 Poincaré is best known for his critique of logicism and for his geometric conventionalism. The two traditions interpreting Poincaré’s work thus reflect, on the one hand, a philosophy of mathematics that endorses his intuitionist tendency and his polemics against logicism or formalism, and, on the other hand, his conventionalism both in the philosophy of science and in a broad linguistic sense. In reality, these intuitionistic and formal aspects are two sides of the same coin, given that Poincaré always supports a single position aimed at a reconstruction of the process of understanding scientific theories (see Heinzmann 2010). Neither formalistic nor intuitionist nor empiricist, Poincare opens a path lying between a realist and an anti-realist theory of mathematical knowledge.