Mario Livio's new book tells the story of the elusive quintic equation and how, from the mysteries of this unsolvable puzzle, group theory was born. This branch of mathematics describes and defines symmetry, and at the core of the book is a strong sense of just how much of our behaviour and appreciation of the world around us depends on our ability to perceive symmetrical proportions.
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.
'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 X-files, 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.
Have you ever wondered what shape a football is? No, it is not a sphere - it is far closer to something called a truncated icosahedron, also known as a "buckyball". It consists of 12 black pentagons and 20 white hexagons and is about the most effective way of creating something nearly spherical out of flat panels. Curious sporting-related mathematical facts like this can be found throughout Eastaway and Haigh's book "How to take a penalty, the hidden mathematics of sport".
The topic of this book - the Banach-Tarski 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.