Mathematical Practitioners and the Transformation of Natural Knowledge in Early Modern Europe

Mathematical Practitioners and the Transformation of Natural Knowledge in Early Modern Europe is a collection of nine papers from various authors from around the globe. In the abstract of the first chapter, the book argues that in order to understand the transformations that took place during what is often called the Scientific Revolution one must seriously look at the interactions that took place between those who do (practitioners and craftsmen) and those who think (scholars or philosophers). Throughout the book, this goal is pursued through various discussions of practical mathematics, mathematical instruments, and Renaissance mechanics, among other topics. Credit must be given to the authors and editors in their unique treatment of mathematics in the Scientific Revolution.

To my knowledge there are no other books that give such treatment to the content at hand. My interest was initially drawn by the unique approach to Early Modern Europe and its mathematics through miscellaneous mathematical practitioners. The book explains some of the mathematical changes and studies some key mathematicians of the time. One of the best parts is exactly the treatment of lesser-known figures, mathematical practitioners who were using mathematics in surveying, fortification and other military endeavors. An example of this is seen in chapter five, which provides a discussion of Edmund Parker, who is noted as a polymath soldier and gunner. There is also an extensive list of primary and secondary sources to assist in searching for more information.

The book has three parts, the first of which further details the argument and goal of the book, discussing the theories of Hessen and Zilsel. The second part of the book discusses the practical mathematics of the sixteenth and seventeenth centuries. Within it there are numerous intriguing thoughts and connections made within the discussion of mathematics, mathematical practitioners and mathematical instruments, including some discussions on the mathematics of fortification and how fortification changed through these centuries. The third part of the book focuses on the relationships between practical mathematics and natural philosophy through various examples, including the Dutch mathematicians Willem Bartjens and Adriaan Metius and their impact on mathematics in the Netherlands.

This book does a good job achieving the goal it sets out for itself. The first few chapters are tough to read, as they tend to be more of a discussion of the science and philosophy of the Scientific Revolution. This was relieved as the chapters transitioned to more mathematical content, but I feel this book would not be easily read by undergraduate students. I do believe that this text could be a good supplement for students, and I firmly believe that this could be very useful for any professor looking for additional historical content. I know that I will be adapting some of this material into my History of Mathematics course, though I will not be requiring this as a textbook for my students to purchase.

Brent Kelderman is a high school math teacher at Millard West High School and an adjunct mathematics professor at Grace University in Omaha, Nebraska.