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La physique dans la recherche en mathématiques constructives

Abstract : In this paper, I focus on a practice of mathematical research which consists in reformulating constructively physical theories. More precisely, I discuss three features of this practice. First, I show that it is stimulated by philosophical views and discuss how physics is used in the debate between classicism and constructivism in the philosophy of mathematics. Secondly, I characterise the methodology of the research in mathematics involved by this practice and show this is a methodology of "logicians" as Poincaré said. Finally, I show that in this practice, physical theories play a heuristic role for the progress of constructive mathematics. Successfully, they stimulate researches on constructive results and lead to the study of new provinces of constructive mathematics.
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Vincent Ardourel. La physique dans la recherche en mathématiques constructives. Philosophia Scientiae, Editions Kime, 2012, 16 (1), pp.183-208. ⟨10.4000/philosophiascientiae.727⟩. ⟨halshs-00939231v2⟩

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