Alfred North Whitehead Quotes About Mathematics
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No Roman ever died in contemplation over a geometrical diagram.
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The pursuit of mathematics is a divine madness of the human spirit.
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Our minds are finite, and yet even in these circumstances of finitude we are surrounded by possibilities that are infinite, and the purpose of life is to grasp as much as we can out of that infinitude.
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In the study of ideas, it is necessary to remember that insistence on hard-headed clarity issues from sentimental feeling, as it were a mist, cloaking the perplexities of fact. Insistence on clarity at all costs is based on sheer superstition as to the mode in which human intelligence functions. Our reasonings grasp at straws for premises and float on gossamers for deductions.
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The study of mathematics is apt to commence in disappointment... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.
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In modern times the belief that the ultimate explanation of all things was to be found in Newtonian mechanics was an adumbration of the truth that all science, as it grows towards perfection, becomes mathematical in its ideas.
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Algebra reverses the relative importance of the factors in ordinary language. It is essentially a written language, and it endeavors to exemplify in its written structures the patterns which it is its purpose to convey. The pattern of the marks on paper is a particular instance of the pattern to be conveyed to thought. The algebraic method is our best approach to the expression of necessity, by reason of its reduction of accident to the ghostlike character of the real variable.
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War can protect; it cannot create.
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Mathematics as a science, commenced when first someone, probably a Greek, proved propositions about "any" things or about "some" things, without specifications of definite particular things.
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It is a profoundly erroneous truism, repeated by all copy books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them.
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There is a tradition of opposition between adherents of induction and of deduction. In my view it would be just as sensible for the two ends of a worm to quarrel.
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"One and one make two" assumes that the changes in the shift of circumstance are unimportant. But it is impossible for us to analyze this notion of unimportant change.
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It is more important that a proposition be interesting than that it be true. This statement is almost a tautology. For the energy of operation of a proposition in an occasion of experience is its interest and is its importance. But of course a true proposition is more apt to be interesting than a false one.
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From the very beginning of his education, the child should experience the joy of discovery.
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The whole of mathematics consists in the organization of a series of aids to the imagination in the process of reasoning.
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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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The science of pure mathematics, in its modern developments, may claim to be the most original creation of the human spirit.
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Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world.
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There is no nature at an instant.
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I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting Hamlet from the play which is named after him. That would be claiming too much. But it is certainly analogous to cutting out the part of Ophelia. This simile is singularly exact. For Ophelia is quite essential to the play, she is very charming . . . and a little mad.
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Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.
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Everything of importance has been said before by somebody who did not discover it.
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Apart from blunt truth, our lives sink decadently amid the perfume of hints and suggestions.
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The study of mathematics is apt to commence in disappointment.
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Life is an offensive, directed against the repetitious mechanism of the Universe.
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Fundamental progress has to do with the reinterpretation of basic ideas.
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So far as the mere imparting of information is concerned, no university has had any justification for existence since the popularization of printing in the fifteenth century.
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On the ostensible exactitude of certain branches of human knowledge, including mathematics. The exactness is a fake.
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Order is not sufficient. What is required, is something much more complex. It is order entering upon novelty; so that the massiveness of order does not degenerate into mere repetition; and so that the novelty is always reflected upon a background of system.
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Alfred North Whitehead
- Born: February 15, 1861
- Died: December 30, 1947
- Occupation: Mathematician
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