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Mathematical Models of Abstract Systems: Knowing abstract geometric forms

Jean-Pierre Marquis (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

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...

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