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Accueil du site > Axes de recherche > Histoire et philosophie des mathématiques > 3 Mathematics and Philosophy, 19th and 20eth Centuries

Axis History and Philosophy of Mathematics

3 Mathematics and Philosophy, 19th and 20eth Centuries

The information from 2018-2023 will replace those of 2012-2017 on this page.
2012-2017 information is now archived, which can be found under the heading
"Archives, Research Axes 2012-2017"



- Thematics
- Members



Thematics

This theme brings together a series of research on the history and philosophy of mathematics in the nineteenth and twentieth centuries, according to two distinct and complementary orientations :
  • on the one hand, research in the history of mathematics focuses on the study of the nineteenth-twentieth centuries, with emphasis on questions of methodology and historiography ; It is in this context to reflect on how different approaches to the history of mathematics (so-called "conceptual" history, social history, history of practices and institutions, etc.) are likely to be usefully associated with the service of Analysis of texts ;
  • on the other hand, research on the philosophy of mathematics developed within the team covers a wide spectrum ranging from the history of the philosophy of mathematics of the nineteenth and twentieth centuries to contemporary research (philosophy of mathematical practices, Logic and formalization, fundamentals and theory of categories, theories of abstraction).

Although they are independent in their own methods and forms of questioning, these two orientations of research are strongly linked by their common anchoring in the mathematics of the nineteenth and twentieth centuries. If, from the point of view of the history of mathematics proper, the caesura between the eighteenth and nineteenth centuries appears to be largely artificial, and if in this perspective it must of course be questioned, the choice we make of To unite in a single axis all this research is nevertheless justified by the fertility of the dialogues crossed between these multiple approaches.


– As regards the history of mathematics proper, the form that is privileged is that of a specific working group in which the PhD students and members of the sub-axis regularly present the progress of their research.

– As regards the philosophy of mathematics, the work carried out within the SPHERE team is organized around several poles :

  • A mixed seminar "Mathematics and philosophy, nineteenth and twentieth centuries" organized by the doctoral students of the team allowing confrontation and exchanges between philosophical perspectives and historical perspectives.
  • A seminar on mathematical abstraction co-organized by Professor Jean-Pierre Marquis of the University of Montreal and Professor Jean-Jacques Szczeciniarz.
  • A research program in the continuity of the ANR "Geometry and physics at the hinge of the nineteenth and twentieth centuries", directed by Jean-Jacques Szczeciniarz (2006-2010), which groups together works on the following themes :
    – A) the relationship between geometry and physics, in the continuity of the book Géométrie au XXe siècle co-edited by J.-J. Szczeciniarz ; In particular the question of the status of complex numbers in mathematical physics ;
    – (B) the status of cosmological science and the role of mathematical conceptual constructions in the constitution of cosmological models (working group of researchers from the team and the APC team - Paris Diderot University) ;
    – C) the mathematical and philosophical question of the unity of mathematics, in the various forms of unification through integral transformations, unification by the theory of Galois, unification by category theory. In this context, a group working on the theory of categories brings together several of the researchers, teacher-researchers and PhD students of the team : Michel De Glas, André Rodin, Jean-Jacques Szczeciniarz and Sylvain Cabanacq.


Members

In Charge
CHORLAY Renaud
SMADJA Ivahn
SZCZECINIARZ Jean-Jacques
Researchers - PhD students - Post-docs
BERTIN Pascal
CABANACQ Sylvain
CATREN Gabriel
DE GLAS Michel
FERREIROS José
GANDON Sébastien
GASTALDI Juan Luis
GROSHOLZ Emily
HAFFNER Emmylou
IKONICOFF Roman
KEBAILI Ramzi
MARONNE Sébastien
MOSCA Antonio
PETROLO Mattia
RABOUIN David
RODIN Andrei
TIMMERMANS Benoît
VERGNERIE Cédric
WANG Xiaofei