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Mathematical Quotes

The life and soul of science is its practical application, and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in the earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind Picture Quote #1

If others would but reflect on mathematical truths as deeply and continuously as I have, they would make my discoveries Picture Quote #1

You may object that by speaking of simplicity and beauty I am introducing aesthetic criteria of truth, and I frankly admit that I am strongly attracted by the simplicity and beauty of mathematical schemes which nature presents us. You must have felt this too: the almost frightening simplicity and wholeness of the relationship, which nature suddenly spreads out before us Picture Quote #1

Mathematical discoveries, like springtime violets in the woods, have their season which no human can hasten or retard Picture Quote #1

Another characteristic of mathematical thought is that it can have no success where it cannot generalize Picture Quote #1

... learning chiefly in mathematical sciences can so swallow up and fix one’s thought, as to possess it entirely for some time; but when that amusement is over, nature will return, and be where it was, being rather diverted than overcome by such speculations Picture Quote #1

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The great problem of today is, how to subject all physical phenomena to dynamical laws. With all the experimental devices, and all the mathematical appliances of this generation, the human mind has been baffled in its attempts to construct a universal science of physics Picture Quote #1

The more I study the things of the mind the more mathematical I find them. In them as in mathematics it is a question of quantities; they must be treated with precision. I have never had more satisfaction than in proving this in the realms of art, politics and history Picture Quote #1

It is probably no exaggeration to suppose that in order to improve such an organ as the eye at all, it must be improved in ten different ways at once. And the improbability of any complex organ being produced and brought to perfection in any such way is an improbability of the same kind and degree as that of producing a poem or a mathematical demonstration by throwing letters at random on a table Picture Quote #1

The usefulness of mathematics in furthering the sciences is commonly acknowledged: but outside the ranks of the experts there is little inquiry into its nature and purpose as a deliberate human activity. Doubtless this is due to the inevitable drawback that mathematical study is saturated with technicalities from beginning to end Picture Quote #1

There is nothing that can be said by mathematical symbols and relations which cannot also be said by words. The converse, however, is false. Much that can be and is said by words cannot successfully be put into equations, because it is nonsense Picture Quote #1

It is possible, of course, to operate with figures mechanically, just as it is possible to speak like a parrot: but that hardly deserves the names of thought. It only becomes possible at all after the mathematical notation has, as a result of genuine thought, been so developed that it does the thinking for us, so to speak Picture Quote #1

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The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking Picture Quote #1

Page after page of professional economic journals are filled with mathematical formulas leading the reader from sets of more or less plausible but entirely arbitrary assumptions to precisely stated but irrelevant theoretical conclusions Picture Quote #1

For far too long economists have sought to define themselves in terms of their supposedly scientific methods. In fact, those methods rely on an immoderate use of mathematical models, which are frequently no more than an excuse for occupying the terrain and masking the vacuity of the content Picture Quote #1

It is in this mutual dependence of the functions and the aid which they reciprocally lend one another that are founded the laws which determine the relations of their organs and which possess a necessity equal to that of metaphysical or mathematical laws, since it is evident that the seemly harmony between organs which interact is a necessary condition of existence of the creature to which they belong and that if one of these functions were modified in a manner incompatible with the modifications of the others the creature could no longer continue to exist Picture Quote #1

Also, it’s not the mathematical skill that’s critical to winning, it’s the discipline of being able to stick to the system. There are very few people who can withstand the losses emotionally and still stick with the system. Probably only one in five hundred people has the necessary discipline to be successful Picture Quote #1

There is, of course, great value in belonging to a group. Safety in numbers, for one. But there is also a mathematical explanation for why the brain is so willing to give up its own opinions: a group of people is more likely to be correct about something than an individual Picture Quote #1

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Life has puffed and blown itself into a summer day, and clouds and spring billow over the heavens as if calendars were a listing of mathematical errors Picture Quote #1

It is utterly implausible that a mathematical formula should make the future known to us, and those who think it can would once have believed in witchcraft Picture Quote #1

The mathematical is that evident aspect of things within which we are always already moving and according to which we experience them as things at all, and as such things. The mathematical is this fundamental position we take toward things by which we take up things as already given to us, and as they must and should be given. Therefore, the mathematical is the fundamental presupposition of the knowledge of things Picture Quote #1

The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there was never any other object for it Picture Quote #1

The calculative exactness of practical life which the money economy has brought about corresponds to the ideal of natural science: to transform the world by mathematical formulas. Only money economy has filled the days of so many people with weighing, calculating, with numerical determinations, with a reduction of qualitative values to quantitative ones Picture Quote #1

A display connected to a digital computer gives us a chance to gain familiarity with concepts not realizable in the physical world. It is a looking glass into a mathematical wonderland Picture Quote #1

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The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation Picture Quote #1

What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating Picture Quote #1

Like works of literature, mathematical ideas help expand our circle of empathy, liberating us from the tyranny of a single, parochial point of view. Numbers, properly considered, make us better people Picture Quote #1

It is clear that the chief end of mathematical study must be to make the students think Picture Quote #1

All the mathematical sciences are founded on the relations between physical laws and laws of numbers Picture Quote #1

Among all of the mathematical disciplines the theory of differential equations is the most important... It furnishes the explanation of all those elementary manifestations of nature which involve time Picture Quote #1

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The life and soul of science is its practical application, and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in the earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind (Mathematical Quotes) If others would but reflect on mathematical truths as deeply and continuously as I have, they would make my discoveries (Mathematical Quotes) You may object that by speaking of simplicity and beauty I am introducing aesthetic criteria of truth, and I frankly admit that I am strongly attracted by the simplicity and beauty of mathematical schemes which nature presents us. You must have felt this too: the almost frightening simplicity and wholeness of the relationship, which nature suddenly spreads out before us (Mathematical Quotes) Mathematical discoveries, like springtime violets in the woods, have their season which no human can hasten or retard (Mathematical Quotes) Another characteristic of mathematical thought is that it can have no success where it cannot generalize (Mathematical Quotes) ... learning chiefly in mathematical sciences can so swallow up and fix one’s thought, as to possess it entirely for some time; but when that amusement is over, nature will return, and be where it was, being rather diverted than overcome by such speculations (Mathematical Quotes) The great problem of today is, how to subject all physical phenomena to dynamical laws. With all the experimental devices, and all the mathematical appliances of this generation, the human mind has been baffled in its attempts to construct a universal science of physics (Mathematical Quotes) The more I study the things of the mind the more mathematical I find them. In them as in mathematics it is a question of quantities; they must be treated with precision. I have never had more satisfaction than in proving this in the realms of art, politics and history (Mathematical Quotes) It is probably no exaggeration to suppose that in order to improve such an organ as the eye at all, it must be improved in ten different ways at once. And the improbability of any complex organ being produced and brought to perfection in any such way is an improbability of the same kind and degree as that of producing a poem or a mathematical demonstration by throwing letters at random on a table (Mathematical Quotes) The usefulness of mathematics in furthering the sciences is commonly acknowledged: but outside the ranks of the experts there is little inquiry into its nature and purpose as a deliberate human activity. Doubtless this is due to the inevitable drawback that mathematical study is saturated with technicalities from beginning to end (Mathematical Quotes) There is nothing that can be said by mathematical symbols and relations which cannot also be said by words. The converse, however, is false. Much that can be and is said by words cannot successfully be put into equations, because it is nonsense (Mathematical Quotes) It is possible, of course, to operate with figures mechanically, just as it is possible to speak like a parrot: but that hardly deserves the names of thought. It only becomes possible at all after the mathematical notation has, as a result of genuine thought, been so developed that it does the thinking for us, so to speak (Mathematical Quotes) The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking (Mathematical Quotes) Page after page of professional economic journals are filled with mathematical formulas leading the reader from sets of more or less plausible but entirely arbitrary assumptions to precisely stated but irrelevant theoretical conclusions (Mathematical Quotes) For far too long economists have sought to define themselves in terms of their supposedly scientific methods. In fact, those methods rely on an immoderate use of mathematical models, which are frequently no more than an excuse for occupying the terrain and masking the vacuity of the content (Mathematical Quotes) It is in this mutual dependence of the functions and the aid which they reciprocally lend one another that are founded the laws which determine the relations of their organs and which possess a necessity equal to that of metaphysical or mathematical laws, since it is evident that the seemly harmony between organs which interact is a necessary condition of existence of the creature to which they belong and that if one of these functions were modified in a manner incompatible with the modifications of the others the creature could no longer continue to exist (Mathematical Quotes) Also, it’s not the mathematical skill that’s critical to winning, it’s the discipline of being able to stick to the system. There are very few people who can withstand the losses emotionally and still stick with the system. Probably only one in five hundred people has the necessary discipline to be successful (Mathematical Quotes) There is, of course, great value in belonging to a group. Safety in numbers, for one. But there is also a mathematical explanation for why the brain is so willing to give up its own opinions: a group of people is more likely to be correct about something than an individual (Mathematical Quotes) Life has puffed and blown itself into a summer day, and clouds and spring billow over the heavens as if calendars were a listing of mathematical errors (Mathematical Quotes) It is utterly implausible that a mathematical formula should make the future known to us, and those who think it can would once have believed in witchcraft (Mathematical Quotes) The mathematical is that evident aspect of things within which we are always already moving and according to which we experience them as things at all, and as such things. The mathematical is this fundamental position we take toward things by which we take up things as already given to us, and as they must and should be given. Therefore, the mathematical is the fundamental presupposition of the knowledge of things (Mathematical Quotes) The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there was never any other object for it (Mathematical Quotes) The calculative exactness of practical life which the money economy has brought about corresponds to the ideal of natural science: to transform the world by mathematical formulas. Only money economy has filled the days of so many people with weighing, calculating, with numerical determinations, with a reduction of qualitative values to quantitative ones (Mathematical Quotes) A display connected to a digital computer gives us a chance to gain familiarity with concepts not realizable in the physical world. It is a looking glass into a mathematical wonderland (Mathematical Quotes) The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation (Mathematical Quotes) What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating (Mathematical Quotes) Like works of literature, mathematical ideas help expand our circle of empathy, liberating us from the tyranny of a single, parochial point of view. Numbers, properly considered, make us better people (Mathematical Quotes) It is clear that the chief end of mathematical study must be to make the students think (Mathematical Quotes) All the mathematical sciences are founded on the relations between physical laws and laws of numbers (Mathematical Quotes) Among all of the mathematical disciplines the theory of differential equations is the most important... It furnishes the explanation of all those elementary manifestations of nature which involve time (Mathematical Quotes)

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