The formative years of the American Mathematical Society coincided with a time of remarkable development in mathematics. During this period, the Bulletin of the American Mathematical Society and its predecessor, ""The Bulletin of the New York Mathematical Society"", served as a primary vehicle for reporting mathematics to American mathematicians. As a result, some of the most important and fundamental work of early twentieth-century mathematics found its way into the Bulletin.Milestone articles include Hilbert's problems presented at the 1900 Paris International Congress of Mathematicians (ICM), Poincare's 1904 lecture on the future of mathematical physics (with commentary suggesting that he was tantalizingly close to capturing the notion of relativity), and Klein's Erlangen program; all of these articles received added publicity when the first English translation was published in the Bulletin. This book reproduces these and other well-written articles from the early Bulletin, offering readers the best way to experience a slice of that time.Other articles in the book include, in particular, a report to American mathematicians about what happened at that important 1900 ICM meeting and three articles from the scientific portion of the 1904 centennial celebration of the Louisiana Purchase: Darboux describing the development of geometry, Pierpont focusing on nineteenth-century mathematics, and Poincare emphasizing the significance of mathematical physics. Accompanying the transition from the nineteenth to twentieth century was that new important thing called 'mathematical rigor'. Included is an article by Klein reflecting the beliefs of the time with his promotion of rigor. These are just some of the many topics characterizing the early days of the developing American mathematical community. The book offers a captivating review of mathematics through the early years of the Bulletin.