In this article, we propose to revisit a debate that began over two decades ago around the question of the naturalization of phenomenology. In particular, we attempt to determine the meaning of this naturalization project in the context of the study of the origin and foundations of geometry. To do so we shall follow the following plan: We begin by briefly reviewing the debate surrounding the possibility of naturalizing phenomenology, and the various conceptual problems involved in this attempt at naturalization. (...) We then turn to the specific object of the article: the genesis of geometrical idealities. First, we review the main theoretical frameworks within the cognitive sciences for a naturalist analysis of the genesis of geometric idealities. Secondly, we show that these approaches are partially theoretically incompatible with the genesis of geometric idealities as conceived by Husserl, and we extract three constraints that should guide any attempt to naturalize it. Finally, we present a program to carry out this naturalization that is based on current research. (shrink)