Mathematics is the art of giving the same name to different things.
Hypotheses are what we lack the least.
To invent is to discern, to choose.
But for harmony beautiful to contemplate, science would not be worth following.
Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.
Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.