Books: Independent choice: Popular maths books

A Russian mathematician has created a theory for computing the average length of a game of Snakes and Ladders. There is a mathematical essay entitled "Can One Hear the Shape of a Drum?" In 1927, Cambridge University Press published a table of 41,600 random numbers (used for statistical sampling). Later analysis demonstrated that these numbers were not actually random or, at least, not random enough.

These facts are just a few of many that I have culled from three new books on mathematics for the purpose of boring people at dinner parties. But is there anything wrong with being enthralled by reading them when I have difficulty with anything more intricate than long division? A part of it, admittedly, is rather like the pleasure of sumptuous cookbooks containing complicated recipes I will never manage. The Jungles of Randomness by Ivars Peterson (Penguin, pounds 11.99) is a beautiful account of the structures and patterns that seem to be mandated even amid apparent disorder. It's extraordinary to see 18th-century theorems by Euler becoming a substantial part of microbiology in the 20th century; or to grasp how the indentations of a coastline are related to the textured surface of a concert-hall wall.

It may, also, be useful to perform some mental press-ups. "Use it or lose it," they say. Sometimes it can feel as if it was lost long ago. Here are three related problems from Deborah J Bennett's Randomness (Harvard UP, pounds 15.50): 1) I meet Jane, who tells me that she has two children, one a girl. What is the probability that the other child is a girl as well? 2) I meet Jane, who tells me that she has two children, the elder of which is a girl. What is the probability that the other is a girl? 3) I meet Jane, who tells me that she has two children, one a girl. The next day I meet her with a little girl, introduced as her daughter. What is the probability that the other child is a girl?

The answers are: 1) one third; 2) one half; 3) one half. For most people, 2) is obvious, 1) is odder but makes sense after some thought; 3) is the difficult one. It seems as if it ought to be the same as 1) and Bennett has a page explaining it. "It is no wonder," she concludes, "that probability is a perplexing science to many people."

And this is where all of these books become not just a pleasing distraction but also a lesson in civic responsibility. Why Do Buses Come in Threes? by Rob Eastaway and Jeremy Wyndham (Robson Books, pounds 12.95) deals in a very entertaining way with problems in normal life related to mathematics: luck, coincidences, gambling. Britain would be a saner place if people reflected that you should never buy your lottery ticket earlier than Friday. The reason is not that Friday is a lucky day, but that only by then is your chance of being run over by a car and killed before Saturday night less than your chance of winning the jackpot.

Such innumeracy may seem less amusing when it becomes an inability to assess relative degrees of risk: when people are more worried by mad cow disease than tobacco-related illness, by air crashes than car crashes. It is books such as these that will redress the balance. They are not just captivating, but may even make you a better, if more awkward, citizen. And to pay for them, all you need is to lay off the lottery for a few weeks.