Bertrand Russell Quotes About Mathematics
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Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.
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Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.
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The true spirit of delight...is to be found in mathematics as surely as in poetry.
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Inferences of Science and Common Sense differ from those of deductive logic and mathematics in a very important respect, namely, when the premises are true and the reasoning correct, the conclusion is only probable.
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Aristotle maintained that women have fewer teeth than men; although he was twice married, it never occurred to him to verify this statement by examining his wives' mouths.
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Only mathematics and mathematical logic can say as little as the physicist means to say.
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What is best in mathematics deserves not merely to be learnt as a task, but to assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement.
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To a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-footed animal is an animal.
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... the word "theory" ... was originally an Orphic word, which Cornford interprets as "passionate sympathetic contemplation" ... For Pythagoras, the "passionate sympathetic contemplation" was intellectual, and issued in mathematical knowledge ... To those who have reluctantly learnt a little mathematics in school this may seem strange; but to those who have experienced the intoxicating delight of sudden understanding that mathematics gives, from time to time, to those who love it, the Pythagorean view will seem completely natural.
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But I simply can't stand a view limited to this earth, I feel life is so small unless it has windows into other worlds...I like mathematics largely because it is not human.
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At the age of eleven, I began Euclid, with my brother as my tutor. This was one of the great events of my life, as dazzling as first love. I had not imagined there was anything so delicious in the world. From that moment until I was thirty-eight, mathematics was my chief interest and my chief source of happiness.
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Mathematics, rightly viewed, possesses not only truth, but supreme beauty-a beauty cold and austere ... yet sublimely pure and capable of stern perfection such as only the greatest art can show.
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Mathematics rightly viewed possesses not only truth but supreme beauty.
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Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.
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Men who are unhappy, like men who sleep badly, are always proud of the fact.
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Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then suchand such another proposition is true of that thing.... Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
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I hold all knowledge that is concerned with things that actually exist - all that is commonly called Science - to be of very slight value compared to the knowledge which, like philosophy and mathematics, is concerned with ideal and eternal objects, and is freed from this miserable world which God has made.
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Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos [mathematics], where pure thought can dwell in its natural home.
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It seems to us unwise to have insisted on teaching geometry to the younger Dionysius, tyrant of Syracuse, in order to make him a good king, but from Plato's point of view it was essential. He was sufficiently Pythagorean to think that without mathematics no true wisdom is possible.
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Sir Arthur Eddington deduces religion from the fact that atoms do not obey the laws of mathematics. Sir James Jeans deduces it from the fact that they do.
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Of these austerer virtues the love of truth is the chief, and in mathematics, more than elsewhere, the love of truth may find encouragement for waning faith. Every great study is not only an end in itself, but also a means of creating and sustaining a lofty habit of mind; and this purpose should be kept always in view throughout the teaching and learning of mathematics.
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A habit of basing convictions upon evidence, and of giving to them only that degree or certainty which the evidence warrants, would, if it became general, cure most of the ills from which the world suffers.
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Mathematics is, I believe, the chief source of the belief in eternal and exact truth, as well as a sensible intelligible world.
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For a good notation has a subtlety and suggestiveness which at times make it seem almost like a live teacher.
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In adolescence, I hated life and was continually on the verge of suicide, from which, however, I was restrained by the desire to know more mathematics. Now, on the contrary, I enjoy life; I might almost say that with every year that passes I enjoy it more.
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Bacon not only despised the syllogism, but undervalued mathematics, presumably as insufficiently experimental. He was virulently hostile to Aristotle , but he thought very highly of Democritus , Although he did not deny that the course of nature exemplifies a Divine purpose, he objected to any admixture of teleological explanation in the actual investigation of phenomena; everything, he held, should be explained as following necessarily from efficient causes .
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Zeno was concerned with three problems... These are the problem of the infinitesimal, the infinite, and continuity.
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The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself.
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It seems to me now that mathematics is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the number of people who feel it, to that of music, but because it gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect and yet true.
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Formality Thus the absence of all mention of particular things or properties in logic or pure mathematics is a necessary result of the fact that this study is, as we say, "purely formal".
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