What Happens, from a Historical Point of View, When We Read a Mathematical Text? - HAL Accéder directement au contenu
Chapitre d'ouvrage Année : 2023

What Happens, from a Historical Point of View, When We Read a Mathematical Text?

Résumé

The history of mathematics can be read in two ways. On the one hand, unlike the history of physics, it does not proceed by conjectures and refutations. New theories rarely refute old theories, but give them new foundations, generalize them, and reinterpret them through new concepts. This reading is unifying, highlighting the unity of the history of mathematics from its origins, through the permanence of its truths. On the other hand, many contemporary historians of mathematics have insisted on the diversity of methods, objects, and practices throughout history. They have shown that the objects of the past mathematics are not the same as those of today. That second reading shatters the illusion of unity. It disjoins what the first reading unifies. Rather than deciding between these two readings, this chapter examines what makes them both possible and legitimate, based on an analysis of the acts of reading that we have to perform when confronted with the pages of a mathematical text, its signs, diagrams and images, and the different language modalities it employs. Starting with a discussion of Husserl's theses in The Origin of Geometry on the role of writing in the history of mathematics, and using a number of historical examples, the chapter shows that any reading of a mathematical text involves at least three divisions, three delimitations made by the reader's gaze: divisions between the true and the false, between language and image, and between what is inside mathematics and what is outside. For the same text, these divisions are traced by the gaze in different ways throughout history. The chapter develops an example in greater detail, concerning the status of the equation in Descartes' Geometry. It discusses the contrasting recent readings of the equation by two historians of science, Henk Bos and Enrico Giusti. It shows the concepts of The Geometry and the ideas the philosopher develops on reading and the nature of the sign. It shows how these ideas can be used to reconstruct how Descartes might have read a mathematical text, and it explains how successive readings of The Geometry can at the same time insert it into the mathematics of later centuries.
Fichier sous embargo
Fichier sous embargo
0 7 18
Année Mois Jours
Avant la publication

Fin d'embargo le lundi 23 décembre 2024

Loading...
Fichier sous embargo

Fin d'embargo le lundi 23 décembre 2024

Dates et versions

halshs-04362622, version 1 (23-12-2023)

Licence

Copyright (Tous droits réservés)

Identifiants

Citer

Lucien Vinciguerra. What Happens, from a Historical Point of View, When We Read a Mathematical Text?. Sriraman, B. Handbook of the History and Philosophy of Mathematical Practice, Springer International Publishing, pp.1-27, 2023, ⟨10.1007/978-3-030-19071-2_80-1⟩. ⟨halshs-04362622⟩
12 Consultations
3 Téléchargements
Dernière date de mise à jour le 28/04/2024
comment ces indicateurs sont-ils produits

Altmetric

Partager

Gmail Facebook Twitter LinkedIn Plus