## book review

With this collection of letters Ian Stewart, accomplished mathematician, science writer, and even science fiction writer, accompanies a young and imaginary student on her path to becoming a professional mathematician. The letters address the questions that arise naturally at the crucial points in "Meg's" career, from leaving school and pondering whether to take a maths degree, through to becoming a fully established mathematician wondering how to juggle teaching and research.
At the earliest age, children around the world ask questions about the nature of existence and how we came to be here. Simon Singh's third and most ambitious work of popular science takes us on a journey through the ages, as man's sense of his own importance in the universe shrank ever smaller and his idea of time stretched from a few thousand to around fifteen billion years.
'This book starts with the story of Larry Walters, who decided to try flying a garden chair with some fifty helium weather balloons attached. Larry didn't do the maths, and ended up at 16,000 feet! Michael de Smith has written a book for all the Larrys who need or ought to do some mathematical analysis of a problem before setting out.
What makes numbers interesting? The subtitle of this beautiful book is the motivation, map, and message of its 188-page journey from zero to infinity. With concise insight, Reid takes the digits from 0 to 9 as chapter titles and starting points of voyages into the history and deep concepts of modern mathematics.
Do you love football, marvel at Beckham's perfect swerving free kicks and find formations fascinating? Or do you love science, and want to find out how aerodynamics affects a ball in flight and discover the insights statistical analysis of real-life data can give?
The hero of this book is Euler's formula: eiπ + 1 = 0 This simple equation has been widely considered through the last two centuries to be one of the most beautiful formulae of mathematics, and Nahin tells us why.
One of the things I enjoy most about biographies of mathematicians is the presentation of mathematics as a very human endeavour. Despite the sometimes abstract nature of mathematics, we see in this biography of Kurt Gödel that it is a very human activity pursued by people within a deeply connected community, but each with their own vision of truth.
'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.
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 hand-drawn 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 "re-invented". But what is this Different Universe, to what extent is it a reinvention, and how well does Laughlin set out his case?
Throughout history, millions have been won and lost on the stock market: lost in the Wall Street Crash of 1929, won in the Dot-Com 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 re-think.