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Here's a good adjacent read that I thought was a much clearer and relatively accessible tour through the Proof - https://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/081... - it's more of a pamphlet than a book, really.

GEB is fun, but it's definitely a bad introduction to the idea itself. It's a lot more fun if you already understand the subject matter and can enjoy the tone of the book.

One more related recommendation would be James Gleick's Chaos book: https://en.wikipedia.org/wiki/Chaos:_Making_a_New_Science

It is a good introduction to Chaos Theory and complexity science and a nice read alongside GEB.

I'm 100 or so pages in to this now. What a book! I'm sure this will be a long time classic for me.