I know enough about this to not have these questions, but not enough to explain the answers to anyone else. So I’ll recommend a book by Torkel Franzén, who was definitely able to both understand and teach this, “Gödel’s Theorem: An Incomplete Guide to Its Use and Abuse”. The book costs money, but as a preview, here’s a review of it.
Douglas Hofstadter has written a lot on the subject for a popular audience, but is better avoided until you understand the subject yourself well enough to recognise the unstated technical underpinnings of his exposition, and to see where he glosses over things a step too far. But when you are at that point, there is no need to read him.
I know enough about this to not have these questions, but not enough to explain the answers to anyone else. So I’ll recommend a book by Torkel Franzén, who was definitely able to both understand and teach this, “Gödel’s Theorem: An Incomplete Guide to Its Use and Abuse”. The book costs money, but as a preview, here’s a review of it.
Douglas Hofstadter has written a lot on the subject for a popular audience, but is better avoided until you understand the subject yourself well enough to recognise the unstated technical underpinnings of his exposition, and to see where he glosses over things a step too far. But when you are at that point, there is no need to read him.