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Poincar\'e held the view that geometry is a convention and cannot be testedexperimentally. This position was apparently refuted by the general theory ofrelativity and the successful confirmation of its predictions; unfortunately,Poincar\'e did not live to defend his thesis. In this paper, I argue that: 1)Contrary to what many authors have claimed, non-euclidean geometries do notrule out Kant's thesis that space is a form of intuition given {\it a priori};on the contrary, Euclidean geometry is the condition for the possibility of anymore general geometry. 2) The conception of space-time as a Riemannian manifoldis an extremely ingenious way to describe the gravitational field, but, asshown by Utiyama in 1956, general relativity is actually the gauge theoryassociated to the Lorentz group. Utiyama's approach does not rely on theassumption that space-time is curved, though the equations of the gauge theoryare identical to those of general relativity. Thus, following Poincar\'e, itcan be claimed that it is only a matter of convention to describe thegravitational field as a Riemannian manifold or as a gauge field in Euclideanspace.

Geometry as an object of experience: Kant and the missed debate between Poincar\'e and Einstein