The word geometry makes one think of circles, triangles, protractors and Pythagoras. By the middle of the 20th Century it all looked dead, as the excitement in maths had moved to computers and chaos theory. But one man - Donald Coxeter - kept the torch burning, showing how geometry is at the core of all mathematics, and indeed governs our life from architecture to car design, from animated films to food molecules. He showed the importance of geometry for data mining - now the most innovative area of computer research - and showed not only how beautiful the mathematics of shape is, but also how vitally important.