Mathematics Quotes
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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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I came into history from a primary concern with mathematics and science. This has been a tremendous help to me as a person and as a historian, although it must be admitted it has served to make my historical interpretations less conventional than may be acceptable of many of my colleagues in the field.
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I didn't feel comfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of everything and explore the world.
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In fact, the answer to the question "What is mathematics?" has changed several times during the course of history... It was only in the last twenty years or so that a definition of mathematics emerged on which most mathematicians agree: mathematics is the science of patterns.
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I had made an empirical discovery and it carried all the weight of a mathematical proof.
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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.
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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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We know that nature is described by the best of all possible mathematics because God created it.
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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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The highest form of pure thought is in mathematics.
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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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Though this be madness, yet there is method in't.
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Perhaps, a bigger point is that it is perfectly OK if something is unclear. That’s how I feel 90 percent of the time when I do mathematics, so welcome to my world! The feeling of confusion (even frustration, sometimes) is an essential part of being a mathematician. But look at the bright side: how boring would life be if everything in it could be understood with little effort! What makes doing mathematics so exciting is our desire to overcome this confusion; to understand; to lift the veil on the unknown. And the feeling of personal triumph when we do understand something makes it all worthwhile.
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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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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 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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On all levels primary, and secondary and undergraduate - mathematics is taught as an isolated subject with few, if any, ties to the real world. To students, mathematics appears to deal almost entirely with things whlch are of no concern at all to man.
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Atheism is the opium of the mathematicians. Atheism is the religion of Mathematics.
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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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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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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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Mathematics is not just a language. Mathematics is a language plus reasoning.
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Being exposed to theory, stimulated by a basic love of concepts and mathematics, was a marvelous experience.
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Mathematics is concerned with "all possible worlds."
