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A Calculating People: The Spreading of Numeracy in Early America

Patricia Cohen
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The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Scott Guthery
, on

In A Calculating People: The Spread of Numeracy in Early America Patricia Cline Cohen takes note of an up-tick in the appearance of counts in American publication and discourse during the first quarter of the nineteenth century and sets out to discover why this might be. Her conclusion is the following:

“What changed by the early nineteenth century was that numeracy had become common because of arithmetic education and the spread of market economy.

Cohen marshals wide-ranging, careful research into the literature of the day to bolster this conclusion. Her analysis of the role of tabulations in the debate over smallpox inoculation in Boston and results of the 1840 census are particularly probative.

A limitation of the study, however, is that for Cohen numeracy is counting. Full stop. Setting out with this definition denies her the opportunity to consider antebellum use of numerical values in general, let alone the use of mathematics in general. It is true that Warren Colburn’s Intellectual Arithmetic, upon the Inductive Method of Instruction sold over three and one-half million copies and made mathematical medicine go down more easily. And yes, American markets expanded rapidly east and west after the war of 1812 and everybody reached for sharper pencils. But were these cultural winds alone strong enough to cause a shift from a qualitative to a quantitative way of doing things?

What we don’t find in A Calculating People is any mention of other forces that may have also contributed to the up-tick that Cohen considers. The construction of massive water-powered mills, the surveying of new territories, the manufacture of steam engines, and the emergence of the insurance industry are all examples of endeavors demanding mathematical skills well beyond those needed in dealing with counts. These are endeavors that might have contributed to a growing trust in numbers.

A Calculating People is a joy to read. Cohen’s research shines a light into rich primary sources that are underexplored in the history of American mathematics canon. It is unquestionable that a maturing understanding of the utility of quantification would be reflected in a broader use of tabulation. But I think that the growth of numeracy that Cohen documents so well was more of an effect than a cause of the broader integration of mathematics into the young nation’s daily life.

Scott Guthery is the author of Practical Purposes: Readers in Experimental Philosophy at the Boston Athenaeum (1827–1850), in which he uses the book borrowing registers of the Athenaeum to characterize the scientific and technical reading preferences of Boston’s antebellum mathematical practitioners. His previous book, A Motif of Mathematics, explored the history and application of the mediant and the Farey sequence. Guthery received a PhD in probability and statistics from Michigan State University and worked for Bell Laboratories, Schlumberger, and Microsoft before co-founding two of his own companies. He can be reached by e-mail at

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