Now that I have already identified myself as a fanatic, perhaps it'll be no surprise that I find Writing the History of Mathematics: Its Historical Development quite fascinating. Some might feel that while it's reasonable to be interested in the history of your subject, taking the extra step of thinking about the history of history is too much. OK, this book isn't for you.
OK, we've settled that. So let me write for my fellow-fanatics. How good is the book? Well, quite good, though not everyone will agree with everything that is in it. (In fact, it has already generated some controversy.) One problem is the decision to organize the book by country: the first 328 pages contain separate essays on historical work in specific countries, from France in section 1 to the Arab Countries, Turkey, and Iran in section 19. There are good reasons for this choice, but it is nevertheless a little strange. Some readers may feel that the international conversation about the history of mathematics is just as important as national traditions, and that the format of this volume privileges the latter a little bit too much.
The most controversial part of the book, however, is the fact that writing about, say, French historians of mathematics often involves us in questions of correctness, bias, and overall value. These judgments are subjective, so there is much space for disagreement. This is particularly so when it comes to evaluating what early modern historians wrote about non-European mathematics. Should we read these authors as heavily implicated in European empire-building, colonialism, and "orientalism"? Or should we eschew this whole framework? As one might expect, the various authors of this book's chapters make different decisions on this issue. I think one can profit from their articles even if we disagree on their pressupositions.
The histories by country account for about half the book. The main content of the other half is a collection of brief biographies of many significant historians of mathematics. I am very glad to have these! Finally, the book includes a few portraits of historians of mathematics, a large bibliography and an extensive index, but the
In their introduction, Dauben and Scriba highlight the fact that this is a first attempt to write a history of the history of mathematics. As such, it is welcome. I hope it will spur others to respond, correct, amplify, and supplement. Meanwhile, most history fanatics will want to have access to this book.
Fernando Q. Gouvêa is Professor of Mathematics at Colby College in Waterville, ME. He is fanatic about number theory, the history of mathematics, Christian theology, poetry, science fiction, comic books, politics, classics, and football (the real thing, not the American version).