Science is built up of facts, as a house is built of stones; but an accumulation of facts is no more a science than a heap of stones is a house."

To doubt everything or to believe everything are two equally convenient solutions; both dispense with the necessity of reflection.

"Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination."

"Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority. To invent is to discern, to choose."

"Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means . . . ."