For an aggregate of sensations to have become a remembrance capable of classification in time, it must have ceased to be actual, we must have lost th… - Henri Poincaré

The syllogism cannot teach us anything essentially new ( ... ). It must be conceded that mathematical reasoning has of itself a sort of creative virtue, and consequently differs from the syllogism.

The greatest chance is the birth of a great man. It is only by chance that two reproductive cells, of different sexes, met, each containing precisely those mysterious elements whose mutual reaction was to produce genius. We will agree that these elements must be rare and that their meeting is even rarer. That it would have taken little to deviate the spermatozoon that carried them from its course; it would have been enough to deviate it by a tenth of a millimeter and Napoleon would not have been born and the destiny of a continent would have been changed. No other example can better explain the true nature of chance.

Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so lone as the relations remain unchanged. Content to them is irrelevant; they are interested in form only.