The aim of Mathematical Physics is not only to facilitate for the physicist the numerical calculation of certain constants or the integration of cert… - Henri Poincaré

La recherche de la vérité doit être le but de notre activité ; c'est la seule fin qui soit digne d'elle. Sans doute nous devons d'abord nous efforcer de soulager les souffrances humaines, mais pourquoi ?

Every definition implies an axiom, since it asserts the existence of the object defined. The definition then will not be justified, from the purely logical point of view, until we have proved that it involves no contradiction either in its terms or with the truths previously admitted.

We see that experience plays an indispensable role in the genesis of geometry; but it would be an error thence to conclude that geometry is, even in part, an experimental science. If it were experimental it would be only approximative and provisional. And what rough approximation!
...The object of geometry is the study of a particular 'group'; but the general group concept pre-exists... in our minds. It is imposed on us, not as form of our sense, but as form of our understanding. Only, from among all the possible groups, that must be chosen... will be... the standard to which we shall refer natural phenomena.
Experience guides us in this choice without forcing it upon us; it tells us not which is the truest geometry, but which is the most convenient.
Notice that I have been able to describe the fantastic worlds... imagined without ceasing to employ the language of ordinary geometry.