Inventing Tradition in 16th- and 17th-Century Mathematical Sciences: Abraham as Teacher of Arithmetic and Astronomy

Abstract

Submissions should be uploaded to http://tmin.edmgr.com or sent directly to David E. Rowe, e-mail: rowe@mathematik.uni-mainz.de I n the history of science, the period between the publication of Nicolaus Copernicus’s famous De revolutionibus orbium coelestium (1543) and Isaac Newton’s epoch-making Philosophiae naturalis principia mathematica (1687) is known as the Scientific Revolution. Indeed, this period was full of spectacular speculations and pragmatic inventions that accompanied stunning developments in the mathematical sciences ranging from the calculus and logarithms to telescopes and microscopes, air pumps and barometers, and the conception of an infinite universe. The mathematical sciences proper were conceived of as a field of knowledge comprised of two pure parts—arithmetic and geometry (scientiae mathematicae purae)—together with many mixed parts (scientiae mathematicae mixtae), which often had a clear practical bent, ranging from the traditional disciplines of astronomy and music to architecture, fortification, geography, hydrology, navigation, and so forth. Looking back, this period seems to reflect a sense of glamour, and it has sometimes been seen as a kind of Golden Age. However, as is so often the case, all that glitters is not gold, and the practitioners of the mathematical sciences were well aware of a variety of means for promoting their work. Indeed, this was an age when mathematicians constantly had to argue for the relevance of their work and research. Yet the context for such arguments during the Scientific Revolution was very different from what it is today. Bacon’s famous motto that ‘‘knowledge is power’’ may sound convincing to us, but in fact the London Royal Society had no means to finance scientific research. Nor was novelty alone the type of argument that was likely to persuade those royal patrons of the arts and sciences who were most likely to promote such work. Within this context, those who sought such support were likely to appeal to arguments that might exalt the reputation of a monarch and his court, where interest in the old was often at least as important as any new invention, however spectacular. Thus a typical strategy for those who sought to legitimize the mathematical sciences was to make use of references to the past, in particular classical antiquity. This type of argument, highlighting the long-accepted role of mathematics in the ancient world, was part of a process that can best be understood as the invention of traditions for the mathematical sciences. Had not Atlas been the first