Equazioni e soluzioni nell’analisi ‘comune’ cartesiana e nella ‘nuova’ analisi leibniziana - Prof. Niccolò Guicciardini (Università di Bergamo)

During the seventeenth century, the advent of what were known as the ‘common’ and the ‘new analyses’, changed the mathematical landscape of European mathematics in a deep way. The narrative which is widely accepted is that the seventeenth-century analyses (algebra and calculus), mostly due respectively to Descartes and Leibniz, promoted a transition from geometrical to symbolical methods, from Euclidean proportion theory to equations.  It is this change that would have allowed the advent of a more abstract way of practicing mathematics, a way that culminated in the eighteenth century with the algebraic approach to calculus and mechanics promoted by Leonhard Euler and Joseph-Louis Lagrange. In this lecture, I will show that, contrary to the accepted narrative [1], for Descartes, Leibniz and their immediate followers, geometrical interpretation and mechanical constructions still played a crucial role.  This is revealed by the way in which they handled equations and how they sought their solutions.

[1] One can read in Morris Kline’s influential, and still fundamental, textbook: ‘Whereas from Greek times until about 1600 geometry dominated mathematics and algebra was subordinate, after 1600 algebra became the basic mathematical subject; in this transposition of roles the calculus was the decisive factor’. Morris Kline, Mathematical Thought from Ancient to Modern Times, New York, Oxford University Press, 1972, p. 323.