to 1940." — Booklist.In this time-honored study, one of the twentieth century's foremost scholars and interpreters of the history and meaning of mathematics masterfully outlines the development of leading ideas and clearly explains the mathematics involved in each.Author E. T. Bell first examines the evolution of mathematical ideas in the ancient civilizations of Egypt and Babylonia; later developments in India, Arabia, and Spain; and other achievements worldwide through the sixteenth century. He then traces the beginnings of modern mathematics in the seventeenth century and the emergence of the importance of extensions of number, mathematical structure, the generalization of arithmetic, and structural analysis. Compelling accounts of major breakthroughs in the 19th and 20th centuries follow, emphasizing rational arithmetic after Fermat, contributions from geometry, and topics as diverse as generalized variables, abstractions, differential equations, invariance, uncertainties, and probabilities.

    From this it follows not only that they remain on the fringes, but in addition they entertain strange ideas about the concept of the infinite, which they must try to use. Although analysis does not require an exhaustive knowledge of algebra, even of all the algebraic technique so far discovered, still there are topics whose con- sideration prepares a student for a deeper understanding. However, in the ordinary treatise on the elements of algebra, these topics are either completely omitted or are treated carelessly. For this reason, I am cer- tain that the material I have gathered in this book is quite sufficient to remedy that defect. I have striven to develop more adequately and clearly than is the usual case those things which are absolutely required for analysis. More- over, I have also unraveled quite a few knotty problems so that the reader gradually and almost imperceptibly becomes acquainted with the idea of the infinite. There are also many questions which are answered in this work by means of ordinary algebra, although they are usually discussed with the aid of analysis. In this way the interrelationship between the two methods becomes clear.