Mathematics Quotes
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My first contact with game theory was a popular article in 'Fortune Magazine' which I read in my last high school year. I was immediately attracted to the subject matter, and when I studied mathematics, I found the fundamental book by von Neumann and Morgenstern in the library and studied it.
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The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation of it.
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Though determinants and matrices received a great deal of attention in the nineteenth century and thousands of papers were written on these subjects, they do not constitute great innovations in mathematics.... Neither determinants nor matrices have influenced deeply the course of mathematics despite their utility as compact expressions and despite the suggestiveness of matrices as concrete groups for the discernment of general theorems of group theory.
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When, therefore, I had long considered this uncertainty of traditional mathematics, it began to weary me that no more definite explanation of the movement of the world-machine established in our behalf by the best and most systematic builder of all, existed among the philosophers who had studied so exactly in other respects the minutest details in regard to the sphere.
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Mathematics is the art of accurate reasoning on inaccurately-drawn figures... let that be our motto.
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Numbers are the most certain things we have.
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The object of mathematics is the honor of the human spirit.
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Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent to a pair of ears. Mathematics can only be "seen" with the "eyes of the mind". It is as if we had no sense of hearing, so that only someone able to sight read music would be able to appreciate its patterns and harmonies.
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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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Both my parents instilled an interest in science and mathematics.
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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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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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We must always emphasize research and development of science and mathematics, and I can think of no better way to achieve this than through our future in space.
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The manuscript looks chaotic, even by mathematics standards.
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Logic has virtually nothing to do with the way we think.
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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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I think that mathematics can benefit by acknowledging that the creation of good models is just as important as proving deep theorems.
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Of Belief Human mathematics, so to speak, like the length of life, are subject to the doctrine of chances.
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With me, everything turns into mathematics.
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Algebraic geometry seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate.
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One can understand nature only when one has learned the language and the signs in which it speaks to us; but this language is mathematics and these signs are methematical figures.
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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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I would love to see music reinstated as an essential part of schooling. The culture that it brings; the knowledge that it brings. Just learning how to read music requires metrics, and I think that helps you with mathematics. A lot of scientists and doctors have a musical background - it's very interesting.
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The proof of Fermat's Last Theorem underscores how stable mathematics is through the centuries - how mathematics is one of humanity's long continuous conversations with itself.
