Mathematical Models of Abstract Systems: Knowing abstract geometric forms

Jean-Pierre Marquis

Annales de la faculté des sciences de Toulouse Mathématiques (2013)

  • Volume: 22, Issue: 5, page 969-1016
  • ISSN: 0240-2963

Abstract

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Scientists use models to know the world. It is usually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they compute various functions and solve equations. In this paper, I want to exhibit models build by mathematicians to study the fundamental components of spaces and, more generally, of mathematical forms. I focus on one area of mathematics where models occupy a central role, namely homotopy theory. I argue that mathematicians introduce genuine models and I offer a rough classification of these models.

How to cite

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Marquis, Jean-Pierre. "Mathematical Models of Abstract Systems: Knowing abstract geometric forms." Annales de la faculté des sciences de Toulouse Mathématiques 22.5 (2013): 969-1016. <http://eudml.org/doc/275364>.

@article{Marquis2013,
abstract = {Scientists use models to know the world. It is usually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they compute various functions and solve equations. In this paper, I want to exhibit models build by mathematicians to study the fundamental components of spaces and, more generally, of mathematical forms. I focus on one area of mathematics where models occupy a central role, namely homotopy theory. I argue that mathematicians introduce genuine models and I offer a rough classification of these models.},
author = {Marquis, Jean-Pierre},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
month = {12},
number = {5},
pages = {969-1016},
publisher = {Université Paul Sabatier, Toulouse},
title = {Mathematical Models of Abstract Systems: Knowing abstract geometric forms},
url = {http://eudml.org/doc/275364},
volume = {22},
year = {2013},
}

TY - JOUR
AU - Marquis, Jean-Pierre
TI - Mathematical Models of Abstract Systems: Knowing abstract geometric forms
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2013/12//
PB - Université Paul Sabatier, Toulouse
VL - 22
IS - 5
SP - 969
EP - 1016
AB - Scientists use models to know the world. It is usually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they compute various functions and solve equations. In this paper, I want to exhibit models build by mathematicians to study the fundamental components of spaces and, more generally, of mathematical forms. I focus on one area of mathematics where models occupy a central role, namely homotopy theory. I argue that mathematicians introduce genuine models and I offer a rough classification of these models.
LA - eng
UR - http://eudml.org/doc/275364
ER -

References

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