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Mathematics Quotes

Browse 2551 quotes about Mathematics.

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Mathematics Quotes

“I am obliged to interpolate some remarks on a very difficult subject: proof and its importance in mathematics. All physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof.”

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Author:G. H. Hardy
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“We chose to do this work mathematically, which has the advantage of precision but is not always appreciated by readers. It is perhaps for this reason that anthropologists have not shown much interest in these models, unlike economists, for example, for whom the use of mathematics poses no problem. However, one could reach the same conclusions by using just a bit of common sense.”

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Author:Luigi Luca Cavalli-Sforza
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“At the other end of the spectrum is, for example, graph theory, where the basic object, a graph, can be immediately comprehended. One will not get anywhere in graph theory by sitting in an armchair and trying to understand graphs better. Neither is it particularly necessary to read much of the literature before tackling a problem: it is of course helpful to be aware of some of the most important techniques, but the interesting problems tend to be open precisely because the established techniques cannot easily be applied.”

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Author:Timothy Gowers
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“Of the properties of mathematics, as a language, the most peculiar one is that by playing formal games with an input mathematical text, one can get an output text which seemingly carries new knowledge. The basic examples are furnished by scientific or technological calculations: general laws plus initial conditions produce predictions, often only after time-consuming and computer-aided work. One can say that the input contains an implicit knowledge which is thereby made explicit.”

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Author:IU?. I. Manin
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“In my own professional work I have touched on a variety of different fields. I've done work in mathematical linguistics, for example, without any professional credentials in mathematics; in this subject I am completely self-taught, and not very well taught.”

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Book:The Chomsky-Foucault Debate: On Human Nature
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“But on the other hand, in discussion and debate concerning social issues or American foreign policy, Vietnam or the Middle East, for example, the issue is constantly raised, often with considerable venom. I've repeatedly been challenged on grounds of credentials, or asked, what special training do you have that entitles you to speak of these matters. The assumption is that people like me, who are outsiders from a professional viewpoint, are not entitled to speak on such things.”

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Author:Noam Chomsky
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“My work on prime gaps lead to lots of media coverage, some good, some bad, some ugly, and some merely ridiculous. For example, a reporter of our university newspaper, who admitted that he is still learning English, wrote that "Prof. Goldston solved one of the most controversial problems in the prime number theory last month with support from his Turkish partner."”

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Author:Daniel Goldston
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“The second [argument about motion] is the so-called Achilles, and it amounts to this, that in a race the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. Statement of the Achilles and the Tortoise paradox in the relation of the discrete to the continuous.; perhaps the earliest example of the reductio ad absurdum method of proof.”

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Author:Zeno of Elea
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“A Christian boy or girl can learn mathematics, for example, from a teacher who is not a Christian; and truth is truth however learned. But while truth is truth however learned, the bearing of truth, the meaning of truth, the purpose of truth, even in the sphere of mathematics, seem entirely different to the Christian from that which they seem to the non-Christian; and that is why a truly Christian education is possible only when Christian conviction underlies not a part but all, of the curriculum of the school.”

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Book:What is Christianity?: And Other Addresses
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“Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. Fermat's Last Theorem is the most beautiful example of this.”

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Author:Andrew Wiles
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“There are problems to whose solution I would attach an infinitely greater importance than to those of mathematics, for example touching ethics, or our relation to God, or concerning our destiny and our future; but their solution lies wholly beyond us and completely outside the province of science.”

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Author:Carl Friedrich Gauss
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“The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. . . . Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.”

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Author:Alfred North Whitehead
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