“Undoubtedly, the capstone of every mathematical theory is a convincing proof of all of its assertions. Undoubtedly, rnathematics inculpates itself when it foregoes convincing proofs. But the mystery of brilliant productivity will always be the posing of new questions, the anticipation of new theorems that make accessible valuable results and connections. Without the creation of new viewpoints, without the statement of new aims, mathematics would soou exhaust itself in the rigor of its logical proofs and begin to stagnate as its substance vanishes. Thus, in a sense, mathematics has been most advanced by those who distinguished thernselves by intuition ratber than by rigorous proofs.”