Gian-Carlo Rota a su concilier un travail mathématique exemplaire et des recherches philosophiques largement inspirées par la phénoménologie husserlienne. Son œuvre philosophique nous semble avoir de fait deux composantes : l’une s’intéresse majoritairement à des phénomènes universels. L’autre se déploie de façon plus subtile en filigrane de ses travaux mathématiques ; sans être thématisée comme telle – comme contribution philosophique –, elle alimente très lar-gement l’aura de Rota dans la communauté mathématique et justifie le rôle qu’il y joue de père (...) fondateur d’une école combinatoire. L’analyse de ces différents moments de sa pensée permet de mieux en cerner les ressorts, l’unité et la portée.Gian-Carlo Rota was able to combine a remarkable mathematical work with philosophical research largely inspired by Husserl’s phenomenology. His philosophical work has two components. One focuses mainly on universal phenomena in mathematics. The other unfolds in a more subtle way in his mathematical work; without being characterized as a proper philosophical contribution, it feeds largely the aura of Rota in the mathematical community and contributes to justify his role of founder of a school of combinatorics.The analysis of these different moments of his thought allows to understand better its origins, unit and scope. Gian-Carlo Rota ha saputo coniugare il propio lavoro matematico esemplare ad una ricerca filosofica in gran parte ispirata dalla fenomenologia di Husserl. La sua opera filosofica ha secondo noi due componenti: una riguarda principalmente i fenomeni universali. L’altra si sviluppa in modo più sottile nel suo lavoro matematico e, senza diventare un tema in quanto tale – come vero e pro-prio contributo filosofico –, alimenta in gran parte l’aura di Rota nella co-munità matematica, contribuendo a giustificare il suo ruolo di fondatore di una scuola combinatoria. L’analisi di questi diversi momenti del suo pensi-ero permette di identificarne meglio le origini, l’unità e la portata.This article is in French. (shrink)

Cet article vise à montrer l’extrême proximité entre ces deux mathématiciens-philosophes que furent Gian-Carlo Rota et Gilles Châtelet disparus la même année. Au moins quatre points communs les relient : une philosophie romantique radicale ; une rigueur intellectuelle exemplaire ; une vision affine de la recherche mathématique ; une révolte intérieure exécrant tout sensus communis.This text shows the great proximity between two mathematicianphilosophers, Gilles Châtelet and Gian-Carlo Rota who both died in the same year 1999. There are at least four (...) common points amongst themselves: a radical romantic philosophy; an exemplary intellectual rigor; a great affinity in their vision of mathematical research; an inmost rebellion against all common sense. Quest’articolo tende a mostrare l’estrema prossimità tra due matematici-filosofi che furono Gian-Carlo Rota e Gilles Châtelet che ci hanno lasciato lo stesso anno. Ci sono almeno quattro punti comuni che le legano: una radicale filosofia romantica; un rigore intellettuale esemplare; una visione affine della ricerca matematica; una rivolta intima che esecra ogni senso comune.This article is in French. (shrink)

The goal of this paper is to connect Rota's discussion of the Husserlian notion of Fundierung with Rota's project of giving combinatorics a foundation in his 1964 paper ‘On the foundations of combinatorial theory I’. Section 2 gives the basic tenets of this seminal paper. Sections 3 and 4 spell out the connections made there between Rota's philosophical writings and his mathematical achievements. Section 5 shows how these two developments fit into Rota's analysis of the place of combinatorics in mathematics.