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« Ars combinatoria » chez Gian-Carlo Rota ou le triomphe du symbolisme (GIAN-CARLO ROTA’S « ARS COMBINATORIA » THE TRIUMPH OF SYMBOLISM) (« ARS COMBINATORIA » IN GIAN-CARLO ROTA O IL TRIONFO DEL SYMBOLISMO)

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Gian-Carlo Rota est l’inventeur d’une nouvelle science : la combi-natoire algébrique qui n’était jusque-là qu’un ensemble de questions dispa-rates, dont la solution, parfois ingénieuse, ne laissait entrevoir la méthode. Il s’agit ici de décrire la stratégie mise en œuvre sous sa forme ma-thématique dont les enjeux philosophiques ne sont pas négligeables, en poursuivant le geste de Rota, pour sortir la combinatoire de son ghetto.Gian-Carlo Rota is the inventor of a new science: algebraic combi-natorics, which until now had been a collection of disparate questions whose solution, sometimes ingenious, did not suggest the method. It is a question here of writing the strategy implemented in its mathematical form, whose philosophical stakes are not negligible, by pursuing Rota’s gesture, to bring out the combinatorics of his ghetto. Gian-Carlo Rota è l’inventore di una nuova scienza: la combinatoria algebrica, che fino ad oggi era solo un insieme di domande disparate, la cui soluzione, a volte ingegnosa, non suggeriva il metodo. Lo scopo qui è descrivere la strategia implementata nella sua forma matematica, i cui interessi filosofici non sono insignificanti, perseguendo il gesto di Rota, per far uscire la combinatoria dal suo ghetto.This article is in French.

* Pierre CARTIER, né en 1932, est mathématicien, directeur de recherche au Cnrs, ancien membre de Bourbaki. Ses travaux portent sur les « groupes formels », les groupes quantiques, les fonctions symétriques en combinatoire, et les algèbres de Hopf. Il a développé une théorie des groupes formels commutatifs et des courbes typiques (dans la tradition de Jean Dieudonné). Un opérateur et un diviseur portent son nom, sans oublier le « tapis de Cartier ». Il a en outre prédit le groupe de Galois « cosmique ». Il est l’auteur avec Cécile DeWitt de Functional Integration. Action and Symetries (Cambridge University Press, 2006) Adresse : IHÉS, 35, Route de Chartres, F-91440 Bures-sur-Yvette (cartier@ihes.fr), http://www.ihes.fr/~cartier/ et http://images.math.cnrs.fr/Mathematiciens-sans-frontieres,825.html
10.1007/s11873-000-0000-05
/content/journals/10.1007/s11873-000-0000-05
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1. Artin Emil 1957 Geometric Algebra Londres, New York Interscience Publishers [tr. fr. M. L azard], Paris, Gauthier Villars, 1962
2. Crapo Henri H., Rota Gian-Carlo 1970 On the foundations of combinatorial theory: combinatorial geometries Cambridge MIT Press
3. Hilbert (Hilbert) 1899 Grundlagen der Geometrie Leipzig B.G. Teubner Les fondements de la géométrie fr. Rossier Paul Paris Dunod 1971
4. Rota Gian-Carlo 1995 Gian-Carlo Rota on Combinatorics, Introductory papers and commentaries Kung Joseph P. S. "« Contemporary Mathematicians »" Boston, Bâle, Berlin Birkhäuser
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2017-01-09
2018-09-24

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