pIt is increasingly clear that the emshapes of realityem - whether of the natural world, or of the built environment - are in some profound sense emmathematicalem. Therefore it would benefit students and educated adults to understand what makes mathematics itself 'tick', and to appreciate why its shapes, patterns and formulae provide us with precisely the language we need to make sense of the world around us. The second part of this challenge may require some specialist experience, but the authors of this book concentrate on the first part, and explore the extent to which elementary mathematics allows us all to understand something of the nature of mathematics emfrom the insideme.ppemThe Essence of Mathematicsem consists of a sequence of 270 problems - with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, she should want to understand something of mathematics embeyond the classroomem, and be willing to engage with