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A beautiful little book, certain to be treasured by several generations of mathematics lovers, by students and teachers so enlightened as to think of mathematics not as a forest of technical details but as the beautiful coherent creation of a richly diverse population of extraordinary people. In twenty chapters (which, though densely cross-linked, can be read in virtually any order) the author reviews the broad sweep of the issues in the principal topical sub- fields of mathematics. His writing is so luminous as to engage the interest of utter novices, yet so dense with particulars as to stimulate the imagination of professionals (even, on occasion, to instruct). Takes a broader view (and is more biographical) than either What is mathematics? (Courant & Robbins, 1941) or Geometry and the imagination (Hilbert & Cohn-Vossen, 1932), and is technically more specific that E.T. Bell's Men of mathematics (1937). Very attractively produced, with nice figures and an excellent bibliography. (NW) Annotation(c) 2003 Book News, Inc., Portland, OR (booknews.com)

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CHOICE Review

Stillwell approaches the history of mathematics from a mathematical viewpoint as compared to Carl B. Boyer's History of Mathematics (CH, Nov '89) which approaches mathematics from a historical viewpoint. The reader should have some mathematical knowledge of basic calculus, algebra, and geometry, and at least some familiarity with advanced topics such as topology, differential equations, and group theory. Stillwell shows how different mathematical topics intertwine and help in each other's development. Biographical notes are added for historical context; illustrations are clear; and an excellent bibliography is included. Stillwell shows the theoretical development of the various branches of mathematics and the interrelationships of that development--a history of mathematics for those who enjoy its logical development. Highly recommended for all libraries. -J. O. Christensen, Brigham Young University