The controversy about whether analytic or synthetic methods should be preferred for the solution of geometrical problems was common all over Europe, in the first half of the nineteenth century. It was related to important issues such as the definition of the new discipline of “pure mathematics”, and it has been taken by recent historiography of science as an exemplary case for the analysis of conceptual change in mathematics. In this study, historical material relating to the under-researched case of Naples is presented, and used to support a new interpretation for the controversy. The study begins by describing the technical contents of the Neapolitan version of the controversy, referring publications involved in one important, emblematic episode: the public challenge between the two rival geometrical schools, which took place in 1839. The competing methods are presented, and it is argued that, far which being caused by some mere “technical” divergence, the controversy arose from two very different conceptions of the nature and goals of geometry, and of mathematics in general. The following step is to look at the cultural environment where these two contrasting conceptions of mathematics were elaborated. Historical evidence supports the claim that both schools emerged in the very same period, the 1780s, and that the common interpretation of a preexisting synthetic school challenged by a new analytic school is misleading. Rather, the synthetic school emerged in reaction to the diffusion of analytic methods in Naples. It is also argued that the synthetic geometers were not simply “backward”, and that they did not ignore the modern analytic methods; they chose to oppose the analytic conception of mathematics; they made the choice of being anachronistic. The wider philosophical and theological meaning of opposing the “spirit of analysis” is investigated, which brings us to the heart of the political and cultural upheaval which Naples experienced in the revolutionary and Napoleonic period. Two opposite networks of philosophers, ecclesiastics, scientists and literati emerge, one siding with the modernization of the country according to the French example, the other defending the semi-feudal structure of the Neapolitan state. It is only against the background of this crucial debate, over the re-shaping Neapolitan society, that the apparently detached controversy over geometrical methods is best understood. It is indeed argued that the production of scientific and mathematical knowledge, as that of any other form of knowledge, was shaped by the wider cultural and social goals of the actors involved. And, in fact, the controversy over geometrical methods, originally emerging in correspondence with the reaction to the French Revolution, eventually lost its scientific relevance in the early 1840s, as the cultural hegemony of Neapolitan reactionary forces declined. It is finally suggested that this socio-historical interpretation of the Neapolitan case could cast light on other similar mathematical controversies of the first half of the nineteenth century.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:657498 |
| Date | January 1999 |
| Creators | Mazzotti, Massimo |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/22464 |
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