ESHS/HSS Annual Meeting

The Values of Numbers: The Roots of European Proto-symbolic Algebra in Late medieval Commercial Capitalism

• In Event: Rewriting the Histories of Algebra

English Abstract

Indo-Arabic numerals (0,1,2,3,4,5,6,7,8,9) first appeared in ancient India, spread west with the expansion of the Arabic world, and reached Latin Europe in the late Middle Ages. As discussed in standard studies on the origins of “modern” algebra in seventeenth-century Europe, the ten figures provided an essential visual and algorithmic tool for the emergence of the “algebraic mode of thought”. However, the “founding fathers” of this algebra drew from centuries of experimentation in mathematical techniques that began with the first adoption of Indo-Arabic numerals among late medieval practical mathematicians. To understand the emergence of this mathematics, hence, we need to explain the adoption of Indo-Arabic numerals among these actors, and appreciate that their adoption was far from obvious. The paper combines a global perspective with a micro-founded approach and weaves the history of science with economic and monetary history to argue that the origins of European proto-symbolic algebra were entwined with the new economic practices of the so-called “commercial revolution” of the thirteenth century. Delving into the economic structures of Italian city states (their units and measures and their monetary systems) and into the new economic practices of the time (accounting and financial), we will see how in late medieval Italy the adoption of the ten figures among practitioners became not only possible, but also necessary. As European proto-symbolic algebra emerged in the vernacular tradition of practical arithmetic, reconstructing this entanglement makes it possible to see “from below” how a new form of mathematics originated from a proto-capitalistic social transformation.

Author

• Raffaele Danna, Sant'Anna School of Advanced Studies