Intuition et invention mathématique

Abstract

This text intends to focus on several questions. First, the issue of generalization and of the generalization process in mathematics. Then that of the problematic idea of a sensitive ground of mathematical activity. Then que question of creativity and mathematical invention. Finally the question of objectivity, or rather of a mathematical reality, and how it affects the intuition of the mathematician. We conclude that, far from being the ontology, mathematics attest ofthe impossibility of any ontology and of the inexorable triumph of new generalizations about any attempt by the thought of going out of his own contextuality and offering a point of view of nowhere.