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Mathematics Quotes

Of all the intellectual faculties, judgment is the last to mature. A child under the age of fifteen should confine its attention either to subjects like mathematics, in which errors of judgment are impossible, or to subjects in which they are not very dangerous, like languages, natural science, history, etc Picture Quote #1

How is it that there are so many minds that are incapable of understanding mathematics?... the skeleton of our understanding,... and actually they are the majority... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education Picture Quote #1

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 Picture Quote #1

This system in which a child is constantly moving objects with his hands and actively exercising his senses, also takes into account a child’s special aptitude for mathematics. When they leave the material, the children very easily reach the point where they wish to write out the operation. They can thus carryout an abstract mental operation and acquire a kind of natural and spontaneous inclination for mental calculations Picture Quote #1

Very few people can communicate with one another. The only language that’s not subject to interpretation is mathematics, chemistry, basic science, engineering principles, and applied agriculture. But other than that, many systems today are subject to interpretation Picture Quote #1

The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It’s like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design Picture Quote #1

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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 Picture Quote #1

Whereas young people become accomplished in geometry and mathematics, and wise within these limits, prudent young people do not seem to be found. The reason is that prudence is concerned with particulars as well as universals, and particulars become known from experience, but a young person lacks experience, since some length of time is needed to produce it Picture Quote #1

All those formal systems, in mathematics and physics and the philosophy of science, which claim to give foundations for certain truth are surely mistaken. I am tempted to say that we do not look for truth, but for knowledge. But I dislike this form of words, for two reasons. First of all, we do look for truth, however we define it, it is what we find that is knowledge. And second, what we fail to find is not truth, but certainty; the nature of truth is exactly the knowledge that we do find Picture Quote #1

To speak freely of mathematics, I find it the highest exercise of the spirit; but at the same time I know that it is so useless that I make little distinction between a man who is only a mathematician and a common artisan. Also, I call it the most beautiful profession in the world; but it is only a profession; Picture Quote #1

While physics and mathematics may tell us how the universe began, they are not much use in predicting human behavior because there are far too many equations to solve. I’m no better than anyone else at understanding what makes people tick, particularly women Picture Quote #1

Now do you not see that the eye embraces the beauty of the whole world? It counsels and corrects all the arts of mankind... it is the prince of mathematics, and the sciences founded on it are absolutely certain. It has measured the distances and sizes of the stars it has discovered the elements and their location... it has given birth to architecture and to perspective and to the divine art of painting Picture Quote #1

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It is hard to know what you are talking about in mathematics, yet no one questions the validity of what you say. There is no other realm of discourse half so queer Picture Quote #1

Now being in such grace and favor by reason I learned him some points of geometry and understanding of the art of mathematics with other things, I pleased him so that what I said he would not contrary Picture Quote #1

If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability Picture Quote #1

What affected me most profoundly was the realization that the sciences of cryptography and mathematics are very elegant, pure sciences. I found that the ends for which these pure sciences are used are less elegant Picture Quote #1

May not music be described as the mathematics of the sense, mathematics as music of the reason? the musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life Picture Quote #1

Mathematics takes us still further from what is human, into the region of absolute necessity, to which not only the world, but every possible world, must conform Picture Quote #1

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There are three intellectual pursuits, and, so far as I am aware, only three, in which human beings have performed major feats before the age of puberty. They are music, mathematics, and chess Picture Quote #1

It was not so much that I was doing mathematics, but rather that mathematics had taken possession of me Picture Quote #1

What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else Picture Quote #1

Mathematics is one of the essential emanations of the human spirit, a thing to be valued in and for itself, like art or poetry Picture Quote #1

The man who blames the supreme certainty of mathematics feeds on confusion, and can never silence the contradictions of sophistical sciences which lead to an eternal quackery Picture Quote #1

Angling may be said to be so like the mathematics that it can never be fully learnt Picture Quote #1

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Symmetry is a vast subject, significant in art and nature. Mathematics lies at its root, and it would be hard to find a better one on which to demonstrate the working of the mathematical intellect Picture Quote #1

It could be that the methods needed to take the next step may simply be beyond present day mathematics. Perhaps the methods I needed to complete the proof would not be invented for a hundred years Picture Quote #1

Well, 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 Picture Quote #1

In studying history we are finding out about ourselves, and in the last resort the natural sciences and even mathematics have the same final end Picture Quote #1

The law embodies the story of a nation’s development through many centuries, and it cannot be dealt with as if it contained only the axioms and corollaries of a book of mathematics Picture Quote #1

So if a man’s wit be wandering, let him study the mathematics; for in demonstrations, if his wit be called away never so little, he must begin again Picture Quote #1

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Of all the intellectual faculties, judgment is the last to mature. A child under the age of fifteen should confine its attention either to subjects like mathematics, in which errors of judgment are impossible, or to subjects in which they are not very dangerous, like languages, natural science, history, etc (Mathematics Quotes) How is it that there are so many minds that are incapable of understanding mathematics?... the skeleton of our understanding,... and actually they are the majority... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education (Mathematics Quotes) 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 (Mathematics Quotes) This system in which a child is constantly moving objects with his hands and actively exercising his senses, also takes into account a child’s special aptitude for mathematics. When they leave the material, the children very easily reach the point where they wish to write out the operation. They can thus carryout an abstract mental operation and acquire a kind of natural and spontaneous inclination for mental calculations (Mathematics Quotes) Very few people can communicate with one another. The only language that’s not subject to interpretation is mathematics, chemistry, basic science, engineering principles, and applied agriculture. But other than that, many systems today are subject to interpretation (Mathematics Quotes) The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It’s like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design (Mathematics Quotes) 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 (Mathematics Quotes) Whereas young people become accomplished in geometry and mathematics, and wise within these limits, prudent young people do not seem to be found. The reason is that prudence is concerned with particulars as well as universals, and particulars become known from experience, but a young person lacks experience, since some length of time is needed to produce it (Mathematics Quotes) All those formal systems, in mathematics and physics and the philosophy of science, which claim to give foundations for certain truth are surely mistaken. I am tempted to say that we do not look for truth, but for knowledge. But I dislike this form of words, for two reasons. First of all, we do look for truth, however we define it, it is what we find that is knowledge. And second, what we fail to find is not truth, but certainty; the nature of truth is exactly the knowledge that we do find (Mathematics Quotes) To speak freely of mathematics, I find it the highest exercise of the spirit; but at the same time I know that it is so useless that I make little distinction between a man who is only a mathematician and a common artisan. Also, I call it the most beautiful profession in the world; but it is only a profession; (Mathematics Quotes) While physics and mathematics may tell us how the universe began, they are not much use in predicting human behavior because there are far too many equations to solve. I’m no better than anyone else at understanding what makes people tick, particularly women (Mathematics Quotes) Now do you not see that the eye embraces the beauty of the whole world? It counsels and corrects all the arts of mankind... it is the prince of mathematics, and the sciences founded on it are absolutely certain. It has measured the distances and sizes of the stars it has discovered the elements and their location... it has given birth to architecture and to perspective and to the divine art of painting (Mathematics Quotes) It is hard to know what you are talking about in mathematics, yet no one questions the validity of what you say. There is no other realm of discourse half so queer (Mathematics Quotes) Now being in such grace and favor by reason I learned him some points of geometry and understanding of the art of mathematics with other things, I pleased him so that what I said he would not contrary (Mathematics Quotes) If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability (Mathematics Quotes) What affected me most profoundly was the realization that the sciences of cryptography and mathematics are very elegant, pure sciences. I found that the ends for which these pure sciences are used are less elegant (Mathematics Quotes) May not music be described as the mathematics of the sense, mathematics as music of the reason? the musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life (Mathematics Quotes) Mathematics takes us still further from what is human, into the region of absolute necessity, to which not only the world, but every possible world, must conform (Mathematics Quotes) There are three intellectual pursuits, and, so far as I am aware, only three, in which human beings have performed major feats before the age of puberty. They are music, mathematics, and chess (Mathematics Quotes) It was not so much that I was doing mathematics, but rather that mathematics had taken possession of me (Mathematics Quotes) What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else (Mathematics Quotes) Mathematics is one of the essential emanations of the human spirit, a thing to be valued in and for itself, like art or poetry (Mathematics Quotes) The man who blames the supreme certainty of mathematics feeds on confusion, and can never silence the contradictions of sophistical sciences which lead to an eternal quackery (Mathematics Quotes) Angling may be said to be so like the mathematics that it can never be fully learnt (Mathematics Quotes) Symmetry is a vast subject, significant in art and nature. Mathematics lies at its root, and it would be hard to find a better one on which to demonstrate the working of the mathematical intellect (Mathematics Quotes) It could be that the methods needed to take the next step may simply be beyond present day mathematics. Perhaps the methods I needed to complete the proof would not be invented for a hundred years (Mathematics Quotes) Well, 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 (Mathematics Quotes) In studying history we are finding out about ourselves, and in the last resort the natural sciences and even mathematics have the same final end (Mathematics Quotes) The law embodies the story of a nation’s development through many centuries, and it cannot be dealt with as if it contained only the axioms and corollaries of a book of mathematics (Mathematics Quotes) So if a man’s wit be wandering, let him study the mathematics; for in demonstrations, if his wit be called away never so little, he must begin again (Mathematics Quotes)

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