This PhD thesis, titled The Spread of Hindu-Arabic Numerals in the European Tradition of Practical Arithmetic, a Socio-Economic Perspective (13th–16th centuries) lies at the intersection of economic history and the social history of mathematics. The main argument of my PhD is that studying the adoption of Hindu-Arabic numerals among European practitioners allows to reconstruct a long-run history of transmission of useful knowledge from the Arabic world to the origins of the so-called European ‘little divergence’. During the commercial revolution of the 13th century, Italian international merchant-bankers started to adopt Arabic mathematics in their business practices. Thanks to the use of figures and fractions, Arabic mathematics allowed to handle rational numbers with an efficiency that could not be matched by the previous Roman system. The fundamental financial instrument of the period – the bill of exchange – could not have been developed in the absence of Hindu-Arabic numerals, as it was based on a proportion between fractions. The thesis provides a multi-layered analysis of the reasons that led Italian merchants to adopt such mathematics and reconstructs their spread among European merchants. To reconstruct such spread, I focus on the main sources used to teach Arabic mathematics to prospective merchants: practical arithmetic manuals. I have reconstructed the European tradition of practical arithmetic collecting detailed information on over 1280 practical arithmetic manuals written throughout western Europe from the 13th to the 16th century. This catalogue, which is based both on secondary sources and on extensive archival research, substantially expands previously available evidence. Combining qualitative, quantitative and spatial (GIS) analysis, I show that Hindu-Arabic numerals slowly spread from Italy to the rest of the European continent, reaching a widespread diffusion only at the end of the 16th century. I complement the evidence offered by practical arithmetic manuals with an analysis of business documents (both public and private accounts) and of a variety of further sources.
The spread of practical arithmetic manuals – which correlated with the diffusion of key financial and organisational innovations – followed a south-to-north pattern based not on the hubs of international trade, as most economic history literature would suggest, but on inland networks. England and the Low Countries – the main centres of the ‘little divergence’ – stand out as the latecomers in this innovations cycle. This suggests that a continuous transmission of useful knowledge played a role during the shift of the core of European trade from the Mediterranean to the Atlantic.