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Be prepared to move frogs, change the course of fish, investigate parties, and consider flight maps. In the process be prepared to experience the same jubilation as Archimedes is reputed to have felt after bathing with a supposedly gold crown. Here there are problems to taunt and delight.This book arose out of a series of articles that were published in Maths In Schools and looked at practical problem solving ideas for the secondary school. The title comes from the author’s belief that mathematics is based on two pillars. The first of these is the content and ideas that we know and teach in schools and universities. The second is the creative side of the subject that is not so well known and not so often taught. At a hectic writing pace the reader is taken on a journey through this creative mathematical landscape and shown the importance of experimenting, guessing, proving, finding counterexamples and even of giving up. But the readers’ pace is up to them. This is a book that demands both thought and play by readers. In this sense the book is like an iceberg with only a relatively small percentage appearing in print while the rest in the reader’s heads and on their paper.The objects of the creativity here are problems that at some level are readily accessible to most secondary students. To make good progress, a knowledge of number and some basic logical skills are sufficient. Algebra isn’t mandatory but a little knowledge is very useful. But the underlying aim of the book is to show that mathematics is more than a collection of results; that there is a creative, people side to the subject; that this side can be shown to secondary students; and they can experience the same highs and lows that professional mathematicians enjoy that keep them thinking motivated even after retirement.

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“At least there can be no doubt of the enthusiasm of the author, nor of his skill at choosing problems which are tough yet accessible and which should be in a problem solver’s armoury. Some of the weapons used are technical induction, contradiction but equally important are the more psychological ones, tenacity, suspicions, choice of byways, spurious or significant similarities and these are treated seriously too.
Much of this is covered, and covered well, in other texts, but the feature which made this book special for me was the technique of using experience gained with one problem to feed into strategies for solving another, often with no obvious connection between the problems. One effect of this is that progress on a problem is often delayed, to be resumed in a later chapter using the weapons developed in an intervening problem – perhaps frustrating, but often very effective.
You and your students will get a lot of serious fun from this book, and for a very attractive price”.

Reviewed by John Baylis

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