Lectures mathématiques : sédimentation, réactivation ou partage ?

• Main Author: Lucien Vinciguerra
• Format: Article
• Language: fra
• Published: Université de Lille 2020-02-01
• Series: Methodos
• Subjects: history of mathematics; Husserl; Peletier du Man Jacques; Descartes; Bachelard; Quine
• Online Access: http://journals.openedition.org/methodos/7065

Historians of mathematics have often noticed a singularity of their discipline: unlike physics, the history of mathematics does not proceed essentially by conjectures and refutations, but by a succession of reinterpretations of the past in order to include it into the actual state of knowledge. This operation involves an act of reading. Taking as its starting point Husserl's theses in The Origin of Geometry on the role of writing in the historicity of mathematics, the article aims to analyze the conditions of possibility of this reading, related to the nature of the mathematical text : this reading involves three delimitations performed by the reader's eye: between true and false, between writing and image, between what is mathematical and what does not. The article illustrates this thesis by examining the status of the equation in the cartesian’s book of Geometry. It shows the links between the latter and the ideas that the philosopher develops on reading and on the nature of the sign. On this basis, it is possible to understand how Descartes could read a mathematical text, how this partly explains some points in his Geometry, but also how other readings of this Geometry can include it into the mathematics of later centuries.