*A Discourse Concerning Algebra: English Algebra to 1685,* Jacqueline A. Stedall, 2002, 294 + xii pp., $116.00, cloth, ISBN 0-19-852495-1, Oxford University Press, New York, http://www.oup.com/us/

Mathematics education for students today emphasizes problem solving that employs the four representations of a function: algebra, geometry, tables of numbers, and verbal descriptions. The origins of these common techniques are brought to life in Jacqueline Stedall’s *A Discourse Concerning Algebra: English Algebra to 1685*. This compelling narrative presents to the reader an in-depth look at the lifetime work of John Wallis, a man who helped forge the irreversible bond between algebra and geometry, thus changing the direction of all future mathematics development.

After reading this book, one can only describe Wallis as the quintessential historian of English mathematics. Primarily self-taught, Wallis pored through medieval texts concerning arithmetic and astronomy as well as printed algebra texts found within the library at the University of Oxford. He also worked closely with other mathematicians of his time: William Oughtred, John Pell and William Brouncker. Stedall nicely weaves a tale depicting the collaboration among Wallis and his peers. In addition, Stedall gives the reader additional detail about contributions to algebra made by Arabic and Italian mathematicians.

For Stedall, sources are not simply endnotes. Throughout Stedall’s detailed accounting of the work of Wallis and his contemporaries, the reader delights in images of title pages from mathematical texts, images of pages from the historic works detailing problems, calculations and conclusions, and lastly samples from correspondence. Inclusion of this material goes a long way to illustrate the passion the 17th century mathematicians felt for their vocation. It brings the mathematics alive. Jacqueline Stedall’s book should be required reading for present and pre-service teachers of all levels. It is a wonderful book to read and should be considered an invaluable resource for those who teach the history of mathematics or those interested in learning the history of algebra.

Kathleen Ambruso Acker, Ph.D.,

See also the MAA Review by Eisso Atzema.