Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences

This is a fundamental reference for those who want to learn more about specific aspects of the history of mathematics. It collects short articles by experts summarizing what is known (or at least what was known in 1994) about their topics. Each article includes a bibliography that allows further research.

The first two chapters are arranged chronologically. In the first, on “Ancient and non-Western traditions,” we find the usual suspects (e.g, Jens Høyrup on Babylonian mathematics, J. C. Martzloff on Chinese mathematics) but also some unusual topics (Alexander Jones on Greek applied mathematics, David King on mathematics related to Islamic religious ritual, G. G. Joseph on Tibetan astronomy and mathematics). In the second, “The Western Middle Ages and the Renaissance,” one finds articles ranging from the Archimedean tradition in Europe to the philosophical context of the mathematics of that period.

From that point on, the chapters focus on specific topics: calculus and analysis, logic and foundations, algebra and number theory, geometry and topology. More surprising (and very useful) are the following chapters, on mechanics and engineering, physics and mathematical physics, probability and statistics (including applications to the social sciences).

Chapter 11 discusses institutions, especially universities, but also includes a section on women and mathematics and one of mathematical journals. Chapter 12 is on mathematics and culture, including several articles on recreational mathematics and even one on the history of the history of mathematics. The final chapter includes a selection of sources for further study.

These short articles cannot, of course, tell the whole story, but they are often an excellent starting point for further research. Grattan-Guinness and his associate editors put together a very useful reference volume.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME, and the editor of MAA Reviews. With William Berlinghoff, he wrote Math through the Ages: A Gentle History for Teachers and Others.