Mathematics is widely accepted as the most "pure" of the sciences. Its origins, of course, have long been related to the needs of surveying, etc. in ancient Egypt and Babylonia; but from that time on, it has been assumed that mathematics has developed largely independantly from the "crass" world of everyday life. "Imaginary numbers" or "non-Euclidean geometries" would seem not likely to have developed when they actually did from any practical application. Astonishingly, however, Dr. Van Egmond has discovered the development of very esoteric mathematics out of a commercial tradition. His discovery has radically shaken our long held understanding of the history of mathematics and the nature of its growth. With this grant, Dr. Van Egmond will prepare an edition and study of the remarkable text which he discovered in 1983. The work which he will edit is a 14th century algebra text attributed to Dardi da Pisa. This work is the single most important text of Algebra written in Europe in the Middle Ages to be discovered to date. Not only does it provide the most comprehensive, advanced, and competent treatment of algebra produced by a European writer before the 16th century, it also contains the correct solution to equations of the third and fourth degrees. This anticipates by more than two centuries the published solution of the cubic and quartic equations which had hitherto been taken to mark the beginning of algebraic studies in Western Europe. The discovery of this work thus shatters the prevailing view that European algebraists were incompetent mathematicians constrained to copying the work of the Arabs and incapable of doing original work of their own, and forces significant revisions in our understanding of how mathematics developed in Europe before modern times. In his study of this work, Dr. Van Egmond will put it in the tradition in which it developed--not that of the academic in the new universities in Europe but that of commercial arithmetic written in the native Italian language. This non-university tradition has remained almost entirely unknown in the history of science. This project thus will not only help us to appreciate the work of one of the most able of medieval mathematicians, but will also shed light on a previously unknown tradition. The study further helps us to understand the nature of science and its growth. Commercial needs clearly drove this work, not the abstract work of the academics. In our quest to understand why science rose to its place of prominence in the West rather than other, previously more scientifically sophisticated civilizations of the East, the research of Dr. Van Egmond will surely play an important role.
