Mathematics is the art of giving the same name to different things. Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. No more than these machines need the mathematician know what he does. Talk with M. Hermite. He never evokes a concrete image, yet you soon perceive that the more abstract entities are to him like living creatures.
Science is built up with facts, as a house is with stones.
But a collection of facts is no more a science than a heap of stones is a house. The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another. 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.