La constitution de l'écriture symbolique mathématique.

Abstract : This dissertation is devoted to the description of the establishment of mathematical symbolic writing, primarily achieved with Descartes geometry to examine some transcendental figures of knowledge organized by the new system, finally to analyze the part of the new symbolic in inventing and creating objects. The first part le system depicts the birth of the symbolic, organizing two registers, combinatoric s and meanings. All was in fact achieved between 1591 and 1637, vieta s isagoge and Descartes geometry we describe from Diophantus to cardan the previous systems, such as cossic s and vieta s use of letters. Descartes ‘contribution was conclusive with three points: symbolic punctuation, Cartesian exponential, and the loop ( sign for equality ). The second part symbolique and invention is primarily organized around Leibniz and his discovery in 1676 of newton s epistola prior containing a lot of combinatory and meaningful questions. The chapter characteristique and new nouveau calcul describes Leibniz creating his fundamental algorithm, primarily by means of combinatory playing ‘with substitutions, apart from any signification. In the art combinatory. Substitutions and metamorphoses, the concept is extended, so as to reach its modern form: tool for mathematical invention, anchored in the symbolic. formes sans significations finally depicts a meta-procedure for building up objets from their form,initially analysed in the correspondance of 1676 between Leibniz and Newton, then in the creation of the field of complex numbers, thus resolving bombelli s riddle of imaginary quantities . We examine some accomplishments of this usual epistemological scheme in Euler s work (complex exponential and new factorial ), in some recent questions (distributions of l. Schwartz), as well as in a personal example.
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Michel Serfati. La constitution de l'écriture symbolique mathématique.. Histoire et perspectives sur les mathématiques [math.HO]. Université Paris I, 1997. Français. ⟨tel-01252590⟩

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