Naples' 1790s civil war was intensified by moral panic over Real Analysis (2023)
6 days ago
- #history-of-mathematics
- #revolutionary-Naples
- #political-imagination
- Massimo Mazzotti explores the entanglement of mathematics and politics through a forgotten episode in revolutionary Naples around 1800.
- The Neapolitan synthetic school resisted French 'very modern mathematics,' advocating for pure geometry over algebraic methods, seeing the latter as morally suspect and socially destabilizing.
- Nicola Fergola, leader of the synthetic school, promoted a new old mathematics, emphasizing self-restraint and rigor, framed as a return to order amidst political turbulence.
- Analytic mathematics, associated with French Jacobins, was seen as a universal problem-solving tool applicable to politics, aiming to transform society through rational administration.
- The synthetic school viewed analytic methods as blind and deceptive, arguing for the specificity and locality of mathematical methods, opposing the idea of a universal algorithmic approach.
- The conflict between synthetic and analytic mathematics reflected deeper debates about the nature of reason, with synthetics advocating for a reactionary, hierarchical order and analytics promoting revolutionary change.
- Augustin-Louis Cauchy's rigorization of analysis mirrored Fergola's quest for order, showing that foundational anxieties in mathematics were tied to broader political stabilization efforts post-French Revolution.
- The synthetic school's decline coincided with the normalization of analysis as a neutral administrative tool, aligning with the liberal constitutional order in Restoration-age Naples.
- Mazzotti argues that mathematical concepts and methods are not neutral but shape political imagination, defining what is logical and possible in social order and action.
- The essay highlights how modern mathematics, with its emphasis on rigor and purity, became part of the post-revolutionary political normalization, embodying a bounded, disciplined reason.