Gödel’s Proof, by Nagel & Newman gives a good explanation for the semi-layman or undergrad coming across this for the first time.
Before picking up this book as an undergrad in pure maths, I still had romantic ideas about a separate platonic universe and the divine authority of mathematics to explain all human thought.
This book, along with studying the various geometries, each with a different choice of axioms not necessarily based in ‘reality’, destroyed the majority of that romance.
Before picking up this book as an undergrad in pure maths, I still had romantic ideas about a separate platonic universe and the divine authority of mathematics to explain all human thought.
This book, along with studying the various geometries, each with a different choice of axioms not necessarily based in ‘reality’, destroyed the majority of that romance.