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.
An unnamed girl in an unnamed, but contemporary, European city enters a rather gloomy old building, reading its address from a crumpled piece of paper. Inside, being given preference over a dozen people sitting in a waiting room, she is ushered into the office of Albert Einstein. "You said that time doesn't exist, so I took the liberty of coming to see you," she says. "You did the right thing," he replies. Thus a conversation ensues that spans all the 176 pages of this book.
This book starts gently enough, easing us in with the unarguable 2+2 = 4. But don't let this lull you into a misplaced sense of comfort; the ride is going to get very unsettling indeed. Martínez writes with an easy-reading clarity to tackle some of the simplest, but no less profoundly important, assumptions of mathematics. We hear how over the recent history of mathematics seemingly innocuous concepts were as controversial as genetic modification or animal testing are nowadays.
Edward Burger and Michael Starbird are both Professors of mathematics and have won numerous teaching and writing awards for their work. Burger has even performed stand-up comedy in night-clubs and is no stranger to appearing on television and radio broadcasts. In their company the reader is clearly in safe hands and these achievements are reflected in the quality of the book. The text is also written with a charm that is lamentably rare in maths literature.
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?