Inventing Mathematics in the 18th Century
Challenges and Disciplines
The overall aim of the talk is to map the transformation of mathematics in the Enlightenment, from the challenges arising from the reception of the Newtonian and Leibnizian inventions to the more autonomous and systematic treatments from the second half of the 18th century, especially the Eulerian treatises.
The reception of Newton’s Principia mathematica (1687), especially on the European Continent, and the priority dispute on the invention of the calculus are used as a battleground for the development of new practices and results, especially integration techniques to solve examples of differential equations, in one then in severable variables, but also variational problems. In the second half of the century, they become mathematical objects in themselves, presented in extensive treatises (Euler and the notion of function) synthesizing the new field of analysis. Alongside the development of analysis, the contributions to the traditional disciplines—algebra, geometry, number theory—will be mentioned, especially complex numbers and the unsolvability of the quintic equation. Along with the general idea of the development of mathematics in the Enlightenment which Jeanne Peiffer wants to convey, and in order to illustrate the method she will apply, an example of the presentation of one specific result will be given.
Jeanne Peiffer was trained in mathematics at the University of Fribourg (Switzerland) and took a doctorate in history of mathematics (EHESS, Paris 1978). She has been a researcher at the French Centre National de la Recherche Scientifique (CNRS) and affiliated to the Centre Alexandre Koyré (Paris). Her research interests focus on early modern mathematics. She has published on Albrecht Dürer’s geometry and his German followers. Moreover she has been interested in correspondences and their role in the production and circulation of mathematics. This interest has been fuelled by her activity as editor of the correspondence of Johann Bernoulli and Pierre Varignon. She is actually working, with Hélène Gispert and Philippe Nabonnand, on the circulation of mathematics in and via journals. A recent special issue of Historia mathematica presents the first results of that research program.