Greeted with terrific reviews, the first edition of this book proved to be widely popular as both a teaching aid and an entertaining introduction to modern mathematics. It succeeded in opening the door for general readers to the power and beauty of a field often thought of as remote and lifeless. In fact, more mathematical research is being done today than ever before, while the field is evolving with unprecedented rapidity and excitement. For this second edition, Ian Stewart has fully revised the text to incorporate recent developments. There are many new illustrations, and three new chapters, including one on Kepler's sphere-packing problem, which has recently been solved, 380 years after it was first articulated. In addition, the book surveys many other areas of current research in nontechnical terms, describing what the key problems are, where they come from, how they get solved, and what can be done with the answers that are forthcoming. Readers will learn what mathematicians are like, and how their work has affected our society and history. Topics include such famous problems as Fermat's last theorem, the Riemann hypothesis, the Poincare conjecture, prime numbers, non-Euclidean geometry, the concept of infinity, probability, catastrophe theory, chaos, fractals, algorithms, and undecidable propositions. A final chapter discusses the relation between mathematics and its applications. Each topic is developed within a historical framework, and a number of recent breakthroughs are presented for the first time in a manner that general readers will find easy to understand. Ideal as supplementary reading in the classroom, The Problems of Mathematics will also be enjoyed by anyone interested in mathematics or who has sought to understand the fascinating work taking place in the field today.