The Companion Encyclopedia of the History and Philosophy of
the Mathematical Sciences was first published in 1994. I coveted those
two big (and very expensive) hardcovers so much that I joined a book club
just so that I could get a slightly better price on the set. It was still
quite expensive. I think it was worth it.Here, ten years later, is a paperback reprint. The two volumes together will still run you $100, so it's still not cheap, though it's less than one third of the price of the hardcover edition. So even non-fanatics can now consider getting a copy.
The Companion Encyclopedia is a collection of short articles on various historical topics. In contrast to most surveys of the history of mathematics, it is organized by topic rather than by period. The emphasis is on modern (i.e., post-medieval) mathematics, and serious attention is paid to applied mathematics. There are also articles on the philosophy of mathematics, on interactions between mathematics and culture as a whole, and even on the history of the history of mathematics.
As in any edited volume, the articles are not all of uniform quality, but in general they offer a valuable short overview of the history of some bit of mathematics, followed by a bibliography. The bibliographies are perhaps the most useful part, and it is really a pity that they weren't updated for this edition. Still, if you're curious about, say, the history of elliptic integrals and elliptic functions, Roger Cooke's article on the subject (Section 4.5 in the first volume) is a great place to start. The same is true for many other topics. And if you need historical information on Recreational Mathematics or Crystallography, there's hardly any other place to look.
Each chapter of Grattan-Guinness's The Rainbow of Mathematics includes references to the Companion Encyclopedia. (There are also a lot of references to it in my own history book.) I think this is the ideal way to use these volumes: they don't replace a survey (such as those by Katz, Suzuki, Grattan-Guinness, Calinger, or Cooke) but rather they are the next place to go when you are looking for more detailed or more specific information. [Fernando Q. Gouvêa]
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]
Jacqueline Stedall's The Greate Invention of
Algebra puts us all in her debt. The meat of this book is a careful
edition of all the pages of Thomas Harriot's mathematical notes that have
to do with algebra. To understand why this is important, we have to go into
a bit of detail about Harriot's contributions to algebra.
Most of what we know about Harriot's algebra goes back to a book called Artis Analyticae Praxis ("The Practice of the Analytic Art"). This was published in 1631, ten years after Harriot's death. This was edited by Walter Warner, despite Harriot's wish that Nathaniel Torporley be the editor. Here is how Stedall describes Warner and his work: "Warner was not previously known as a mathematician, and never understood Harriot's work as well as Torporley did. Instead of editing the manuscripts as they stood, he chose to select and reorder the material... In doing so he not only destroyed the coherence of Harriot's treatise but made it appear considerably less sophisticated than in fact it was."
Thus, up to now, historians had to either use a corrupt edition of Harriot's work or to consult the actual papers (thousands of pages of papers!) and select out the algebraic portions. This is what Stedall has done for us: as she says, this book "offers, for the first time since 1632, a complete version of Harriot's Treatise on Equations."
Well, as "complete" as possible. The book contains a translation of all of the pages containing Harriot's notes for the planned Treatise. There is not a whole lot of connective tissue (in fact, there isn't very much text at all). But it is quite possible to make sense of Harriot's material, and therefore it is now possible to have a fairer measure of what Harriot actually did. (One can find Stedall's own estimate of Harriot's contribution in her book A Discourse Concerning Algebra: English algebra to 1685, to be reviewed soon on MAA Online. Stedall is an author to watch: I understand her edition of the Arithmetica Infinitorum of John Wallis is also forthcoming.).
The upshot is that this is a book that should be in any library that tries
to have a complete set of historical source material. [Fernando
Q. Gouvêa]
Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, volume 1, edited by I. Grattan-Guinness. Johns Hopkins University Press, 2003. Paperback, $49.95. ISBN 0-8018-7396-7.
Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, volume 2, edited by I. Grattan-Guinness. Johns Hopkins University Press, 2003. Paperback, $49.95. ISBN 0-8018-7397-5.
Writing the History of Mathematics: Its Historical Development, edited by Joseph W. Dauben and Christoph J. Scriba on behalf of the International Commission on the History of Mathematics. Birkäuser, 2002. Softcover, 689 pp., $89.95, ISBN 3-7643-6167-0. Hardcover, 689 pp., $139.00, ISBN 3-7643-6166-2.
The Greate Invention of Algebra: Thomas Harriot's Treatise on Equations, by Jacqueline A. Stedall. Oxford University Press, 2003. Hardcover, 322pp., $115.00. ISBN0-19-852602-4.
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).
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Read This! is the MAA Online book review column. Contributions are welcome; contact the editor if you'd like to be one of our reviewers. Books for review should be sent to the editor: Fernando Gouv&ecric;a, Dept. of Math&CS, Colby College, Waterville, ME 04901. Publishers, please check our reviews information page.
MAA Online is edited by Fernando Q. Gouvêa (fqgouvea@colby.edu). Last modified: Sat Nov 06 13:01:22 Eastern Standard Time 2004