The mind uses its creative faculty only when experience requires it. - Henri Poincaré

Most striking at first is this appearance of sudden illumination, a manifest sign of long, unconscious prior work. The role of this unconscious work in mathematical invention appears to me incontestable.

[T]wo difficulties: (1) Can we transform psychologic time, which is qualitative, into a quantitative time? (2) Can we reduce to one and the same measure facts which transpire in different worlds [of conscious beings]!

In reality, space is therefore amorphous, a flaccid form, without rigidity, which is adaptable to everything, it has no properties of its own. To geometrize is to study the properties of our instruments, that is, of solid bodies.