book review
Throughout history, millions have been won and lost on the stock market: lost in the Wall Street Crash of 1929, won in the DotCom Boom of the 1990s. We all know that playing on the markets is a dicey game, but after decades of research we now have a better understanding of the way markets work. Or do we? According to Benoît Mandelbrot, modern financial theory is based on unrealistic assumptions that need a complete rethink.

Cartoons can help to bring down governments, but can they help to revolutionise science? This seems to be the hope of Robert Laughlin, whose book on the exciting field of emergence is littered with his handdrawn cartoons. His Nobel Prize in physics has given him the confidence to share his art and to hope that his cartoons help to explain how science can be revolutionised, or "reinvented". But what is this Different Universe, to what extent is it a reinvention, and how well does Laughlin set out his case?

'If I had to describe this book using just one word, then this word would be "passionate". This may be surprising seeing that we are dealing with maths, or, to be precise, metamaths, the study of mathematical truth. But this book is as much about the author's love for his subject as it is about the maths itself, and this love shines through on every page. Chaitin doesn't just describe his mathematical ideas to you, he also tells you where he was when he had them, how it felt having them, and about the mysterious creative processes that are involved.

Over the last few years there has been a rush of 'The Science of ...' books  popular science titles written to tie in with the recent release of a popular film or book. These include: The Science of The Xfiles, The Science of Star Wars, The Science of Superheroes, The Science of Supervillains, The Science of Discworld (volumes I, II and III), and The Science of Harry Potter. And into this fray now strides Michael Hanlon with his own offering to the genre.

The topic of this book  the BanachTarski Paradox  is a result so strange and counterintuitive that the author says he didn't believe it when he first saw it. The "paradox"  in fact an impeccable mathematical theorem  says that a small sphere, for example a pea, can be cut into as few as five pieces which can then be reassembled so as to make a far bigger sphere, for example the sun.

Anyone who has ever tried to analyse a game mathematically knows that things can get very complicated very quickly. In a game like chess, the number of possibilities for just the first three moves is already enormous, while, in poker, the roles played by chance, strategy and psychology seem to be mysteriously interlinked.

The author of this book is Statistics Editor of the Financial Times, the only newspaper in Britain to employ someone with this job title. He is therefore uniquely well placed to write this fascinating and timely book, which sets out to provide a factbased picture of the society we live in.

Keith Devlin is a wellknown populariser of mathematics, author of many books and appearing regularly on American radio as "The Math Guy" In this latest offering he walks us through the astounding mathematical capabilities of both plants and animals, and on to the abstract abilities of humans.

"Tribute to a Mathemagician" is the third book in a series of publications based on the Gathering for Gardner meetings, a regular gathering of enthusiasts who share Martin Gardner's interests in mathematics, magic and puzzle creation. Martin Gardner, the father of recreational mathematics, has influenced readers all over the world with his "Mathematical Games" column in Scientific American, which ran for 25 years.

This book is a curious mixture of biography, history and mathematics, all neatly packaged into an entertaining and enlightening read. In essence it is a biography of the brilliant and eccentric mathematician, John von Neumann, who began life, much like many of the other great mathematicians, by being able to do basic arithmatic before other children could speak and with an ability to calculate exceptionally well before he even went to school.
