Stefan Banach Quotes
Good mathematicians see analogies. Great mathematicians see analogies between analogies.
Quotes to Explore
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I often make the analogy with tennis. Every match the rules are the same, but no game is ever the same. Theatre is like that. Every time is different.
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An artist has to train his responses more than other people do. He has to be as disciplined as a mathematician. Discipline is not a restriction but an aid to freedom. It prepares an artist to choose his own limitations.
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Mathematicians aren't satisfied because they know there are no solutions up to four million or four billion, they really want to know that there are no solutions up to infinity.
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Life is like a box of terrible analogies...
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I myself, a professional mathematician, on re-reading my own work find it strains my mental powers to recall to mind from the figures the meanings of the demonstrations, meanings which I myself originally put into the figures and the text from my mind. But when I attempt to remedy the obscurity of the material by putting in extra words, I see myself falling into the opposite fault of becoming chatty in something mathematical.
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The Internet gives you access to a lot of material, and it's fun to sit and read. I go to something like Wikipedia and look at different topics... I find the subject fascinating. I like to read about concepts and mathematicians.
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A mathematician of the first rank, Laplace quickly revealed himself as only a mediocre administrator; from his first work we saw that we had been deceived. Laplace saw no question from its true point of view; he sought subtleties everywhere; had only doubtful ideas, and finally carried the spirit of the infinitely small into administration.
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Dess shook her head. "Before he walked off, Rex said for you to wait. He said it's totally important you don't touch Angie until he comes back. and he said that if you were a pain about it, I get to hit you with that." She pointed to where the darkling had flung Flabbergasted Supernumerary Mathematician, its tip blackened by ichor and fire. "So, go ahead.
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It seems to me that the poet has only to perceive that which others do not perceive, to look deeper than others look. And the mathematician must do the same thing.
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The mathematicians are the priests of the modern world.
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“A mathematician who is not also something of a poet will never be a complete mathematician.”
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In short, I do not write for mathematicians, nor as a mathematician, but as an economist wishing to convince other economists that their science can only be satisfactorily treated on an explicitly mathematical basis.
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Eventually, I believe, current attempts to understand the mind by analogy with man-made computers that can perform superbly some of the same external tasks as conscious beings will be recognized as a gigantic waste of time.
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I do not think that G. H. Hardy was talking nonsense when he insisted that the mathematician was discovering rather than creating... The world for me is a necessary system, and in the degree to which the thinker can surrender his thought to that system and follow it, he is in a sense participating in that which is timeless or eternal.
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I love only nature, and I hate mathematicians.
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While analogies are useful, however, they can also be misleading. They smuggle in assumptions that can be wrong.
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If there is a God, he's a great mathematician.
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A mathematician is a scientist who can figure out anything except such simple things as squaring the circle and trisecting an angle.
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One of the unique aspects of rowing is that novices strive to perfect the same motions as Olympic contenders. Few other sports can make this claim. In figure skating, for instance, the novice practices only simple moves. After years of training, the skater then proceeds to the jumps and spins that make up an elite skater's program. But the novice rower, from day one, strives to duplicate a motion that he'll still be doing on the day of the Olympic finals.
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It's not what we eat but what we digest that makes us strong; not what we gain but what we save that makes us rich; not what we read but what we remember that makes us learned; and not what we profess but what we practice that gives us integrity.
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You say, "Where goest Thou?" I cannot tell, And still go on. But if the way be straight I cannot go amiss: before me lies Dawn and the day: the night behind me: that Suffices me: I break the bounds: I see, And nothing more; believe and nothing less. My future is not one of my concerns.
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Good mathematicians see analogies. Great mathematicians see analogies between analogies.
