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The History of Mathematics: A Very Short Introduction

Jacqueline Stedall
Oxford University Press
Publication Date: 
Number of Pages: 
Very Short Introductions
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The Basic Library List Committee considers this book essential for undergraduate mathematics libraries.

[Reviewed by
Fernando Q. Gouvêa
, on

The Oxford University Press series of Very Short Introductions has existed since 1995; there seem to be more than 350 of them. The idea is to ask an expert to introduce readers to the essential ideas of a subject. The books are small (roughly 4 × 7 inches) and, of course, short. For the most part, the series seems to focus on the humanities; the web site currently lists as forthcoming, among others, volumes on Comedy, Rastafari, American Politics, The Avant Garde, Thought, The Napoleonic Wars, and Buddhism. But, of course, the sciences do get a look in; among the recent volumes we see Networks, Magnetism, Stars, The Antarctic, and Robotics.

The first mathematical book in the series (ten years ago) was a very short introduction to Mathematics, by Tim Gowers. (One book for all of mathematics!) I am aware of only a few others: an introduction to Probability was reviewed here recently, and there are volumes on Statistics and Numbers. Presumably some portions of the volumes on Isaac Newton, Cryptography, Logic, Bertrand Russell, and Galileo are mathematical, but in general we are under-represented. (The volume on The Elements is, alas, not about Euclid.) So it is great news that now The History of Mathematics has its own VSI.

An introduction to the history of mathematics might be two different things. One possibility is to provide a kind of summary of what is known about the history of mathematics. The other is to write an introduction to the discipline called “history of mathematics,” focusing on what mathematical historians do and how they do it. The first kind of book would really be an introductory textbook; there are many of those and it’s hard to imagine how it might be done in a “very short” book. What we have here, appropriately for this series, is the latter.

Jackie Stedall is a prolific author and a respected historian whose work deals mostly with the history of algebra. She has written a terrific little book that will be useful both to students and to the “educated general reader” who wants to know more about what historians of mathematics do. She starts gently, with a chapter that focuses on Fermat’s Last Theorem and visits several moments in its history. This chapter is really making an argument: to investigate the history of mathematics, she claims, one should go beyond the story of individuals and their “contributions” to the development of mathematical theories.

In the rest of the book, Stedall considers questions such as

What is mathematics and who counts as a mathematician?
How do mathematical ideas get disseminated?
How was mathematics learned and taught?
How did mathematicians earn their living?

Considering this kind of question gives Stedall the chance to give many examples that demonstrate the richness of this “thick” approach to the history of mathematics. For the most part, these are both interesting and accessible to readers who may not themselves be mathematicians. Of course, the “history of ideas” aspect also comes in, but at the end, where it can enter into useful conversation with the more external and social issues. A final short chapter addresses the history of the history of mathematics, focusing especially on the changes that happened over the previous fifty or so years.

I once read of a historian of mathematics who was asked what she did by a cab driver. When she said she studied the history of ancient mathematics, they driver pulled out a notebook and wrote it down. She asked him why, and he said he collected exotic occupations, and that this was one of the strangest ever. So there’s a need for a little book like this. Perhaps it will enlarge the circle at least a little.

I will be teaching Colby’s History of Mathematics course this spring, and this little book will be the first piece of required reading. I am hoping that it will introduce my students to a subject that is broader than they think it is, and perhaps get them excited for what comes after.

Mathematicians should read it too.

Fernando Q. Gouvêa is a mathematician who has fallen in love with the history of mathematics. With William P. Berlinghoff, he is the author of Math through the Ages: A Gentle History for Teachers and Others.

1. Mathematics: myth and history
2. What is mathematics and who is a mathematician?
3. How are mathematical ideas disseminated?
4. Learning mathematics
5. Mathematical livelihoods
6. Getting inside mathematics
7. The evolving historiography of mathematics