Nineteenth-century German mathematician Leopold Kronecker once said

God created the integers, all the rest is the work of man.

Although some people might find maths deadly boring, very few of us would think it could ever be deadly dangerous. But deadly it was in 16th century England, and one of those who followed the dangerous and mystical path of a mathematician was John Dee, the subject of this book.

Sherman Stein's motivation for writing this book grew out of a course on the history of calculus for undergraduates he taught for several years. Before that, like most of us, he didn't know where Archimedes' reputation as one of the greatest mathematicians of all time had come from - and now he wants us to know too.

First the executive summary: read these excellent books, and make sure all your friends and relations and bright pupils (if you are a teacher) or teachers (if a bright pupil) do so too. Mathematical Vistas (MV) is the sequel to the same authors' earlier Mathematical Reflections (MR). Each book is a series of explorations of mathematical topics, informed by a definite idea of what mathematics is, and how it should be taught.

This book is by the same authors as "Why do buses come in threes?", which was reviewed in Issue 10 of Plus. Like its predecessor, it consists of entertaining and thoughtprovoking questions on topics not obviously related to maths, and a discussion of each. The authors say that "give us a topic that we care about, and we all become mathematicians", and set out to prove it.

More mathematical misfits for you to master

In the real world, balls bounce and water splashes because of the laws of physics. In computer games, a physics engine ensures the virtual world behaves realistically. Mathematician and computer programmer Nick Gray tells us about playing God in a virtual world.

Theoretical physicists are searching for a 'Theory of Everything' to reconcile quantum mechanics and relativity - the two great physical theories of the twentieth century. String theory is a current hot favourite, and some of the world's most eminent physicists tell us why.

Today's digital world with its free flow of information, would not exist without cryptography to guarantee our privacy. Plus meets mathematician, author and broadcaster Simon Singh to find out about the science of secrecy.

What tactics should a soccer player use when taking a penalty kick? And what can the goalkeeper do to foil his plans? John Haigh uses Game Theory to find the answers, and looks at his World Cup predictions from last issue.