Among mathematicians in general, three main categories may be distinguished; and perhaps the names logicians, formalists, and intuitionists may serve to characterize them.
Felix KleinEveryone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.
Felix KleinThus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.
Felix KleinRegarding the fundamental investigations of mathematics, there is no final ending ... no first beginning.
Felix Klein