Abstract
Husserlian phenomenology has played an important role in French mathematical philosophy (Cavaillès, Desanti ; Vuillemin at the Collège de France). However, the phenomenological method is only partially compatible with the French epistemological tradition, which has always believed in a certain form of necessity for mathematical objects, whereas phenomenology tends to insist on the constitutive role of consciousness. This is the essence of Cavaillès' philosophical testament and his program for a " philosophy of the concept ". The relationship with history also poses a problem, with on the one hand a rather archaeological approach (that of the Husserl of The Origin of Geometry), and on the other an interest directed more towards the dynamics of conceptual creation and the underlying necessities. The talk will return to and clarify this epistemological context, and then revisit these questions in the light of mathematical practice and what the phenomenological method can contribute today to talk about " mathematical phenomena ".
