The Geometers of God: Mathematics and Reaction in the Kingdom of Naples

The controversy about whether analytic or synthetic methods should be employed to solve geometrical problems was particularly lively in Naples during the first half of the nineteenth century. I investigate the origin of this controversy, arguing that, far from being based on a mere technical divergence, it was deeply rooted in the cultural and social milieu of the protagonists. I also show that the Neapolitan debate cannot be reduced to an opposition between "traditional" and "modern" mathematicians. The establishment and institutionalization of the "ancient" synthetic school was in fact accomplished in response to recent developments in mathematics, by practitioners who were themselves competent in the algebraic method. The proposed interpretation of the controversy links choices about problem-solving methods to more general orientations regarding the cultural and social changes that shattered the kingdom in the age of the French Revolution.