The first third of the nineteenth century was the formative period for American mathematics: Nathaniel Bowditch emerged as a leader with an international reputation; American scientific journals began publishing mathematical papers; and American mathematicians began to turn away from the British-dominated mathematical philosophy of their past and to turn towards the modern mathematical approach as represented by the French textbook authors. Each of these factors contributed to a work-in-progress as American mathematicians struggled to build a foundation upon which a research community would form. This book traces the development of that that foundation.