I'm writing a math book, for general audiences, tentatively titled Connections and Classification. It'll be a journey through some interesting mathematical topics (polyhedra, surfaces, knot theory etc.) in the context of some history and philosophy. I'll also try to show how seemingly disparate topics are connected through common themes and techniques. I hope the book will help readers gain some appreciation for mathematics.
For now, here's a preview of Chapter 1 of the book, which serves as an introduction to mathematical thinking. Any feedback or suggestions (via the form at the bottom) would be very welcome.