This book has a rather grandiose title and an interesting premise: take one important concept from the history of mathematics (the ability to split up a line into infinitesimally small parts), and trace its path through the very turbulent 1600s. As someone who has taught math classes to people afraid of math, I have found that sometimes attaching a bit of history and a human being to a concept makes it seem somehow more approachable. A few tidbits about Descartes can make y=mx+b more palatable to the math-phobe sometimes. So it was with this in mind that I embarked on this book to see if I could extract some stories about people and concepts that I could add to my repertoire.

What I found was that the book had rather too many interesting sidelights, all heavily intertwined. While the book has many anecdotes that would be good to drop while teaching, there are too many of them to keep track of very easily and they are presented in ways that are rich with background, so rich that it is hard to keep track of who wanted to do what; it would be difficult to pull out one story, since they are all packed into a dense weave that is not easy to pull apart.

The net result is that it is a little tough to define the audience for this book. The names and dates come very thick and fast; if you are not already a student of history, then you may find it demanding to follow all of the characters. It is sort of 17th-century “inside baseball.”

On the other hand, if you are an historian who is not comfortable with math, you may find the interspersed mathematical diagrams a bit daunting to follow. The author has included a list of people and what they contributed and a timeline that helps some, but the book really needs those things. This makes for heavy lifting if you had assumed it would be a good, light airplane read. The book also includes a lengthy section of notes and an index. However, the notes are a little obscure: they cite contemporary (published in the 1600s) manuscripts in many cases, and it’s not very clear what one is supposed to do with these citations if one wanted more information.

In general, it feels like a PhD thesis in the history of mathematics rather than the popular book I was expecting. There were definitely some great moments, like the description of the Jesuit Revisors General who were more or less in charge of defining what was real about the world and what was not. It is mind-bending to think of theology as queen of the sciences and mathematics as a bit of a backwater. There were sudden insights into how differently we think now than people did 350 or so years ago. The book gives the reader the opportunity that good history books provide, to step outside the current world and try to gain some perspective on it. But it does make you work pretty hard in between those illuminations, perhaps a metaphor for the mathematics of the time itself.

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