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.
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.
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.
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.
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.
This is a new edition of an old classic. Abbott wrote this beautiful tale over a hundred years ago under the pseudonym A Square. It still is one of the best introductions to a mathematical world of higher dimensions, and it's an amazingly imaginative social satire, too.