://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567

These are entertaining presentations of the theorem in which one doesn't get lost in the details.

If you want to learn more, I would recommend reading Meta-Math by Gregory Chaitin, where he takes things to a higher level. http://arxiv.org/abs/math/0404335