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

Enqu\^ete sur les modes d'existence des \^etres math\'ematiques (version  augment\'ee) [An inquiry into the modes of existence of mathematical beings  (expanded version)]