The rest of the first half of the book slowly builds up a description of number theory, culminating in a proof of Gödel’s Incompleteness Theorem, which shows that formal mathematics itself contains a self-referential strangeloop. Sometimes, the structure of the dialogue itself is the “message” – one such example is a dialogue that is structured like a fugue – and other times the dialogue obliquely describes a concept – such as the use of a “universal record player” to explore the concepts of self-reference and formal undecidability. It’s an exciting build-up of a proof of Gödel’s incompleteness theorem: starting with an introduction of formal systems, transitioning to an explanation of number theory and propositional logic, and ending with an intuitive proof of the incompleteness theorem.