  This essay inquires how mathematical beings could be inserted into the
architecture of modes of existence proposed by Bruno Latour in the framework of
his pluralist and renewed ontology of the modern world. After a description of
the problem, the work of Reviel Netz on the emergence of Greek mathematics, and
of Charles Sanders Peirce on the diagrammatic dimension of mathematical
practice are presented, as well as their impact on our essay. Its central part
is the development of an empirical conception of mathematics that plays a
central r\^ole in the sequel. Our analysis is based on the notion of experience
according to William James; it is also inspired by certain aspects of Per
Martin-L\"of's philosophy. It provides a way of thinking the firm certainty
with which proofs endow theorems, while invalidating the interpretation of this
certainty as the mark of a direct access to an absolute and transcendental
truth. The sequel of our essay builds on this analysis for defining a sort of
quasi-mode of existence appropriate for mathematical beings that respects the
principal features of modes of existence according to the latourian ontology.
In the conclusion, the way this quasi-mode might be integrated into this
ontology is discussed, in particular with respect to the mode of reference that
prevails in many other sciences.
