Recorded on October 17, 2023, this video features an "Authors Meet Critics" panel on the book Reactionary Mathematics: A Genealogy of Purity, by Massimo Mazzotti, Professor in the UC Berkeley Department of History and the Thomas M. Siebel Presidential Chair in the History of Science. Professor Mazzotti was joined in conversation by Matthew L. Jones, the Smith Family Professor of History at Princeton University, and David Bates, Professor of Rhetoric at UC Berkeley. Thomas Laqueur, the Helen Fawcett Distinguished Professor Emeritus at UC Berkeley, moderated.  This event was co-sponsored by the Center for Science, Technology, Medicine, & Society and the UC Berkeley Department of History. The Social Science Matrix “Authors Meet Critics” book series features lively discussions about recently published books authored by social scientists at UC Berkeley. For each event, the author discusses the key arguments of their book with fellow scholars. Learn more at https://matrix.berkeley.edu. ABOUT THE BOOK 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. A transcript of this talk is available at https://matrix.berkeley.edu/research-article/reactionary-mathematics/