The Fifth Postulate: How unraveling the two-thousand-year-old mystery unraveled the universe by Jason Socrates Bardi
I remember the first time I learned of non-Euclidean geometries, and how shocked I was that you could model the normal axioms using a sphere, indentifying “lines” with great circles and “points” with pairs of opposite points in order to produce a model where the parallel postulate didn’t apply.
This book covers the story of the discovery of non-Euclidean geometry, starting with the Greeks and the book of Euclid, covering some of the numerous attempts to prove the fifth postulate from the other axioms. The story then focuses on Gauss who was connected to the two people, Lobachevsky and Bolyai, who eventually published their (at the time) controversial ideas of hyperbolic geometry. Gauss never published on the subject, but may well have had such ideas himself.
The book is full of interesting anecdotes and biographical detail about the central characters, though there is a little too much repetition. I’m not sure it really explains how non-Euclidean geometry unravelled the universe, but it was an interesting read nevertheless.