A collection of essays from "The Evolution of..." column appearing in the American Mathematical Monthly.

When the techniques of mathematics are integrated with its historical, philosophical, and critical aspects, mathematics becomes more meaningful to mathematicians and mathematical amateurs alike. In this book, its many authors provide such integration by presenting informed accounts of the mathematical ideas and issues of the past 300 years, with emphasis on developments since 1800.

The book deals with ideas that are 'classical,' that is, of established weight and importance, with special attention paid to those that overlap different domains of mathematics or disciplines such as physics and philosophy. The articles cover a large number of topics in analysis, algebra, geometry, probability, and logic, and are grouped by subject matter.

Mathematical Evolutions makes use of the history of mathematics from the perspective of the mathematician rather than the historian. The approach is genetic: from a problem to its solution. It explores mathematical ideas, their uses, and their historical evolution.

The book is lively and readable and of very high mathematical quality. Its contributors include some of the finest mathematicians of the 20th Century such as Atiyah, Doob, Luzin, Magnus, Tits, and H. Weyl. The book will appeal to a broad audience, from students to professional mathematicians.