The psychology of accurate intuition involves no magic. Perhaps the best short statement of it is by the great Herbert Simon, who studied chess masters and showed that after thousands of hours of practice they come to see the pieces on the board differently from the rest of us. You can feel Simon’s impatience with the mythologizing of expert intuition when he writes: “The situation has provided a cue; this cue has given the expert access to information stored in memory, and the information provides the answer. Intuition is nothing more and nothing less than recognition.

We have all heard such stories of expert intuition: the chess master who walks past a street game and announces “White mates in three” without stopping, or the physician who makes a complex diagnosis after a single glance at a patient. Expert intuition strikes us as magical, but it is not. Indeed, each of us performs feats of intuitive expertise many times each day. Most of us are pitch-perfect in detecting anger in the first word of a telephone call, recognize as we enter a room that we were the subject of the conversation, and quickly react to subtle signs that the driver of the car in the next lane is dangerous. Our everyday intuitive abilities are no less marvelous than the striking insights of an experienced firefighter or physician — only more common. The psychology of accurate intuition involves no magic. Perhaps the best short statement of it is by the great Herbert Simon, who studied chess masters and showed that after thousands of hours of practice they come to see the pieces on the board differently from the rest of us. You can feel Simon’s impatience with the mythologizing of expert intuition when he writes: “The situation has provided a cue; this cue has given the expert access to information stored in memory, and the information provides the answer. Intuition is nothing more and nothing less than recognition.

The fact that human intuition is ill suited to situations involving uncertainty was known as early as the 1930's, when researchers noted that people could neither make up a sequence of numbers that passed mathematical tests for randomness nor recognize reliably whether a given string was randomly generated.

We [at the Bauhaus, in Dessau - where Klee was art teacher with Kandinsky ] construct and construct, and yet intuition still has its uses. Without it we can do a lot, but not everything.. .When intuition is joined to exact research it speeds the progress of exact research..

It's through science that we prove, but through intuition that we discover.

INTUITION (L. intueri, ‘to look at or into’). I regard intuition as a basic psychological function (q.v.). It is the function that mediates perceptions in an unconscious way. Everything, whether outer or inner objects or their relationships, can be the focus of this perception. The peculiarity of intuition is that it is neither sense perception, nor feeling, nor intellectual inference, although it may also appear in these forms. In intuition a content presents itself whole and complete, without our being able to explain or discover how this content came into existence. Intuition is a kind of instinctive apprehension, no matter of what contents. Like sensation (q.v.), it is an irrational (q.v.) function of perception. As with sensation, its contents have the character of being “given,” in contrast to the “derived” or “produced” character of thinking and feeling (qq.v.) contents. Intuitive knowledge possesses an intrinsic certainty and conviction, which enabled Spinoza (and Bergson) to uphold the scientia intuitiva as the highest form of knowledge. Intuition shares this quality with sensation (q.v.), whose certainty rests on its physical foundation. The certainty of intuition rests equally on a definite state of psychic “alertness” of whose origin the subject is unconscious.

Intuition is the art, peculiar to the human mind, of working out the correct answer from data that is, in itself, incomplete or even, perhaps, misleading.

No incident in my scientific career is more widely known than the part I took many years ago in certain psychic researches. Thirty years have passed since I published an account of experiments tending to show that outside our scientific knowledge there exists a Force exercised by intelligence differing from the ordinary intelligence common to mortals. This fact in my life is, of course, well understood by those who honored me with the invitation to become your president. Perhaps among my audience some may feel curious as to whether I shall speak out or be silent. I elect to speak, although briefly. … To ignore the subject would be an act of cowardice — an act of cowardice I feel no temptation to commit. To stop short in any research that bids fair to widen the gates of knowledge, to recoil from fear of difficulty or adverse criticism, is to bring reproach on science. There is nothing for the investigator to do but to go straight on; "to explore up and down, inch by inch, with the taper his reason; "to follow the light wherever it may lead, even should it at times resemble a will-o'-the-wisp. I have nothing to retract. I adhere to my already published statements. Indeed, I might add much thereto. I regret only a certain crudity in those early expositions which, no doubt justly, militated against their acceptance by the scientific world. My own knowledge at that time scarcely extended beyond the fact that certain phenomena new to science had assuredly occurred, and were attested by my own sober senses and, better still, by automatic record. I was like some two-dimensional being who might stand at the singular point of a Riemann's surface, and thus find himself in infinitesimal and inexplicable contact with a plane of existence not his own. I think I see a little farther now. I have glimpses of something like coherence among the strange elusive phenomena; of something like continuity between those unexplained forces and laws already known. This advance is largely due to the labors of another association, of which I have also this year the honor to be president — the Society for Psychical Research. And were I now introducing for the first time these inquiries to the world of science I should choose a starting point different from that of old. It would be well to begin with telepathy; with the fundamental law, as I believe it to be, that thoughts and images may be transferred from one mind to another without the agency of the recognized organs of sense — that knowledge may enter the human mind without being communicated in any hitherto known or recognized ways.

It is through science that we prove, but through intuition that we discover.

In mathematics, as in any scientific research, we find two tendencies... [T]he tendency toward abstraction seeks to crystallize the logical relations inherent in the maze of material in a systematic and orderly manner. On the other hand, the tendency toward intuitive understanding fosters a more immediate grasp of the objects... a live rapport with them... which stresses the concrete meaning of their relations. ...[I]ntuitive understanding plays a major role in geometry. ...[S]uch concrete intuition is of great value not only for the research worker, but... for anyone who wishes to study and appreciate the results of research in geometry.

Humans are good, she knew, at discerning subtle patterns that are really there, but equally so at imagining them when they are altogether absent.

Scientists work by a combination of intuition and insight in trying to understand a question.

The idea that any art is achieved 'intuitively' is a dehumanization of the brains, effort, and the traditions of the artist, and a classification of said artist as subhuman. It is those supposed incapable of intelligence, training, or connection with a tradition who are described as working by instinct or intuition.

But though every normal man thus cherishes the soothing unction that he is the intellectual superior of all women, and particularly of his wife, he constantly gives the lie to his pretension by consulting and deferring to what he calls her intuition. That is to say, he knows by experience that her judgment in many matters of capital concern is more subtle and searching than his own, and, being disinclined to accredit this greater sagacity to a more competent intelligence, he takes refuge behind the doctrine that it is due to some impenetrable and intangible talent for guessing correctly, some half mystical super sense, some vague (and, in essence, infra-human) instinct.