Historiography of Mathematics in the 19th and 20th Centuries

The editors have compiled eleven articles with the aim of showing “through detailed case studies how the historiography of mathematics has been influenced by the contexts and motivations of its practitioners.” Here historiography refers both to the best practices for research, interpretation, and presentation as well as the methods employed by certain historians. Thus the focus is on historians first, mathematics secondarily — if at all.

What audience will enjoy this compilation? There is very little actual mathematics here. I counted two equations and one mathematical diagram, both in the second to last article. Those interested in how historians strive to study mathematics in its original setting will find many examples of how various early accounts and more recent surveys came to be written, with attention to the impact of social constraints, personal ambitions, and simple errors or misunderstandings. This book reminds us to choose reliable guides when trying to understand second-hand an era or an individual’s milieu.

David Rowe gives a lively account of Neugebaur’s vision of ancient mathematics and the later attacks on his opinions. In Jeremy Gray’s review of several midcentury writers of histories of mathematics, including Coolidge, Struik, Boyer, and Kline, he points out that few of them did any research themselves in the subject, relying instead on the work of others. Boyer was an exception. This observation leads Gray to thoughtful reflection on how history should be done and written.

Other authors consider Thomas Heath, Bourbaki, the 19th century European understanding of mathematics in the Islamic world, and a Norwegian schoolteacher-tuned-historian who helped revive interest in Harriott’s mathematics, among others.

Each article can be read independently of the rest. Taken as a whole, they are uneven in style and approach, and a few suffer from academic jargon, but all are readable and, to me, enjoyable. Professional historians and mathematicians with a curiosity about the work of historians will find much of interest here.

Daniel J. Curtin has just retired after 38 years of service to Northern Kentucky University. His primary historical interest is the development of algebra from the 16th through the 18th centuries.