A Quote by Joseph Warren
Mathematicians use intuition, conjecture and guesswork all the time except when they are in the classroom.
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Philosophers need not much use the word 'intuition' or the concept of intuition, except when they happen to be working on the epistemology of the a priori.
Mathematicians create by acts of insights and intuition. Logic then sanctions the conquests of intuition.
Intuition is a combination of insight and imagination that was once attributed to spiritual communication. Mathematicians call it 'fuzzy logic,' drawing conclusions from vague or subjective input. The mind becomes aware without the direct intervention of reasoning. Once you can imagine something you can begin the process of creating it. Executives use intuition to make many product, investment, and hiring decisions, even if they deny it. Success in business may depend on an accurate gut.
Women never use their intelligence, except when they need to prop up their intuition.
The educational highlights I remember were not in the classroom. My father spent a lot of time with me when he could. He taught me how to take square roots, a skill I have retained but do not use often, except to check that I still remember.
It is not rational to assume, without evidence, that rationality can disclose everything about the world, just because it can disclose some things. Our intuition in favour of rationality, where we are inclined to use it, is just that - an intuition. Reason is founded in intuition and ends in intuition, like a pair of massive bookends.
Coming back to America was, for me, much more of a culture shock than going to India. The people in the Indian countryside don't use their intellect like we do, they use their intuition instead, and their intuition is far more developed than in the rest of the world. Intuition is a very powerful thing, more powerful than intellect in my opinion. That's had a big impact on my work.
The fact is that everybody around a college basketball game - the coaches, the announcers, even the referees at a lower level - calculates when the game is really over. They calculate it with intuition and guesswork.
Mathematicians have been hiding and writing messages in the genetic code for a long time, but it's clear they were mathematicians and not biologists because, if you write long messages with the code that the mathematicians developed, it would more than likely lead to new proteins being synthesized with unknown functions.
Every man has a feminine side, and every woman a masculine side. It is important to use discipline with intuition, and to use intuition with objectivity.
Bilingual-education advocates say it's important to teach a child in his or her family's language. I say you can't use family language in the classroom - the very nature of the classroom requires that you use language publicly.
Conjecture as to things useful, is good; but conjecture as to what it would be useless to know, is very idle.
Relations between pure and applied mathematicians are based on trust and understanding.
Namely, pure mathematicians do not trust applied mathematicians, and applied mathematicians do not understand pure mathematicians.
Because Mathematicians frequently make use of Time, they ought to have a distinct idea of the meaning of that Word, otherwise they are Quacks.
[Adams] supposed that, except musicians, everyone thought Beethoven a bore, as every one except mathematicians thought mathematics a bore.
They [the mathematicians of the Enlightenment] defined their terms vaguely and used their methods loosely, and the logic of their arguments was made to fit the dictates of their intuition. In short, they broke all the laws of rigor and of mathematical decorum. The veritable orgy which followed the introduction of the infinitesimals... was but a natural reaction. Intuition had too long been held imprisoned by the severe rigor of the Greeks. Now it broke loose, and there were no Euclids to keep its romantic flight in check.
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