Magical Maze
Ian Stewart

A review written in 1997 for The Times.

Only in Britain would a TV station consider scientific lectures suitable entertainment for the festive season. Nonetheless, each year the BBC broadcasts the Royal Institution Christmas Lectures, which reach an audience of up to two million viewers each day, for five days. This year the lecturer will be mathematician Professor Ian Stewart, who has written a book, "The Magical Maze", to accompany his lectures.

The Christmas Juvenile Lectures, as they were called by their founder Michael Faraday, began in 1826 and were intended to educate and entertain young people - Faraday's own great scientific career was inspired by attending just such lecture. In recent years such diverse figures as Carl Sagan, Desmond Morris, David Attenborough and Richard Dawkins have all attempted to continue Faraday's mission, and, if the book is anything to judge by, Ian Stewart will carry on the tradition of scientific fun and fascination.

The book consists of a series of puzzles. Some of them are curious observations of the natural world, while others are more abstract, but in either case the explanations are intriguing, vivid and playful. The title of the book derives from the fact that Stewart views his subject as a mysterious exploration rather than a logical progression. Hence, he tries to convey the idea that when trying to find the answer to a problem a mathematician is often stumbling in unknown territory, confused and bewildered, and occasionally arriving at a dead-end. Much of the joy of mathematics comes from this intrepid intellectual journey.

The entire book is constructed as a journey through a giant maze, with Stewart guiding the reader through the eight passages (as opposed to chapters). The passages cover some of the juiciest topics within mathematics, such as chaos, undecidability and probability. The probability part of the maze starts with the Monty Hall problem, which was inspired by an American quiz show of the 1960s. Contestants were given the chance to win a car by tackling an essentially probablistic problem, but week after week they would make terrible decisions, thus illustrating the counter-intuitive nature of the subject.

Stewart then observes that juries can sometimes be confronted with a whole series of issues involving probability, and argues that our poor grasp of probabilities could lead to miscarriages of justice, most notably when it comes to assessing the significance of DNA evidence. He concludes with a marvellous demonstration that there are circumstances when the existence of a confession adds weight to the view that the accused is innocent rather than guilty.

Stewart is this country's greatest and most prolific populariser of mathematics, having written over sixty books, which over the years have been aimed increasingly at the general reader, rather than the converted. Not surprisingly, much of "The Magical Maze" contains material which has already appeared in previous books. This will annoy some of his fans, but others may appreciate a "Best of Ian Stewart" collection - a sort of "Now That's What I Call Mathematics! Vol 1".

By publishing a book to accompany the Christmas Lectures, Stewart is following in Faraday's footsteps . In 1861 Faraday published "The Chemical History of a Candle" to accompany his own series of lectures. However, it is unlikely that "The Magical Maze" will be quite so successful.  More than a century after being published, Faraday's book is still widely available, and is required reading for students in Japan.

Stewart has yet to deliver his lectures, but it is intended that, in addition to providing background to ideas discussed on television, the book will cover some completely new material.  On occasions, the ideas do become quite complex, which may be too much for 'juveniles', and, in a few cases, will even confuse more mature minds. However, this is a minor criticism. All in all, Stewart's efforts to publish his lectures should be applauded, and is something which future Royal Institution Lecturers ought to consider.

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