Practical Mathematics in Early Modern Europe

During the early modern period, the mathematical sciences dramatically upgraded its status. It went from having a secondary role and ancillary status in the mid 16th century, up to be considered the most powerful tool of scientific research by the turn of the 18th century. As recognized by a large historiography, these transformations cannot be accounted for in terms of internal developments. It is necessary to look outside universities and scholarly mathematics, taking into account the broader social context, in particular the role of social practices of arithmetic, geometry and metrology. These provided essential impulses that help explain the momentous conceptual and methodological transformations mathematics went through in early modern Europe. Our hypothesis, based on several case studies, is that a general mathematization of civil life took place. Elementary arithmetic and geometry became ubiquitous for merchants, gaugers, architects, instrument-makers and engineers, with growing impact on education practices and far-reaching epistemological consequences. To track this evolution, one can study the material culture of practical mathematics, i.e. objects closely linked to what people socially do, both in the higher court culture and in the artisan’s workshops. New literary forms developed, such as practitioners commonplace books, booklets and other forms of modern teaching material, printed metrological tables and comptes faits to make mathematics readily usable. We hope to show that these widespread practices, backed by social and political authority, help explain the success of mathematical values (of precision, “application” of mathematics, computation and forecasting) and of new mathematical concepts (most notably “arithmetical” ratios and proportionality), as well as the changing status of early modern mathematical sciences.