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Mathematical thought from ancient to modern times. In 3 volumes. Paperback edition. (English) Zbl 0864.01001
New York, NY: Oxford University Press. xv, 1211 p. with appendix (1990).
Morris Kline’s monumental work on the history of mathematics was first published in 1972 (see Zbl 0277.01001), in one volume with more than 1200 pages. This book is now available in a new three-volume paperback edition. Volume 1 starts with the origins of mathematics in Mesopotamia and Egypt. It contains chapters on Greek and Alexandrian mathematics, Hindu and Arabic contributions, Renaissance mathematics, arithmetic and algebra in the sixteenth and seventeenth centuries and ends with the work of Newton, Leibniz and others on the creation of calculus. Volume 2 focuses on calculus and the theory of differential equations in the eighteenth and nineteenth centuries, functions of a complex variable, Galois theory, determinants, matrices and vectors. Volume 3 treats the theory of numbers and geometry in the nineteenth century, abstract algebra, topology and analysis in the twentieth century and ends with a chapter on the foundations of mathematics. The aim of the book is to present the central ideas with particular emphasis on those currents of activity that have been influential in promoting subsequent mathematical activity. Kline describes the motivations for the various creations and shows how the character of mathematics has changed over the centuries. Each chapter is provided with its own bibliography guiding the reader to special subjects and original sources. It is interesting that half of the matter is devoted to mathematics in the nineteenth and twentieth century. The author presents his material with many mathematical formulas rather than verbal exposition and the real understanding of these topics need a mathematical well trained reader. We recommend these highly readable volumes to all interested in the history of mathematics.

01A05 General histories, source books
01-02 Research exposition (monographs, survey articles) pertaining to history and biography
01-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to history and biography