Number Words and Number Symbols. A Cultural History of Numbers: By Karl Menninger. (Translated by Paul Broneer from the revised German edition.) Cambridge, Mass.: The M.I.T. Press, 1969. 480 pp.

Karl Menninger (1898-1963) was a German mathematician who established a unique reputation in German-speaking countries as a scholarly popularizer of mathematics and the history of mathematics. The English translation1 of his works is winning him a growing reputation in this country.

Number Words and Number Symbols is his crowning achievement. It is a masterpiece and the translation by Broneer is superb. The book is unreservedly recommended to the psychoanalyst with more than a casual interest in linguistics, philology, mathematics, or cultural anthropology. Menninger traces the origins and developments of number sequence and number language, and written numerals and computation. He ranges widely and incisively, historically and geographically, crossing interdisciplinary boundaries effortlessly. His writing is a model of painstaking scholarship, presented in a most engaging style without a trace of pedantry.

Optimal use is made of almost three hundred illustrations aligned with or placed within the text. The format for integrating illustrations and text is excellent. Lucid comparative tables also enhance the factual and theoretical presentations.

It is impossible to select a brief example from the riches in this