A forgotten episode of mathematical resistance reveals the rise of modern mathematics and its cornerstone, mathematical purity, as political phenomena.
 
The nineteenth century opened with a major shift in European mathematics, and in the Kingdom of Naples, this occurred earlier than elsewhere. Between 1790 and 1830 its leading scientific institutions rejected as untrustworthy the “very modern mathematics” of French analysis and in its place consolidated, legitimated, and put to work a different mathematical culture. The Neapolitan mathematical resistance was a complete reorientation of mathematical practice. Over the unrestricted manipulation and application of algebraic algorithms, Neapolitan mathematicians called for a return to Greek-style geometry and the preeminence of pure mathematics.
 
For all their apparent backwardness, Massimo Mazzotti explains, they were arguing for what would become crucial features of modern mathematics: its voluntary restriction through a new kind of rigor and discipline, and the complete disconnection of mathematical truth from the empirical world—in other words, its purity. The Neapolitans, Mazzotti argues, were reacting to the widespread use of mathematical analysis in social and political arguments: theirs was a reactionary mathematics that aimed to technically refute the revolutionary mathematics of the Jacobins. During the Restoration, the expert groups in the service of the modern administrative state reaffirmed the role of pure mathematics as the foundation of a newly rigorous mathematics, which was now conceived as a neutral tool for modernization. What Mazzotti’s penetrating history shows us in vivid detail is that producing mathematical knowledge was equally about producing certain forms of social, political, and economic order.
 

"“The complex relationship between tradition and modernization is the pulsing heart of this engaging book. Beside a valuable historical analysis, Reactionary Mathematics offers an interesting and useful synthesis vision to help us understand, in these times of rapid and convulsive transformation, the mathematics of the present and, most importantly, the reasons for the mathematics that will come.”" - Nature

"“Reactionary Mathematics is an ambitious book that is more than just a history of mathematics but an episode in the history of reason, furnished with a delightful display of different kinds of evidence, from archival documents to political satires to theological treatises to paintings to mathematics textbooks. . . . [It] is a deftly written and timely book brimming with empirical, conceptual and historiographical insights.”" - British Journal for the History of Science

"For anyone interested in the "politics of mathematical modernity," this book shows how allegiances to particular types or styles of mathematics may indeed be related to Neapolitan academicians' personal responses to the urgent political pressures of their day." - Choice

"“One notable strength of Mazzotti’s book is its ability to transition seamlessly between different levels of analysis. It connects an in-depth historical exploration of a specific local context, such as Naples, with the social and political constraints unique to that site. Simultaneously, it addresses major upheavals and broad conceptual changes such as the evolution of purity, rigor, and abstraction and the very definition of 'modernity' in mathematics. In doing so, the book tackles a critical methodological challenge in the social history of mathematics, bridging the gap between the claim of universality associated with mathematical knowledge and the intricate study of the local contexts and social practices that underpin the production of such knowledge. Mazzotti’s thought-provoking narrative not only demonstrates . . . that mathematics is intimately connected to its cultural, social and political context, but it also prompts readers to consider new avenues of research.”" - Historia Mathematica

"“Mazzotti’s sustained treatment of the interlacing of mathematics and politics, which becomes evident once we recognize mathematics as historical, is fascinating and worth careful study. It is on the vanguard of a new and much-needed shift in perspective on mathematical practice.”" - Physis