On Intuition (Unsourced)

"But it should always be required that a mathematical subject not be considered exhausted until it has become intuitively evident […]" (Felix Klein)

"Cognitive psychology has shown that the mind best understands facts when they are woven into a conceptual fabric, such as a narrative, mental map, or intuitive theory. Disconnected facts in the mind are like unlinked pages on the Web: They might as well not exist." (Steven Pinker)

"Intuition is the supra-logic that cuts out all routine processes of thought and leaps straight from the problem to the answer." (Robert Graves)

"Logic merely sanctions the conquests of the intuition." (Jacques S Hadamard)

"[…] mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs." (Felix Klein)

"The disclosure of a new fact, the leap forward, the conquest over yesterday’s ignorance, is an act not of reason but of imagination, of intuition." (Charles Nicolle)

"The supreme task is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can lead to them." (Albert Einstein)

"Undoubtedly, the capstone of every mathematical theory is a convincing proof of all of its assertions. Undoubtedly mathematics 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 soon exhaust itself in the rigor of its logical proofs and begin to stagnate as its substance vanish. Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs." (Felix Klein)