Reviews

During September and October, the Isaac Newton Institute for Mathematical Sciences showed a small exhibition of two suites of photo-etchings with mathematical components by the Canadian artist Catherine M Stewart, who studied both maths and physics in the course of her undergraduate degree at the University of Toronto. Elements of Grace is a collection of 12 photo-etchings which combine diagrams from Newton's Principia Mathematica (1729) with photodetails of the human body.
Despite its title, Carl Djerassi's latest play, Calculus, is more like a lesson in history or even psychology than one in mathematics. This is because Djerassi's intention was to explore the moral calculus that was involved in the discovery of the mathematical technique, rather than the technique itself.
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.
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.
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.
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.
If "How to solve it" really contained an infallible recipe for doing so, mathematics would not be mathematics and the world would be quite different. Of course it doesn't - it can't - but it can - and does - contain a great deal of food for thought for the budding mathematician. Like many other Central Europeans, Pólya relocated to the US at the beginning of the Second World War. There he worked at Stanford University and wrote this immensely successful book (more than a million copies sold) in 1945.
This book is built on an extended metaphor, which casts equations as the poetry of science. According to the editor Graham Farmelo (head of Science Communication at the Science Museum in London), great equations and great poems are alike in a number of ways. Both suffer if anything is added, changed, or taken away, both are a rich stimulus to the prepared imagination, and both draw much of their power from their conciseness.