We try, in this article, to enlighten Henri Poincaré's "style" in theoretical physics and mathematics, by analyzing in particular the case of his theoretical formulation of relativistic electrodynamics, and the place occupied in it by the principle of relativity. A comparison of this creative work with the parallel one done at the same time by Einstein (of the special relativity) allows to put in evidence the contrast between these two approaches. We evoke then the novelties that Poincaré's work and thought bring into the domain of philosophy concerning the problem of scientific creation and its relation to rationality.
Scientific creation; Intuition; Invention; Rationality; Principle of relativity; Electrodynamics; Theoretical physics; Mathematics