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“Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning. The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.”

“Work incessantly, cultivate discrimination, gather freedom from your own hard-earned results. Disregard successes but go back for help in an immediate problem. The possibility of discovery is everywhere. Freedom from your own work allows for intuition that draws from all your experience and perception but goes beyond it.”

“While I do not think it was so intended I have always been of the opinion that this turned out to be much the best for me. I had no national experience. What I have ever been able to do has been the result of first learning how to do it. I am not gifted with intuition. I need not only hard work but experience to be ready to solve problems. The Presidents who have gone to Washington without first having held some national office have been at great disadvantage.”