EULER THE MASTER OF US ALL

Euler: The Master of Us All by William Dunham

Without question, Leonhard Euler (1707-1783) ranks among history's greatest mathematicians. Over six decades of unmatched productivity, and despite a visual impairment that grew ever worse, charted the course of mathematics throughout the eighteenth century and beyond. His reputation is captured in Laplace's famous admonition, "Read Euler, read Euler. He is the master of us all." Written for the mathematically literate reader, this book provides a glimpse of Euler in action. Following an introductory biographical sketch are chapters describing his contributions to eight different topics-number theory, logarithms, infinite series, analytic number theory, complex variables, algebra, geometry, and combinatorics. Each chapter begins with a prologue to establish the historical context and then proceeds to a detailed consideration of one or more Eulerian theorems on the subject at hand. Each chapter concludes with an epilogue surveying subsequent developments or addressing related questions that remain unanswered to this day. At the end of the book is a brief outline of Euler's collected works, the monumental Opera Omnia, whose publication has consumed virtually all of the twentieth century. In all, the book contains three dozen proofs from this remarkable individual. Yet this is merely the tip of the scholarly iceberg, for Euler produced over 30,000 pages of pure and applied mathematics during his lifetime. Euler: The Master of Us All samples the work of a mathematician whose influence, industry, and ingenuity are of the very highest order.