The history of mathematics starts in earnest with one of Pythagoras’ most important proofs, the Pythagorean theorem. This proof was the first link in a chain of ground-breaking ideas, all interconnected with each other, that turned mathematics into an “art of the mind.” The chain continues to be extended today. There would be no computers, science, engineering, or philosophy without Pythagoras’ legacy. This book sketches an outline of that legacy by presenting and discussing ten of the greatest ideas in the mathematical chain. Its aim is to illustrate why mathematics can be designated an intellectual art, a creative enterprise that mirrors any art, from music to painting. Pythagoras actually connected music and mathematics into a theory of the world called the Harmony of the Spheres. The book is intended for a general audience, and especially those who may think that mathematics is uninteresting or boring. Each of its ten chapter ends with five exploratory puzzles that will allow readers to become engaged in some of the ideas treated in the chapter without any technical knowledge. This will allow readers to use this book as well as a collection of fairly easy math problems.