I read again into Hadamard’s1 wonderful book which is about mathematicians’ minds according to its title, about the psychology of mathematical invention according to its subtitle, however, its real subject is good old intuition. No matter how old the concept of intuition, it is unknown and therefore mysterious. But we have everyday experience in it. Not only mathematicians, artists, scientists "use" it but all people do the same every day, without knowing it. Its everydayness is uncovered by the Hungarian proverb "sleep on it", in other words, "the morning is wiser than the evening". These phrases actually advise us to listen not only to our minds but to our insights as well when making difficult decisions. So it is an ancient experience that intuition appears after a short “problem resting" which is called “incubation” by Hadamard.
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1 Jacques Hadamard, The Mathematician’s Mind – The Psychology of Invention in the Mathematical Field
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