Reprinted with permission from CHOICE, © American Library Association.

*Jacqueline Stedall* (University of Oxford, UK)

**From Cardano’s great art to Lagrange’s reflections: filling a gap in the history of algebra**

Heritage of European Mathematics

ISBN 978-3-03719-092-0

DOI 10.4171/092

March 2011, 236 pages, hardcover, 17 x 24 cm.

68.00 Euro

Stedall (The Queen's College, Univ. of Oxford, UK) provides a thoroughly engaging book that bridges the gap between 16th- and 17th-century methods of solving equations and what is now dubbed modern or abstract algebra. Though the published works of Cardano elaborated techniques for solving cubic and quartic equations, they lacked a general approach that would lend itself to answering questions about higher-order equations. Stedall leads the reader through advances in algebra that gave rise to the more general theory of equations. Later writers failed to recognize that the ideas of the mathematicians of the 16th and 17th centuries led to the advances that allowed Lagrange to make important insights into a more unified approach in algebra. The author provides generous examples of the actual mathematical techniques developed throughout this period. The book is organized into three sections: "From Cardano to Newton," "From Newton to Lagrange," and "After Lagrange." The one chapter in this last section is the shortest and touches on the beginning of group theory. This wonderful book offers a much-needed guide through the early study of equations, a period of study that provided the fertile basis for Lagrange's important seminal ideas.

Summing Up: Highly recommended. Upper-division undergraduates, graduate students, and researchers/faculty.