Cassius Jackson Keyser Quotes
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Absolute certainty is a privilege of uneducated minds and fanatics. - It is, for scientific folk, an unattainable ideal.
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If people would stop objectifying abstractions (which they probably never will), or if they would stop objectifying the abstractions they make consciously (which they might learn to do), at least half the pseudo-questions befuddling the world today - as they have befuddled it since time immemorial - would vanish. And that would be a very, very great gain.
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Mathematics is, in many ways, the most precious response that the human spirit has made to the call of the infinite.
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Mathematics, even in its present and most abstract state, is not detached from life. It is just the ideal handling of the problems of life.
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The pursuit of excellence is the proper vocation of man.
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The validity of mathematical propositions is independent of the actual world-the world of existing subject-matters-is logically prior to it, and would remain unaffected were it to vanish from being. Mathematical propositions, if true, are eternal verities.
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If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.
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[The] humanization of mathematical teaching, the bringing of the matter and the spirit of mathematics to bear not merely upon certain fragmentary faculties of the mind, but upon the whole mind, that this is the greatest desideratum is. I assume, beyond dispute.
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It is commonly, but erroneously, believed that it is easy to ask questions. A fool, it is said, can ask questions that a wise man cannot answer. The fact is that a wise man can answer many questions that a fool cannot ask.
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The next-most difficult thing in the world is to get perspective. The most difficult is to keep it.
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The present is no more exempt from the sneer of the future than the past has been.