Mathematics is a gentleman's art: Analysis and synthesis in American college geometry teaching, 1790-1840
The story of geometry education in the American college has been subject to neglect, with most historians assuming that all available information was published in secondary sources around the turn of the twentieth century. However, recent trends in the history of science include the revelation of the development of the scientific community before the Civil War and an interest in the study of textbooks. Additionally, the literature lacks attempts to place geometry education and mathematics professors within the scientific community. There are also no modern biographies of the three principal actors, Jeremiah Day, John Farrar, and Charles Davies. Finally, mathematicians in the early nineteenth century often framed their discussions according to various understandings of two key terms, "analysis" and "synthesis.";This study, therefore, seeks to address these gaps. Day, Farrar, and Davies were the first three American authors to write series of mathematical textbooks, and their volumes on geometry were the most popular in nineteenth-century American colleges. As these facts are explored, the existence of a significant community of mathematics professors is demonstrated. These professors made incremental adjustments to the traditional liberal arts curriculum while carrying out "normal science" and publicizing European mathematics in colleges which were themselves friendly to Mathematics; Day, Farrar, and Davies weighed British and French influences, had much in common with their contemporaries in Scotland, and formed an essential step between elite colonial amateur mathematicians and university research Mathematics;;The dissertation is presented in six chapters. The first reviews the literature on the history of American mathematics and science between 1790 and 1840. This chapter also establishes French mathematics and the history of analysis and synthesis as "givens" in the background of the story of American college geometry education. The second chapter evaluates the Scottish experience with geometry textbooks, paying special attention to the manifestation of analysis and synthesis as mathematical styles, method of proof, and educational techniques in John Playfair's Elements of Geometry. Then, the third, fourth, and fifth chapters lay out the biographies and careers of Day, Farrar, and Davies, and these chapters discuss the professors' geometry textbooks with respect to analysis and synthesis. Finally, the conclusion ties together the themes raised above and outlines the history of American geometry education after 1840.