Mathematics Quotes
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Poincaré was a vigorous opponent of the theory that all mathematics can be rewritten in terms of the most elementary notions of classical logic; something more than logic, he believed, makes mathematics what it is.
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It has been a fortunate fact in the modern history of physical science that the scientist constructing a new theoretical system has nearly always found that the mathematics. . . required. . . had already been worked out by pure mathematicians for their own amusement. . . . The moral for statesmen would seem to be that, for proper scientific "planning", pure mathematics should be endowed fifty years ahead of scientists.
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The indispensability argument says (roughly) that if you have ample reason to accept an empirical scientific theory that makes indispensable use of mathematics, and that theory entails that numbers exist, then you have ample reason to accept that numbers exist. The argument affirms the antecedent of this conditional, and concludes that you have ample reason to believe that numbers exist. What is striking about this argument is that it seems to show that the empirical reasons that suffice for accepting a scientific theory also suffice for accepting a metaphysical claim.
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Everybody who reasons carefully about anything is making a contribution ... and if you abstract it away and send it to the Department of Mathematics they put it in books.
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Perhaps the most surprising thing about mathematics is that it is so surprising. The rules which we make up at the beginning seem ordinary and inevitable, but it is impossible to foresee their consequences. These have only been found out by long study, extending over many centuries. Much of our knowledge is due to a comparatively few great mathematicians such as Newton, Euler, Gauss, or Riemann; few careers can have been more satisfying than theirs. They have contributed something to human thought even more lasting than great literature, since it is independent of language.
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Though a skilled mathematician, Alfred Marshall used mathematics sparingly. He saw that excessive reliance on this instrument might lead us astray in pursuit of intellectual toys, imaginary problems not conforming to the conditions of real life: and further, might distort our sense of proportion by causing us to neglect factors that could not easily be worked up in the mathematical machine.
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I think mathematics is a vast territory. The outskirts of mathematics are the outskirts of mathematical civilization. There are certain subjects that people learn about and gather together. Then there is a sort of inevitable development in those fields. You get to the point where a certain theorem is bound to be proved, independent of any particular individual, because it is just in the path of development.
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It seems to me there's this grand mathematical world out there, and I am wandering through it and discovering fascinating phenomena that often totally suprise me. I do not think of mathemaatics as invented but rather discovered.
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The more I study the things of the mind the more mathematical I find them. In them as in mathematics it is a question of quantities; they must be treated with precision. I have never had more satisfaction than in proving this in the realms of art, politics and history.
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Atheism is the opium of the mathematicians. Atheism is the religion of Mathematics.
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It is given to us to live for the most part under the guidance of mathematics ... It is impossible to distinguish from other living creatures anyone who does not understand how to quantify.
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The propositions of mathematics are devoid of all factual content; they convey no information whatever on any empirical subject matter.
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Mathematics is often erroneously referred to as the science of common sense. Actually, it may transcend common sense and go beyond either imagination or intuition. It has become a very strange and perhaps frightening subject from the ordinary point of view, but anyone who penetrates into it will find a veritable fairyland, a fairyland which is strange, but makes sense, if not common sense.
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In mathematics I can report no deficiency, except it be that men do not sufficiently understand the excellent use of Pure Mathematics.
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There isn’t an education system on the planet that teaches dance everyday to children the way we teach them mathematics. Why?
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Religion has the same relation to man's heavenly condition that mathematics has to his earthly one: both the one and the other are merely the rules of the game. Belief in God and belief in numbers: local truth and truth of location.
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All the truths of mathematics are linked to each other, and all means of discovering them are equally admissible.
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Mathematics is like draughts in being suitable for the young, not too difficult, amusing, and without peril to the state.
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Mathematics is not a spectator sport!
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Strange as it may sound, the power of mathematics rests on its evasion of all unnecessary thought and on its wonderful saving of mental operations.
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Just like a man grieving because he has recently lost in his dreams some thing that he had never had in reality, or hoping that tomorrow he would dream that he found it again. That is how mathematics is created; it has its fatal flaw.
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Mathematics is universal. It's discovered by human beings, but the rules of mathematics are the same throughout the universe and the laws of the universe.
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[The error in the teaching of mathematics is that] mathematics is expected either to be immediately attractive to students on its own merits or to be accepted by students solely on the basis of the teacher's assurance that it will be helpful in later life. [And yet,] mathematlcs is the key to understanding and mastering our physical, social and biological worlds.
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My interest in the sciences started with mathematics in the very beginning, and later with chemistry in early high school and the proverbial home chemistry set.
