## book review

In 2006 the Fields Medal — one of the highest honours in mathematics — was awarded to Grigory Perelman for solving the Poincaré conjecture, a famously difficult problem that had stumped mathematicians for a century. To the surprise of many, and the excitement of the media, Perelman declined the award and withdrew not only from mathematics but from the world generally. In *Perfect rigour* Masha Gessen sheds some light on this brilliant and perplexing character and the reasons why he would renounce both the worldly rewards of his mathematical achievement and also his beloved vocation, mathematics itself.

*Loving and hating mathematics* is an intriguing title, but it doesn't tell you what this book is about. More informative is the subtitle: *Challenging the myths of mathematical life*. The book is a collaboration between a mathematician, Reuben Hersh, and a psychologist in the fields of linguistics and education, Vera John-Steiner.

With twenty skillfully written essays Tony Crilly paints a broad-stroke picture of modern mathematics, focusing on some of the most exciting topics. This book is intended for people whose acquaintance with mathematics is limited to their high school years, but who want to know "what all this fuss is about". It is ideal for those who have heard that mathematicians talk about imaginary numbers and unbreakable codes, and want to know how much of it, if any, is true.

*Gems of Geometry*arrived through the post it seemed the Gods had conspired to despatch the perfect book for me to review. Like the author, John Barnes, I have a fascination with Edwin Abbot Abbot’s

*Flatland*and spent many childhood hours gluing paper models of fantastical geometric constructions together.

Computing is at the heart of our modern world, but what are its frontiers? This book presents new trends in this fast growing field. Although the topics covered range from spacecraft control to embedding intelligence in bacteria, they all coincide in one fundamental point: the future of computing is a synthesis with nature.

*Mathematics of life*weaves a history of biology with examples of how mathematics can help solve the unanswered questions that were created along the way. Mathematics, Stewart argues, will be the next biological revolution.

*How to read historical mathematics*and this is precisely what it is about. It is an introduction to the marvellous world of the history of mathematics, aimed at the general public. You will not learn a lot either about mathematics or its history, but you will be much better prepared for reading old mathematical masterpieces after this book.

This is an excellently researched and well-written book. It distinguishes itself from the body of popular science books by interspersing and motivating the mathematics it contains using stories, interviews and conversations with a variety of people, ranging from mathematicians and linguists to mystics. The result is a mixture of journalism, travel literature and mathematical history that will have a much wider appeal than many other accessible texts on mathematics.

This book is a mixture between an encyclopedia and a collection of intriguing ideas. In some sense, it's a plain English encyclopedia of maths, embellished with some examples for entertainment. So whether you're trying to get at the "true" meaning of something textbooks only define using passionless symbols, or are looking for a little diversion before going to sleep, this book can give you both.

This book tells the fascinating story of strange geometric objects that have achieved some fame outside of maths and even inspired a Woody Allen joke: they're called *Calabi-Yau manifolds*. When *Plus* recently interviewed one of its authors he was adamant that maths should be brought to the masses without dumbing down or glossing over the tricky parts. And this is just what this books sets out to achieve.