# 39

 Groups are some of the most fundamental objects in maths. Take a system of interacting objects and strip it to the bone to see what makes it tick, and very often you're faced with a group. Colva Roney-Dougal takes us into their abstract world and puzzles over a game of Solitaire. When Kurt Gödel published his incompleteness theorem in 1931, the mathematical community was stunned: using maths he had proved that there are limits to what maths can prove. This put an end to the hope that all of maths could one day be unified in one elegant theory and had very real implications for computer science. John W Dawson describes Gödel's brilliant work and troubled life. On the 25th of May 1997 a dramatic collision tore a hole into the space station Mir and sent it hurtling through space. As NASA astronaut Michael Foale tells Plus, the fate of Mir and its crew hinged on a classical set of equations. In last issue's Graphical methods I Phil Wilson used maths to predict the outcome of a cold war in slug world. In this self-contained article he looks at slug world after the disaster: with only a few survivors and all infra-structure destroyed, which species will take root and how will they develop? Graphs can tell it all. Two designers tell us how they took the long way round to design, and how the maths and science they took in on the way helps them with their work today. A proof with a hole 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. How to keep warm and safe