Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.
Sentiment: NEGATIVE
Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.
Intuition is the clear conception of the whole at once.
Intuition is reason in a hurry.
Intuition enlightens and so links up with pure thought. They together become an intelligence which is not simply of the brain, which does not calculate, but feels and thinks.
Logic obviously is important. You need to be able to figure things out, to go to the end of a particular problem. But intuition is very important because it references things that logic alone cannot.
I have hardly ever known a mathematician who was capable of reasoning.
Most intuitive ideas have to be clarified, so there is a trial and error process.
Intuition is a suspension of logic due to impatience.
The two operations of our understanding, intuition and deduction, on which alone we have said we must rely in the acquisition of knowledge.
Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality.
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