Scientists do not operate in a vacuum. Even those most "pure" of scientists, mathematicians, who ostensibly need only pencil, pad, and eraser to carry our their research, have actually been found to need to communicate with each other about their research. These social networks of communication help to explain why certain questions or lines of research are "popular"--even in mathematics--while others are ignored. Sociologists along with historians and philosophers of science have long been interested in these so-called "invisible colleges." In the rise of modern science, we can turn to the correspondence of certain scientists who served as the conduit for these exchanges of views. The French priest, Pierre Mersenne, served in this role in the first half of the 17th century. The secretary of the Royal Society, Henry Oldenburg, played a similar role in the latter half of the century. As the scientific community grew and became more specialized, no one person could hold such a central role. For mathematics in the 18th century, Brook Taylor became for those interested in what was going on, the major conduit for the mathematical "invisible college." Known by students of the calculus as the inventor of the series that bears his name, Taylor played a crucial role in the development of mathematics in the early 18th century. By virtue of his participation in both the Newton-Leibniz calculus priority controversy and in the collaborative effort to extend, apply, and promote the new infinitesimal analysis, Taylor attracted illustrious friends and enemies in the European mathematical community. Dr. Feigenbaum, under this grant, is continuing to prepare an annotated edition of Taylor's collected correspondence, accompanied by an historical commentary. This edition should be of interest for several reasons. Taylor's letters shed light on the concerns and activities of British as well as Continental mathematicians, on their professional and personal connections, and on their forms of communication and collaboration. Moreover, they help to illuminate the Newton-Leibniz controversy by supplying us with details missing in the available accounts and by allowing us to view the dispute from the perspective of those who, if not centrally involved, were nevertheless deeply affected. They also dovetail with, and therefore nicely complement, the already existing editions of mathematical and scientific correspondence of the early 18th century. Ultimately, this study will contribute to our understanding of the nature and role of scientific communities and communications in the development of science. The project thus is of great importance for the history, philosophy and sociology of science.
