I was a born juggler, and after seven years of teaching college math students how to juggle, I was disenchanted. I had begun to feel like a painting teacher who taught color wheels but never let his students paint pictures, let alone engaged them in discussions of why art is meaningful or why artists differ in their styles. My students weren't complaining, really. Some of them were also born jugglers. The rest simply shouldered the burden, as if accustomed to the idea that math is no more than a kit full of tools.

So I scrambled my calculus class to place the discovery of calculus at the end. I intended to teach calculus as the culmination of an intellectual pursuit that lasted two thousand years. I could not find a suitable textbook, so I taught for three years using my own notes and homework problems. Then, on sabbatical, I wrote this book.

At first, I expected the book to be a synthesis of my notes and problems, but my research led me down new paths to many pleasant surprises. I had not realized the extent to which scholars in countries like Egypt, Persia, and India had absorbed and nourished Greek geometry when the western world went dark. Nor had I fully grasped how carefully ancient thinkers treated puzzles that lurk in the infinite. I gradually learned that because of these puzzles, calculus was not discovered in a way that would allow me to place its discovery at the “end” of anything.