Mutis and the Introduction of Analytic Method in Colombia

Abstract

In this work we study the different ways of teaching the analytical method by José Celestino Mutis (1732-1808) as the chair of mathematics at the Colegio del Rosario in Bogotá during the second half of the 18th century. As a framework to better appreciate the transformations of this teaching, we will begin by recalling some of the most important historical and philosophical characteristics of the Cartesian distinction between analysis and synthesis in mathematical thought. Mutis begins by introducing the logicist approach of Wolff’s Discourse on Method. He then explains the Cartesian rules of analysis and synthesis, for which he translates fragments of Rabuel’s Commentaries on Descartes’ geometry. He also presents Newton's ideas on the analytical method, both in the experimental modality of Optics and in the physical-mathematical perspective of Principia. We will analyze the difficulty inherent to the understanding of this change of perspective in the process of the reading and translation of Principia by Mutis. Then it is shown that by focusing the teaching on Bails’ Elementos de Matemáticas —as a consequence of the reform of the curriculum of the chair promoted by Mutis—, it ends up adopting the operative mode of analysis as an application of algebra to geometry. Finally, we show how the introduction of the Bails text entailed a fundamental transformation in the epistemological, cognitive and pedagogical approach to teaching by the analytical method in the Cátedra del Rosario, as compared to Wolff’s Elementa Matheseos Universae in its foundational stage.