A History of Mathematics in the United States and Canada: Volume 1: 1492-1900

It might come as a mild shock to a university student of differential equations if the full professor in the front of the room wasn’t a mathematician. It might also come as a bit of a shock to the professor. But so it has often been in the history of mathematics. If the professor taught advanced topics, authored a book, say, on the history of mathematics and perhaps contributed an article or two to the American Mathematical Monthly, but had not yet made an original contribution to an A journal, she would merely be a mathematical practitioner or worse from point of view of many historians of mathematics.

David Zitarelli duly cites this definition of a mathematician in A History of Mathematics in the United States and Canada. Volume 1: 1492–1900, but — to his credit and to our good fortune — he is, shall we say, relaxed in its application. The consequence is that we meet in Zitarelli’s history people with fascinating mathematical interests and enthusiasms who didn’t make the cut in previous histories of mathematics in the United States and Canada. Yes, there are potted histories of all the usual Big Names, but even these exhibit fresh, off-the-beaten-path research. Zitarelli’s own enthusiasm is for the mathematics community in the large and it is on full-color display in this history.

Inevitably, there will be individuals who one thinks should have been included in a work with the sweep of Zitarelli’s but weren’t; I might mention Oliver Evans, Charles Storrow, and Uriah Boyden. But what is truly gratifying is to come across individuals who you didn’t imagine would be included but are: John Parker, Jr., George Ticknor, Daniel Treadwell, and Daniel Coit Gilman, among others. Likewise, there will be topics that might one thinks might have been covered but weren’t; the mathematics curriculum in Boston high schools was more advanced in the early nineteenth century than in the institutes of higher learning across the Charles, for example.

But such quibbling misses the message of Zitarelli’s book: the mathematics community is broad and deep. Mentoring a high school mathematics club or computing a mathematical table or tuning equations in space probe software are just as much a part of the history of mathematics as contributing theorems to the tens of thousands published every year. Many times while reading book I wished I could have asked him if I’m right.

The development is in three parts, linear in time, and organized primarily though not exclusively around institutions of higher learning. The three parts are Colonial Era and Period of Confederation, 1492–1800 (85 pages), The New Republic, 1800–1876 (120 pages), and Research Community, 1876–1900 (200 pages). Zitarelli ends his Preface by writing “…the higher the level of attainment in mathematics, the more the reader will understand the development” but in fact there is very little mathematics in the book. What little is there is elementary and wouldn’t inhibit any understanding by the general reader of science.

The hundreds (yes, hundreds) of biographical sketches of mathematicians that are the bedrock of the book are cleverly and usefully organized into topics within each chapter. Each topic is not simply an arbitrary grouping but is a shared context within which the constituent individuals worked, learned, and interacted. Thus, in addition to educational institution topics, we have the Sylvester School, the Klein Klub, the American Philosophical Society, The Mathematical Correspondence, Chicago Congress, etc.

The sketches themselves vary widely in length. Some are only a paragraph and some may span a page or two but never more. All of them sparkle with Zitarelli’s diligent, dogged research. Not infrequently does the reader wonder to himself “How in the world did he find that out?”. And while Zitarelli for the most part sticks to the professional facets of his mathematicians he is not completely immune to the siren call of a good side story.

The sketches are augmented with additional gloss in thirty-three backgrounders currently residing on Zitarelli’s website (they are also linked to at the “additional materials” page on the AMS Bookstore website). There is, as you might expect, a much more eminently readable history of mathematics on Zitarelli’s website, including the backgrounders for Volumes II and III of the title under review for those who like to peek ahead.

The MAA classifies Zitarelli’s history as a textbook. While it has been many years since I stood in front of a calculus class, I think it would be a difficult primary text for a history of mathematics course. First, as noted above, one doesn’t get any sense of the mathematics; the book is about the people. Second, either one would have to cover everyone or figure out some way of corralling a teachable subset; to the credit of the book, that would be a difficult task. I would classify the work much more as a sourcebook. One could open the text to any random page and start a productive line of original research in the history of mathematics.

The literature of the history of mathematics is impoverished because of the caste system that academic historians of mathematics insist on laying over the field. The unfortunate consequence of this ultimately subjective classification is that all we end up reading about is the Brahmans … again and again and again. In his Preface Zitarelli writes: “…it is my fervent hope to make household names out of leading figures like Benjamin Peirce, E. H. Moore, Oswald Veblen, George Birkhoff, R.L. Moore, and Marston Morse, but also Caleb Cheeshahteamuch, Isaac Greenwood, Mary Winston, Anna Pell Wheeler, Li-fu Chiang, Elwood Cox, and William Claytor.” Zitaralli’s hope has been fulfilled at least in my house and I eagerly look forward to meeting more of his mathematical friends in Volume II.

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