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The Search for Certainty: A Journey Through the History of Mathematics from 1800–2000

Frank J. Swetz, editor
Dover Publications
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The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Fernando Q. Gouvêa
, on

In 1994, Open Court published an interesting anthology of articles on the history of mathematics called From Five Fingers to Infinity. Aimed at the general reader, the book concentrated on texts that would be accessible and easy to read. Some of the articles were a little old or one-sided, so it was not intended as a source for scholars or as a definitive statement of any kind. But it was interesting and useful.

The Search for Certainty is an extract from From Five Fingers to Infinity. It contains all of the material originally included in the section of that book called (of course) “The Search for Certainty.” The articles focus on mathematics in the 19th and 20th centuries. A few of them treat foundational issues (set theory, logic, the controversy over the use of infinity in mathematics), but “certainty” here includes the desire for rigor and abstraction, the development of statistics, the creation of the first computers, and even Fermat’s Last Theorem (the article is from 1988, but the editor has added a note about the proof).

The book opens with an article that is on everyone’s list of favorites, Grabiner’s “The Changing Concept of Change,” a beautiful account of the evolution of the notion of derivative. I was also happy to see several articles dealing with matrices and linear algebra, a subject whose history is complicated and not really well known. The new edition includes some new material: an article on series and convergence, a survey of the evolution of group theory, and Margie Hale’s picture of “The Tree of Mathematics,” which originally appeared, I believe, in her textbook Essentials of Mathematics.

The recent history of mathematics is rarely discussed in undergraduate courses. As someone once joked, if we’re lucky we get to Euler and run out of steam. This book could be used to remedy that by introducing several modern themes in a friendly and accessible way.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME. He is the author, with William P. Berlinghoff, of Math through the Ages.

The table of contents is not available.