We should like to represent... the... universe, and... feel... we understood it. We... never can attain this representation: our weakness is too grea… - Henri Poincaré

The true geometrician makes this selection judiciously, because he is guided by a sure instinct, or by some vague consciousness of I know not what profounder and more hidden geometry, which alone gives a value to the constructed edifice.
To seek the origin of this instinct, and to study the laws of this profound geometry which can be felt but not expressed, would be a noble task for the philosophers who will not allow that logic is all. But this is not the point of view I wish to take, and this is not the way I wish to state the question. This instinct I have been speaking of is necessary to the discoverer, but it seems at first as if we could do without it for the study of the science once created. Well, what I want to find out is, whether it is true that once the principles of logic are admitted we can, I will not say discover, but demonstrate all mathematical truths without making a fresh appeal to intuition.

It is often said that experiments should be made without preconceived ideas. That is impossible. Not only would it make every experiment fruitless, but even if we wished to do so, it could not be done. Every man has his own conception of the world, and this he cannot so easily lay aside. We must, for example, use language, and our language is necessarily steeped in preconceived ideas.

C’est parce que la simplicité, parce que la grandeur est belle, que nous rechercherons de préférence les faits simples et les faits grandioses, que nous nous complairons tantôt à suivre la course gigantesque des astres, tantôt à scruter avec le microscope cette prodigieuse petitesse qui est aussi une grandeur, tantôt à rechercher dans les temps géologiques les traces d’un passé qui nous attire parce qu’il est lointain.