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Infinity is a floorless room without walls or ceiling.
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It is as if mathematics were the vegetables of the academic dinner: Everyone knows that they are good for you, but no one forces you to eat them.
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It is not of the essence of mathematics to be occupied with the ideas of number and quantity.
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It is the merest truism, evident at once to unsophisticated observation, that mathematics is a human invention.
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It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences.
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I’ve dealt with numbers all my life, of course, and after a while you begin to feel that each number has a personality of its own. A twelve is very different from a thirteen, for example. Twelve is upright, conscientious, intelligent, whereas thirteen is a loner, a shady character who won’t think twice about breaking the law to get what he wants. Eleven is tough, an outdoorsman who likes tramping through woods and scaling mountains; ten is rather simpleminded, a bland figure who always does what he’s told; nine is deep and mystical, a Buddha of contemplation….
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Like the crest of a peacock so is mathematics at the head of all knowledge.
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Math is like love : a simple idea but it can get complicated.
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Math is radical!
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Math is the queen of the sciences.
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Math is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.
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Math may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
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Math seems to endow one with something like a new sense.
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Mathematicians are like Frenchman: whatever you say to them they translate Into their own language, and forthwith it is something entirely different.
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Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.
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Mathematics are the most abstracted of knowledge.
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Mathematics has not a foot to stand upon which is not purely metaphysical.
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Mathematics is as much an aspect of culture as it is a collection of algorithms.
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Mathematics is not a book confined within a cover and bound between brazen clasps, whose contents it needs only patience to ransack; it is not a mine, whose treasures may take long to reduce into possession, but which fill only a limited number of veins and lodes; it is not a soil, whose fertility can be exhausted by the yield of successive harvests; it is not a continent or an ocean, whose area can be mapped out and its contour defined: it is limitless as that space which it finds too narrow for its aspirations; its possibilities are as infinite as the worlds which are forever crowding in and multiplying upon the astronomer’s gaze.
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Mathematics is the door and key to die sciences.
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