The Nature and Growth of Modern Mathematics

by Edna E. Kramer

Now available in a one-volume paperback, this book traces the development of the most important mathematical concepts, giving special attention to the lives and thoughts of such mathematical innovators as Pythagoras, Newton, Poincare, and Godel. Beginning with a Sumerian short story--ultimately linked to modern digital computers--the author clearly introduces concepts of binary operations; point-set topology; the nature of post-relativity geometries; optimization and decision processes; ergodic theorems; epsilon-delta arithmetization; integral equations; the beautiful "ideals" of Dedekind and Emmy Noether; and the importance of "purifying" mathematics. Organizing her material in a conceptual rather than a chronological manner, she integrates the traditional with the modern, enlivening her discussions with historical and biographical detail.

Genres: Mathematics, Science, Nonfiction, History

784 pages, Hardcover

First published January 1, 1981

Reviews

[Liquidlasagna · Rating 5 out of 5]

The leading books on the history of mathematics are:
Bell 1945 - D
Coolidge 1949 - D
Smith 1958 - C star
Boyer 1968 - A star
Kramer 1970 - B star ***
Kline 1971 - A star
Kline 1972 - A star
Morgan 1972 - D
Dedron 1973 - D
Cajori 1974 - B star
Dieudonne 1978 - D
Cajori 1980 - C star
Eves 1980 - D
Eves 1981 - D
Temple 1981 - D
Struik 1987 - A star
Fauvel 1987 - A star
Phillips 1987 - D
Stillwell 1989 - C star
Hollingdale 1989 - D
Rowe 1989 - D
Eves 1990 - A star
Burton 1991 - C star
Grattan-Guinness 1994 - D
Cooke 1997 - D
Katz 1998 - D

[the A to D scale merely reflects the importance of the work, nothing to do with how good it is]


Hawthorn Press 1970 hardcover
Princeton 1982 paperback
758 pages

[Nader · Rating 5 out of 5]

This book is full of great context, but the one I return to often is the story of Évariste Galois who died in a duel at age 20, attempting to avenge a woman's honor, and spent the entire night before furiously scribbling in his notebook, "I do not have enough time!" adorning the margins. Those scribbles, not comprehendible til decades later, became the cornerstone of abstract algebra.

[Kevin · Rating 4 out of 5]

A good overview of the history of math. It balances technical details about the math, written explanations of things too complicated to adequately show and mini biographies of prominent mathematicians throughout history.