title: [Bachelard and the mathematical pulsation].
abstract: The working mathematician knows a specific gesture named « mathematical pulsation », a necessary creative moving in diagrams of thoughts and interpretations of mathematical writings. In this perspective the fact of being an object is definitely undecided, and related to the game of relations. The purpose of this paper today is to construct this pulsation, starting from the epistemology of Bachelard, concerning mathematics as well as mathematical physics. On the way, we recover links between ideas of Bachelard and more recent specific propositions by Gilles Ch-let, Charles Alunni, or René Guitart. Also are used authors like Jacques Lacan, Arthur Koestler, Alfred N. Whitehead, Charles S. Peirce. We conclude that the mathematical work consists with pulsative moving in the space of diagrams; we claim that this view is well compatible with the Bachelard's analysis of scientific knowledge: the intellectual or formal mathematical data preceeds the empirical objects, and in some sense these objects result from the pulsative gestures of the thinkers. So we finish with a categorical scheme of the pulsation.
authors.affiliation: IMJ-PRG université Paris Diderot, bât. Sophie Germain, F-75013, Paris, France, rene.guitart@orange.fr.
authors.forename: René
authors.initials: R
authors.lastname: Guitart