Building the Modernity: New Data and Approaches on the Introduction of Calculus in Spain (1717-1787)

Abstract

This paper studies the introduction of calculus in Spain, as paradigm of the modernity of mathematics in the Enlightenment, in its institutional environment —especially its teaching. This process is analyzed in terms of number of students, available manuscripts, and printed works. This cross-sectional analysis of calculus in Spain uses known data and provides new documentary evidence, which enable to close the educational issue of calculus in the Engineering Academy, reconsider it in Jesuit colleges, and substantiate new conclusions on the role of military men, Jesuits, and civilians in this process. This analysis has been extended until 1787 in order to include both the first widely circulated text in Spanish that extensively included calculus (Elements of Mathematics by Bails) as well as the documentary evidence of resistance to the teaching of calculus among military engineers.