Republic of Numbers: Unexpected Stories of Mathematical Americans Through History

David Roberts writes with commitment and insight about the lives of mathematicians as lived on the outside of the ivy wall. In an earlier book, American Mathematicians as Educators, 1893-1923: Historical Roots of the “Math Wars”, Roberts analyzed in depth and detail the three-way scrum of academic mathematicians, high school teachers of mathematics, and mathematical practitioners over the contours and contents of the American mathematics curriculum. In Math Wars we met familiar mathematicians — Simon Newcomb, E.H.Moore, Felix Klein, and Florian Cajori to name just a few — but in a unique mathematical context: the contentious writing, editing, and debating of the 1923 Report of the National Committee on Mathematical Requirements. The centerpiece of the book is the report, and Roberts uses it to elucidate the wide-ranging views of our colleagues on mathematics in the large.

Roberts’ latest book, Republic of Numbers: Unexpected Stories of Mathematical Americans through History, is less satisfactory, at least as a contribution to the history of mathematics. The centerpiece of this book is social justice and injustice as lived and witnessed by twenty-three individuals (see the table of contents) who, to one degree or another, in the author’s words, “interacted with mathematics.” The weakness of Republic of Numbers is structural, not literary. Unlike Math Wars, the connection between mathematics and the theme of the book is too often tenuous.

Republic of Numbers is divided into twenty chapters, each one cast as a cameo of social justice issues as experienced by one or two of the twenty-three individuals. We get a sketch of each individual’s youth and education and a description of the arc of their career. When the connection of an individual to mathematics is strong, as with J. Willard Gibbs, John Nash, and E. H. Moore, for example, the social justice connection is strained. When the social justice story is strong as, with Abraham Lincoln and Catherine Beecher, the connection to mathematics adds little to their stories.

Yes, Lincoln kept a cyphering book just like millions of other students of his time and age. And he doubtless used mathematics in surveying. However, solving \(3/17 = 48/x\) hardly makes him an American mathematician. The Lincoln chapter serves as the launching pad for commentary on slavery and white settlers that ranges far afield in both time and space from Lincoln.

The section on Catherine Beecher is another case in point. Roberts uses Beecher’s undistinguished arithmetic as the beginning of an extended discussion of racism and religious conservatism in Cincinnati, the abolitionist views of Beecher’s father and sister, and the appeal of the McGuffey readers to “white Protestant America.” It is hard to categorize these excursions as unexpected stories of mathematical Americans.

Republic of Numbers is nominally about twenty-three Americans, thinking about and doing mathematics. This is a refreshing departure from Big Name historical narratives, and Roberts is to be congratulated for reminding us that the history of mathematics includes those who teach and practice useful mathematics as well as those who create abstract mathematics. Sadly, however, the uneven balance of mathematics and call-out commentary throughout the book attenuates the inspirational and historical value of their stories.

Scott Guthery is the founder and editor of Docent Press and co-founder of Life-Notes.