Your review picks out what I think is the key aim of his book: “math provides a unique lens into the lives and society of those in eighteenth century England which held a complicated relationship with the discipline that faced ridicule and respect and was applied in both reason and jest.”

I took two key things from the book. First, by the end of the 17C “everybody” in the broader English world understood that symbolic manipulation, whether reading or arithmetizing, was pervasive and unreasonably useful. It seems clear, too, that there was some degree of mistrust and resentment among the less-skilled toward the adept. Second, mathematics (and by implication, science) was, for the vast majority of people a mysterious “other,” and its practicioners were akin to magicians.

Popular education slowly removed the mystery; the mathematics club was open to all comers. And as the efficiency and effectiveness of symbolic reasoning became more visible, more people wanted to learn to read, write, and figure. With England’s mercantile and imperial ambitions demanding more sophisticated analyses, this growing pool of symbolic reasoners gave England a key strategic resource that its leaders would use in the 18th and 19th centuries.

Nice review. Im glad I wasn’t the only one who thought the book was a bit all over the place (though in fairness to the author, so was mathematical practice during Georgian Britain). The work would have benefitted from subheadings. I can forgive the structure of the work, but like you I found it jarring that the sources were not listed. I can forgive no footnotes in a popular history, but not including sources seems to fly in the face of all we’ve been taught as historians. Regarding the content of the book, I thought that the method was quite clever, actually. I see Wardhaugh as using Poor Robins birth, life, and death as a lens through which we can see the rise of popular involvement and interest in mathematics. In the first chapter we are introduced to Poor Robin and his readership, who are only concerned with math as it pertains to their daily life. Throughout the book we see interest grow as usefulness decreases, which interestingly corresponds with the advancement of mathematics. At the end math is used for fun instead of essential daily tasks or interest tables. In sum, I think what Wardhaugh is doing is tracing the democratization of math in Georgian Britain; though, like you say, it would be much easier to grasp the argument if he had an introduction and conclusion. Something to keep in mind for our own works, I suppose.
Looking forward to the discussion.

Given your review and Katie’s comment, I think Wardaugh’s book is a great example of why historians should always include introductions. If the flow of a book is going to be unusual, then the author absolutely needs to prepare readers with a full explanation of its structure at the beginning. Even if he or she doesn’t follow that plan, I bet readers will be forgiving.

All I can say for myself was that I wasn’t as frustrated as Katie and you were. I think the main reason for that was that I was so busy last week that I only had time to read one chapter at a time. I don’t think I was paying attention to how the chapters fit together. Plus, I had my usual experience of being so interested in the individual items Wardaugh brought up that I kept forgetting to think about the bigger picture of the book. Again, thanks for a good review that reminded me how to read a history text.

I want to comment on your caveat about Dixon’s assumptions about his readers and his explanations falling short. When I was first reading this book, I wasn’t enjoying it, and your comment made me realize why. There was something about his introduction to the Enlightenment that seemed to move too quickly, if that makes sense. I’m thinking back in chapter one. This line is a good example from page 14:

“Another Frenchman, Descartes, abandoned all ancient knowledge and began with the simple proposition, “Cogito ergo sum” (I think therefore I am), from which he extrapolated a complicated account of the cosmos.”

“I think therefore I am” is probably the only thing I remember from Descartes from my philosophy classes when I was an undergrad, and it’s a complicated argument. I don’t believe that Dixon characterized it correctly. He doesn’t even summarize how such a key argument fits into the bigger cosmological picture for Descartes or doesn’t give readers much information about why Descartes was important in the first place. Dixon might be correct, but he doesn’t give readers the full explanation. I think most general readers would know who Newton and Galileo were, but not Descartes. Dixon’s editor should have pushed him to skip the reference to Descartes’ altogether.

It was a lot easier for me to follow Dixon when he discussed ideas and events — the Moderate Enlightenment and intellectual currents and politics in Scotland and Britain, for example – closer to Cadwallander Colden’s life. He went into more detail, and he made it clearer how the Scottish educational system, for example, influenced Colden’s choices.

Going back to your caveat, I agree that Dixon’s overviews fall short of being helpful to general readers. I’d add that elaborating more would have been helpful, especially when he makes claims, like the “Cogito ergo sum” being part of some cosmological argument, that I’m not sure add up. Thanks again for your review. It summarized the book well and helped me focus on a gripe that I hope isn’t off base.