Todd Timmons’s latest book, Mathematics in Nineteenth-Century America, examines the knowledge, strength, and progress of early American practitioners of mathematics, largely through the lens of their writings in generalized scientific journals and their other publications. His book highlights the period from 1800 to 1834, although reaching back to 1771, for the analysis of the mathematics contained in the Transactions of the American Philosophical Society, the Memoirs of the American Academy of Arts and Sciences, and the American Journal of Science and the Arts. The book includes a delightful section about the short-lived specialized mathematical publications of the period, such as the Mathematical Correspondent.
The book is not a history of mathematical ideas as much as a history of the process, often the struggle, of forming a community of experts in mathematics in a new country. This is a thoroughly appropriate approach, since mathematics in the new United States consisted largely of arithmetic, algebra, and geometry, with a few practitioners of Newtonian fluxions. The contributors to American mathematical writing were not necessarily college professors or even college graduates, for that matter. Many of them, however, were an integral part of the new American patriotism following the War of 1812 that included a trend toward American intellectuals not being satisfied with being “scientific doormats to Europe.”
Timmons gives a few well-selected examples to illustrate the elementary level of American mathematics. One that caught my eye was an article by A.D Wheeler, “An Easy Solution to a Diophantine Problem,” in the American Journal of Science and Arts, that laid out a process for finding Pythagorean triples using the fact that \( (x+x+2)^2 + (x^2+2x)^2 = (x^2+2x+2)^2\). I regret that the book contained only a few such examples of the actual mathematics appearing in the articles. In any case, Timmons inspires the reader (me in this case) to want to learn more by reading the original publications, many of which are freely available on the internet or through JSTOR. For example, Wheeler’s article can be found at An Easy Solution to a Diophantine Problem, in a volume also containing an article entitled “Halos,” and another entitled “Chemical Examination of the Bark of a White Birch.”
One of the book’s themes is a new country’s need for science to be useful. Mathematics was seen as the proverbial “handmaiden to science” in that it helped with practical topics such as navigation and surveying — both useful to the new United States. A well-established society, like Britain and France, had the time and resources to devote to poetry, literature, history and pure mathematics. With a “first things first” approach, the United States needed to focus on practical needs before cultural enrichment.
Another theme is the transition from a British synthetic approach to mathematics to the “new-fangled” French analytic approach. Essentially, the British approach started with definitions and developed a theory. The French approached mathematics starting with interesting examples and then finding explanations. Timmons highlights the key annotated translation of Laplace’s Mécanique Céleste by Nathaniel Bowditch and translations of works by Lacroix, Legendre, and Euler by John Farrar. Timmons devotes an entire chapter to Nathaniel Bowditch. Indeed, the book is subtitled The Bowditch Generation. Appendix D contains the list of Farrar’s translations that formed his mathematics curriculum.
An accessible and enjoyable read, Mathematics in Nineteenth-Century America will appeal to a general audience interested in the history of mathematics and/or science in the United States.
Diann Porter is a member of the Mathematics Faculty at Pima Community College in Tucson, Arizona. Her own recent book William Fogg Osgood at Harvard, Agent of a Transformation of Mathematics in the United States was also published by Docent Press.