This book is based on an in-depth conversation between Howard Burton and Ian Stewart, Emeritus Professor of Mathematics at the University of Warwick and bestselling science and science fiction writer. For Ian Stewart, mathematics is far more than dreary arithmetic, while mathematical thinking is one of the most important—and overlooked—aspects of contemporary society. This wide-ranging conversation explores what mathematics is and why it's worth doing, symmetry, networks and patterns, the relationship between logic and proof, the role of beauty in mathematical thinking, the future of mathematics, linking mathematical oscillations to animal gaits, how to deal with the peculiarities of the mathematical community, and much more.This carefully-edited book includes an introduction, Counting Sheep, and questions for discussion at the end of each chapter:I. Fear and Loathing - Mathematics and the wider worldII. Doing Mathematics - An insider’s viewIII. Teaching Mathematics - How to get unstuck and other valuable lessonsIV. Mathematics and Gender - Portuguese mysteriesV. Mathematics Everywhere - And widely underappreciatedAbout Ideas Roadshow Conversations:This book is part of a series of 100 Ideas Roadshow Conversations. Presented in an accessible, conversational format, Ideas Roadshow books not only explore frontline academic research featuring world-leading researchers but also reveal the inspirations and personal journeys behind the research.