What we call geometry is nothing but the study of formal properties of a certain continuous group [...]. The notion of this continuous group exists i… - Henri Poincaré

What we call geometry is nothing but the study of formal properties of a certain continuous group; so that we may say, space is a group. The notion of this continuous group exists in our mind prior to all experience; but the assertion is no less true of the notion of many other continuous groups; for example, that which corresponds to the geometry of Lobatchevski.

Si donc un phénomène comporte une explication mécanique complète, il en comportera une infinité d’autres qui rendront également bien compte de toutes les particularités révélées par l’expérience.

Naukę buduje się z faktów tak jak dom buduje się z cegieł, ale samo nagromadzenie faktów nie jest jeszcze nauką, podobnie jak kupa cegieł nie jest domem.

The continuum so conceived is only a collection of individuals ranged in a certain order, infinite to one another, it is true, but exterior to one another. This is not the ordinary conception, wherein is supposed between the elements of the continuum a sort of intimate bond which makes of them a whole, where the point does not exist before the line, but the line before the point. Of the celebrated formula “the continuum is unity in multiplicity”, only the multiplicity remains, the unity has disappeared. The analysts are none the less right in defining the continuum as they do, for they always reason on just this as soon as they pique themselves on their rigor. But this is enough to apprise us that the veritable mathematical continuum is a very different thing from that of the physicists and the metaphysicians.