Mathematicians study not objects, but relations between objects; the replacement of these objects by others is therefore indifferent to them, provide… - Henri Poincaré

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.

Mathematicians do not study objects, but relations between objects. Thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only...

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.

Does the harmony the human intelligence thinks it discovers in nature exist outside of this intelligence? No, beyond doubt, a reality completely independent of the mind which conceives it, sees or feels it, is an impossibility. A world as exterior as that, even if it existed, would for us be forever inaccessible.

The essential characteristic of reasoning by recurrence is that it contains, condensed so to speak, in a single formula, an infinite number of syllogisms.

The task of the educator is to make the child's spirit pass again where its forefathers have gone, moving rapidly through certain stages but suppressing none of them. In this regard, the history of science must be our guide.