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Benjamin Franklin's Numbers: An Unsung Mathematical Odyssey

Eugene Boman, reviewer

Benjamin Franklin’s Numbers: An Unsung Mathematical Odyssey, by Paul C. Pasles, 2008, x + 254, hardcover, pp., $26.95, ISBN-10 0-691-12956-8, ISBN-13 978-0-691-12956-3, Princeton University Press, 41 William St., Princeton, New Jersey, 08540,

I thoroughly enjoyed reading this book. It is written in a pleasant, conversational style and the author’s enthusiasm for his subject is infectious. The text is richly embroidered with colorful details, both mathematical and historical.  

As one of our “Founding Fathers” Benjamin Franklin is very familiar to every schoolchild in the United States. Indeed, he is so iconic in the US that I have sometimes been taken aback to learn that my non-American friends know only his name, often for the myriad institutions named after him or simply because his picture appears on the $100 bill. Equally surprising is that many Americans, while familiar with his role in our Revolution, are completely unaware that during the American colonial period Franklin was internationally known as a scientist and was a recognized experimenter with electricity.

Early on in the first chapter the author states that “The editors of The Papers of Benjamin Franklin observe that Franklin” was not a mathematician.  Nevertheless, he did spend a great deal of his time doing what we would now call recreational mathematics. Specifically, early in his life he came across the “Luo Shu” magic square which figures prominently in the mythology and culture of ancient China. This is a 3 by 3 grid in which each of the integers from one to nine is placed in such a way that the sum of the numbers in each row, column and diagonal is the same. Restless genius that he was, Franklin immediately set about creating larger and more complex “magical” shapes. The creation of magic squares of varying levels of complexity constitutes the bulk of Franklin’s mathematical recreations; this is the primary topic of the book. However it should not be supposed that Franklin contented himself with mundane patterns. The most complex of his “magical” shapes (including his “magical circle”) are truly breath-taking.

The target audience of the book is clearly the mathematically knowledgeable layman.  However, there is much here that would interest, a mathematician as well. The arithmetical properties of Franklin’s more complex creations are quite delightful and there are numerous problems of varying levels of difficulty, both solved and unsolved, scattered throughout the text. I was sufficiently intrigued by some of them that I arrived late for my calculus class once or twice while solving them.

I recommend this book as good summer reading. In a history of mathematics course it could provide the starting point for a student paper on recreational mathematics or mathematics in the United States.

Eugene Boman, Associate Professor of Mathematics, The Pennsylvania State University, Middletown, PA

See also the MAA Review by Darren Glass.

Eugene Boman, reviewer, "Benjamin Franklin's Numbers: An Unsung Mathematical Odyssey," Convergence (April 2008)