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 o… - Henri Poincaré

Il n’y pas d’infini actuel; les Cantoriens l’ont oublié, et ils sont tombés dans la contradiction. Il est vrai que le Cantorisme a rendu des services, mais c’était quand on l’appliquait à un vrai problème, dont les termes étaient nettement définis, et alors on pouvait marcher sans crainte.

Mathematicians do not study objects, but the relations between objects; to them it is a matter of indifference if these objects are replaced by others, provided that the relations do not change. Matter does not engage their attention, they are interested in form alone.

Formal logic is nothing but the study of the properties common to all classifications; it teaches us that two soldiers who are members of the same regiment belong by this very fact to the same brigade, and consequently to the same division; and the whole theory of the syllogism is reduced to this.