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Take a Number: Mathematics for the Two Billion

Lillian R. Lieber
Dover Publications
Publication Date: 
Number of Pages: 
[Reviewed by
Amy Ackerberg-Hastings
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Between 1931 and 1963, Lillian Rosanoff Lieber (1886–1986) wrote at least a dozen books popularizing various aspects of mathematics. (She was fond of updating and enlarging her books, making it sometimes difficult to ascertain which publications were truly distinct, so counts readers find online may vary.) At least four have been republished since 2007; Fernando Q. Gouvêa reviewed The Education of T. C. Mits and Infinity. David L. Roberts has been looking at The Education of T. C. Mits as part of a wave of popularizations around 1940.

Lieber’s 1914 PhD from Clark University was in chemistry, earned under her brother, Martin André Rosanoff, but she was at Clark during the mathematics department’s period as a leader in American graduate education, with her years of study overlapping with those of Solomon Lefschetz. Indeed, Lieber and Rosanoff apparently both had an aptitude for mathematics — besides conducting research in chemistry, Rosanoff later lectured on “A Practical Simplification of the Method of Least Squares” and wrote Select Topics of Plane Analytic Geometry for Scientific and Technical Workers (Long Island University Press, 1944), while Lieber worked in mathematics education for most of her career.

She was employed briefly as head of the Wells College physics department (1917–1918) before moving to the relatively-new Connecticut College for Women (1918–1920). She then disappears from the written record for a decade. Meanwhile, Hugh Gray Lieber (1896–1961) earned an MA from Columbia University in 1923, married Lillian in 1926, and joined the mathematics department of the two-year-old Long Island University in Brooklyn in 1928, becoming chair in 1931.

That same year, Lillian began to write books in her characteristic style of short lines of prose with liberal use of all caps, beginning with Non-Euclidean Geometry. Hugh supplied the illustrations (he later became Professor of Art at LIU). Lillian joined the mathematics faculty in 1934 and became the chair in 1945, when Hugh moved into the chair of the fine arts department. He retired in 1953; she in 1954. Lillian apparently founded a “Galois Institute of Mathematics and Art” around 1934 and edited several volumes of Galois lectures, including Rosanoff’s on least squares, several talks by Alonzo Church, and “Lattice Theory” by Garrett Birkhoff. Birkhoff later helped arrange Lillian’s donation of Hugh’s portfolio to Harvard University. Robert Jantzen and Joseph Alper have gathered some additional information on the Liebers.

The book under review, with its subtitle referring to the then-current global population, first appeared in 1946, one year into L. Lieber’s role as mathematics chair and roughly in the middle of her publication career. It may be the most elementary and least philosophical of her books, as its twenty chapters walk readers through the rules and operations of arithmetic, which are then employed in algebraic equations. She next included some geometrical properties and constructions before ending with a summary and eighteen pages of practice problems. (The answers are printed upside-down a few pages later.) Lieber promised to follow up on the potential for combining algebra with geometry by writing a book on graphs, which seems not to have appeared. Readers whose appetite was whetted for geometry in its own right could turn to Non-Euclidean Geometry for more information.

Readers will also find a relatively brief version of Lieber’s justification for studying mathematics, which is mainly that learning to use one’s brain helps one get along in the world, along with a plea for utilizing Science, Art, and Mathematics in combination to bring world peace. The content is probably most appropriate for adults who desire a refresher of secondary school math, as some descriptions — particularly of how to work out equations — struck me as unclear if one had not previously encountered the concept. Lieber’s charts are useful for showing how and why to set up expressions. The cartoons are likely too whimsical for 21st-century children to find entertaining, but the whole book should be fun for mathematicians who collect popular books. Take a Number also provides a snapshot of approaches to teaching before the emergence of New Math — Lieber is like a (pre-computers) auto mechanic opening the hood and showing how the different parts work.

Amy Ackerberg-Hastings is an independent scholar who researches the histories of American and Scottish mathematics education, among other things. The first popular mathematics book added to her own library was a gift from best friend Jean (Patterson) Davis when both were undergraduates: Ivars Peterson’s 1988 The Mathematical Tourist: Snapshots of Modern Mathematics.

The table of contents is not available.