*(2012) Jaqueline Stedall, Oxford University Press, £7.95/ US $11.95, pbk, 123pp, ISBN 978-0-199-59968-4*

The most important thing that any review of this book can do is to guide the potential reader as to whether they will get something out of it. So an initial caveat: anyone expecting a whistlestop tour of the high points of mathematical achievement through the ages will be disappointed in this book.

It might be argued that the book does not live up to its title, but the author attempts to persuade us that the history of mathematics is in need of serious revision to include a broader perspective that reflects the practice of the majority of mathematical users: children in schools, traders, engineers, and also the social matrix that surrounds the work of the great mathematicians who provide the “theorem” history of mathematics. These are familiar themes to historians, who have reassessed many areas of historical research to include a more diverse range of experience than just that of the kings and priests.

The book begins with an overview of these ideas, and then proceeds through 7 chapters covering the myths of mathematical history, who mathematicians are and what is to be considered as mathematics. It then goes on to look at how mathematical ideas are disseminated, how it is learned, and how people have made their livelihoods through mathematics, before looking at some specific points about how we understand mathematical discoveries, and then finishing with a look at the history of the history of mathematics - that is, how have historians considered mathematical history over time.

Readers of this book who keep an open mind may come away with a better appreciation of how mathematical ideas have been transmitted from person to person; how the people who we would today call mathematicians perceived themselves in their own times, and how they made their livings; and perhaps a wider view of what mathematics is and who uses it.

Of course, this book is 'a very short introduction', so none of these themes can be treated in great depth, and the inclusion of these considerations means that there is less room in general for discussion of mathematical discoveries. Overall though, it is probably better to have a short book that opens the reader’s mind to a new view of its subject matter even if it gives them less of what they expect, than another, inevitably superficial, tour of the mathematical peaks – there are plenty of good books that cover this ground already, and the author has taken a bold step in showing us that this is not the only way of looking at mathematics.

Matt Freestone

**Matt Freestone** designed the original *SF2 Concatenation* website at the beginning of the 21st century as a way to archive a sample of the decade run of the original print editions (1987-1997). Most of *SF2 Concatenation's* core team are scientists and engineers. Matt, however, is also an Oxbridge mathematics graduate, and maths -- as the scientists on the *SF2 Concat* team appreciate -- is the discipline that underpins both science and engineering.

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