*Companion Encyclopedia of the History & Philosophy of the Mathematical Sciences,* 2 vols. I. Grattan-Guinness, ed. 2003. Paper: vol 1, pp xiv + 842 pp, ISBN 0-8018-7396, $49.95; vol II, xii+ 843-1806 pp, ISBN 0-8018-7397, $49.95; illustrations, diagrams, index. Baltimore, MD: The Johns Hopkins University Press (410) 516-6956, www.press.jhu.edu

This two volume edition is the paperback release of the hardcover *Encyclopedia* published as part of the Routledge Reference Series in 1994. The original hardcover edition costs $525, limiting its acquisition to large libraries. Now, this less expensive, more accessible edition provides a valuable resource to a wider audience. This work contains 176 articles divided into thirteen sections. In turn, the articles are grouped in categories, each considering various historical aspects of our mathematical heritage from the development of content and processes of specific mathematical disciplines to their uses and interpretations. These categories span: analysis; logic and foundations; algebra and number theory; geometries and topology; probability and statistics; philosophical foundations; mathematical applications in physics and engineering; academic support systems; and the place of mathematics in culture. The last category provides a potpourri of insights into such important subjects as ethnomathematics, women in mathematics, mathematics in art and literature and so on. The coverage is broad, in that it considers mathematics developing and evolving in a societal context. It allows for varied perceptions on the importance and uses of mathematics. The final section of this work provides further research support with a selected bibliography and additional reference information.

A reader must bring to this work a knowledge of mathematics. The authors, each an expert in his or her field, do not teach the mathematics in question. Rather, they write about it, its history, its uses and its interpretations. Each contribution is a survey that adequately informs but also encourages further research by including a relevant bibliography. Both Western and non-Western mathematical traditions are examined. The historical sweep encompasses developments from ancient times through the twentieth century. While the Encyclopedia provides a cornucopia on mathematics history for the inquiring student, it still offers intriguing information for the more sophisticated scholar. This is a wonderful basic research resource. Every academic library should have a copy of this work.

Frank J. Swetz, Professor Emeritus, The Pennsylvania State University

See also the MAA Review by Fernando Q. Gouvêa.