With respect to history

Last winter, I had the privelege of teaching our History of Mathematics (Math 181) course at UC Santa Cruz. As I had lobbied previously for the course to satisfy the campuswide “textual analysis” requirement, I had to focus on primary sources in the class. Fortunately, I had plenty of fair warning and spent a few months reading and pretending to be a historian before the first day of class.

My goal in teaching was to have every student engage directly with at least two primary mathematical sources, in translation of course. The first resource was the textbook I chose: The Mathematics of Egypt, Mesopotamia, China, India, and Islam: a Sourcebook, edited by Victor Katz. This book is a goldmine, if you understand what it is. It is not a history of math textbook; rather, it presents a huge number of primary sources, some in short excerpts and some in extended passages, with background and guidance from five experts. This covered everything I wanted, except for Greek mathematics, for which primary and secondary source material is plentiful and free online. I enjoyed teaching from the Sourcebook and I have referred to it often, for enjoyment, and also in teacher education projects.

After reading the Sourcebook and other modern scholarship in the history of mathematics, I found the typical treatment of history in math textbooks inadequate (and often just plain false). Certainly some great mathematicians have ventured into a study of history; Dickson and Weil and van der Waarden are three prime examples. But I find their treatments most useful as annotated bibliographies. More appealing to me are treatments by David Fowler of Greek Mathematics; after reading Fowler I am convinced that “translating” Euclid into modern algebraic notation is historically destructive. On the other hand, I don’t have the time to bury myself in Chapter X of the Elements, trying to understand the whole text as Euclid’s contemporaries might have understood it.

Historical Notes, from Chapter 2
Click to enlarge the historical notes from Chapter 2.

In writing the Illustrated Theory of Numbers, I am trying to give respect to history.  Even if I devote less space to history than to mathematics, I hope I give them the same scholarly respect.  To that end, I have avoided spreading legends (like Gauss adding the numbers from 1 to 100) and I have avoided relying on secondary accounts as much as possible. I sometimes “translate” older sources into modern notation, but I try to raise a caution flag when this might be misleading. I incorporate historical information from China and India and elsewhere, to avoid Western bias as much as possible (given the history of scholarship and my Western-only language skills). At the end of each chapter, I am including some historical notes. These contain historical highlights and bits of primary source material and historical scholarship. In the style of Tufte, I have provided annotated citations in the margins.