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Mathematics Quotes

The writing in mathematics text is not only laconic to a fault; it is cold, monotonous, dry, dull, and even ungrammatical... The books are not only printed by machines; they are written by machines Picture Quote #1

One of the chief duties of the mathematician in acting as an advisor... is to discourage... from expecting too much from mathematics Picture Quote #1

I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total Picture Quote #1

Mathematics and art are quite different. We could not publish so many papers that used, repeatedly, the same idea and still command the respect of our colleagues Picture Quote #1

I have tried, with little success, to get some of my friends to understand my amazement that the abstraction of integers for counting is both possible and useful. Is it not remarkable that 6 sheep plus 7 sheep makes 13 sheep; that 6 stones plus 7 stones make 13 stones? Is it not a miracle that the universe is so constructed that such a simple abstraction as a number is possible? To me this is one of the strongest examples of the unreasonable effectiveness of mathematics. Indeed, I find it both strange and unexplainable Picture Quote #1

It was not until some weeks later that I realized there is no need to restrict oneself to 2 by 2 matrices. One could go on to 4 by 4 matrices, and the problem is then easily soluable. In retrospect, it seems strange that one can be so much held up over such an elementary point. The resulting wave equation for the electron turned out to be very successful. It led to correct values for the spin and the magnetic moment. This was quite unexpected. The work all followed from a study of pretty mathematics, without any thought being given to these physical properties of the electron Picture Quote #1

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Arithmetic starts with the integers and proceeds by successively enlarging the number system by rational and negative numbers, irrational numbers, etc... But the next quite logical step after the reals, namely the introduction of infinitesimals, has simply been omitted. I think, in coming centuries it will be considered a great oddity in the history of mathematics that the first exact theory of infinitesimals was developed 300 years after the invention of the differential calculus Picture Quote #1

It is exceptional that one should be able to acquire the understanding of a process without having previously acquired a deep familiarity with running it, with using it, before one has assimilated it in an instinctive and empirical way... Thus any discussion of the nature of intellectual effort in any field is difficult, unless it presupposes an easy, routine familiarity with that field. In mathematics this limitation becomes very severe Picture Quote #1

Mathematics is ordinarily considered as producing precise and dependable results; but in the stock market the more elaborate and abstruse the mathematics the more uncertain and speculative are the conclusions we draw there from. Whenever calculus is brought in, or higher algebra, you could take it as a warning that the operator was trying to substitute theory for experience, and usually also to give to speculation the deceptive guise of investment Picture Quote #1

If it squirms, it’s biology; if it stinks, it’s chemistry; if it doesn’t work, it’s physics; and if you can’t understand it, it’s mathematics Picture Quote #1

One might say the computer is being used to program the child. In my vision, the child programs the computer, and in doing so, both acquires a sense of mastery over a piece of the most modern and powerful technology and establishes an intense contact with some of the deepest ideas from science, from mathematics, and from the art of intellectual model building Picture Quote #1

The mathematics are the friends of religion, inasmuch as they charm the passions, restrain the impetuosity of the imagination, and purge the mind of error and prejudice Picture Quote #1

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Quantum physics is a bit of a passion of mine. It’s extraordinary. There’s a branch of mathematics that is based on lunacy, and that’s wonderful Picture Quote #1

I hated science in high school. Technology? Engineering? Math? Why would I ever need this? Little did I realize that music was also about science, technology, engineering and mathematics, all rolled into one Picture Quote #1

One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That’s so unlike the true nature of mathematics Picture Quote #1

The increased abstraction in mathematics that took place during the early part of this century was paralleled by a similar trend in the arts. In both cases, the increased level of abstraction demands greater effort on the part of anyone who wants to understand the work Picture Quote #1

It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations Picture Quote #1

Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It’s the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation Picture Quote #1

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The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation of it Picture Quote #1

Neumann, to a physicist seeking help with a difficult problem: Simple. This can be solved by using the method of characteristics. Physicist: I’m afraid I don’t understand the method of characteristics. Neumann: In mathematics you don’t understand things. You just get used to them Picture Quote #1

I wasn’t actually very naturally good at economics. My brain doesn’t work very well, in terms of mathematics Picture Quote #1

The problem is that modern fundamental physics is so far from you and me. The mathematics has become so much more complicated that you need at least 10 years to understand it. Fundamental physics has advanced so far from the understanding of most people that there is really a big disconnect Picture Quote #1

It was as though applied mathematics was my spouse, and pure mathematics was my secret lover Picture Quote #1

Mathematics directs the flow of the universe, lurks behind its shapes and curves, holds the reins of everything from tiny atoms to the biggest stars Picture Quote #1

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The tree is made by nature, mathematics by people. And combining the two is creating this beautiful alliance between humanity and nature. That’s why my forests are mathematical expansion systems, all of them Picture Quote #1

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 Picture Quote #1

Mathematics is not merely an idle art form, it is an essential part of our society Picture Quote #1

You know we’re constantly taking. We don’t make most of the food we eat, we don’t grow it, anyway. We wear clothes other people make, we speak a language other people developed, we use a mathematics other people evolved and spent their lives building. I mean we’re constantly taking things. It’s a wonderful ecstatic feeling to create something and put it into the pool of human experience and knowledge Picture Quote #1

I was lucky to get into computers when it was a very young and idealistic industry. There weren’t many degrees offered in computer science, so people in computers were brilliant people from mathematics, physics, music, zoology, whatever. They loved it, and no one was really in it for the money Picture Quote #1

I work with a lot of mathematicians, and one thing I notice about them is that they are not particularly fast with numbers; in fact some of them are rather slow. This is not a bad thing; they are slow because they think deeply and carefully about mathematics Picture Quote #1

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The writing in mathematics text is not only laconic to a fault; it is cold, monotonous, dry, dull, and even ungrammatical... The books are not only printed by machines; they are written by machines (Mathematics Quotes) One of the chief duties of the mathematician in acting as an advisor... is to discourage... from expecting too much from mathematics (Mathematics Quotes) I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total (Mathematics Quotes) Mathematics and art are quite different. We could not publish so many papers that used, repeatedly, the same idea and still command the respect of our colleagues (Mathematics Quotes) I have tried, with little success, to get some of my friends to understand my amazement that the abstraction of integers for counting is both possible and useful. Is it not remarkable that 6 sheep plus 7 sheep makes 13 sheep; that 6 stones plus 7 stones make 13 stones? Is it not a miracle that the universe is so constructed that such a simple abstraction as a number is possible? To me this is one of the strongest examples of the unreasonable effectiveness of mathematics. Indeed, I find it both strange and unexplainable (Mathematics Quotes) It was not until some weeks later that I realized there is no need to restrict oneself to 2 by 2 matrices. One could go on to 4 by 4 matrices, and the problem is then easily soluable. In retrospect, it seems strange that one can be so much held up over such an elementary point. The resulting wave equation for the electron turned out to be very successful. It led to correct values for the spin and the magnetic moment. This was quite unexpected. The work all followed from a study of pretty mathematics, without any thought being given to these physical properties of the electron (Mathematics Quotes) Arithmetic starts with the integers and proceeds by successively enlarging the number system by rational and negative numbers, irrational numbers, etc... But the next quite logical step after the reals, namely the introduction of infinitesimals, has simply been omitted. I think, in coming centuries it will be considered a great oddity in the history of mathematics that the first exact theory of infinitesimals was developed 300 years after the invention of the differential calculus (Mathematics Quotes) It is exceptional that one should be able to acquire the understanding of a process without having previously acquired a deep familiarity with running it, with using it, before one has assimilated it in an instinctive and empirical way... Thus any discussion of the nature of intellectual effort in any field is difficult, unless it presupposes an easy, routine familiarity with that field. In mathematics this limitation becomes very severe (Mathematics Quotes) Mathematics is ordinarily considered as producing precise and dependable results; but in the stock market the more elaborate and abstruse the mathematics the more uncertain and speculative are the conclusions we draw there from. Whenever calculus is brought in, or higher algebra, you could take it as a warning that the operator was trying to substitute theory for experience, and usually also to give to speculation the deceptive guise of investment (Mathematics Quotes) If it squirms, it’s biology; if it stinks, it’s chemistry; if it doesn’t work, it’s physics; and if you can’t understand it, it’s mathematics (Mathematics Quotes) One might say the computer is being used to program the child. In my vision, the child programs the computer, and in doing so, both acquires a sense of mastery over a piece of the most modern and powerful technology and establishes an intense contact with some of the deepest ideas from science, from mathematics, and from the art of intellectual model building (Mathematics Quotes) The mathematics are the friends of religion, inasmuch as they charm the passions, restrain the impetuosity of the imagination, and purge the mind of error and prejudice (Mathematics Quotes) Quantum physics is a bit of a passion of mine. It’s extraordinary. There’s a branch of mathematics that is based on lunacy, and that’s wonderful (Mathematics Quotes) I hated science in high school. Technology? Engineering? Math? Why would I ever need this? Little did I realize that music was also about science, technology, engineering and mathematics, all rolled into one (Mathematics Quotes) One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That’s so unlike the true nature of mathematics (Mathematics Quotes) The increased abstraction in mathematics that took place during the early part of this century was paralleled by a similar trend in the arts. In both cases, the increased level of abstraction demands greater effort on the part of anyone who wants to understand the work (Mathematics Quotes) It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations (Mathematics Quotes) Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It’s the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation (Mathematics Quotes) The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation of it (Mathematics Quotes) Neumann, to a physicist seeking help with a difficult problem: Simple. This can be solved by using the method of characteristics. Physicist: I’m afraid I don’t understand the method of characteristics. Neumann: In mathematics you don’t understand things. You just get used to them (Mathematics Quotes) I wasn’t actually very naturally good at economics. My brain doesn’t work very well, in terms of mathematics (Mathematics Quotes) The problem is that modern fundamental physics is so far from you and me. The mathematics has become so much more complicated that you need at least 10 years to understand it. Fundamental physics has advanced so far from the understanding of most people that there is really a big disconnect (Mathematics Quotes) It was as though applied mathematics was my spouse, and pure mathematics was my secret lover (Mathematics Quotes) Mathematics directs the flow of the universe, lurks behind its shapes and curves, holds the reins of everything from tiny atoms to the biggest stars (Mathematics Quotes) The tree is made by nature, mathematics by people. And combining the two is creating this beautiful alliance between humanity and nature. That’s why my forests are mathematical expansion systems, all of them (Mathematics Quotes) 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 (Mathematics Quotes) Mathematics is not merely an idle art form, it is an essential part of our society (Mathematics Quotes) You know we’re constantly taking. We don’t make most of the food we eat, we don’t grow it, anyway. We wear clothes other people make, we speak a language other people developed, we use a mathematics other people evolved and spent their lives building. I mean we’re constantly taking things. It’s a wonderful ecstatic feeling to create something and put it into the pool of human experience and knowledge (Mathematics Quotes) I was lucky to get into computers when it was a very young and idealistic industry. There weren’t many degrees offered in computer science, so people in computers were brilliant people from mathematics, physics, music, zoology, whatever. They loved it, and no one was really in it for the money (Mathematics Quotes) I work with a lot of mathematicians, and one thing I notice about them is that they are not particularly fast with numbers; in fact some of them are rather slow. This is not a bad thing; they are slow because they think deeply and carefully about mathematics (Mathematics Quotes)

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