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In Math Quotes

Can the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesn’t make any sense since things follow from each other and, in principle, whoever knows the bases knows everything. All of the results of a mathematical theorem are in the axioms of mathematics in embryonic form, aren’t they? Picture Quote #1

Math is the beautiful, rich, joyful, playful, surprising, frustrating, humbling and creative art that speaks to something transcendental. It is worthy of much exploration and examination because it is intrinsically beautiful, nothing more to say. Why play the violin? Because it is beautiful! Why engage in math? Because it too is beautiful! Picture Quote #1

Logic leaves us no choice. In that sense, math always involves both invention and discovery: we invent the concepts but discover their consequences. … in mathematics our freedom lies in the questions we ask – and in how we pursue them – but not in the answers awaiting us Picture Quote #1

Deductivism in mathematical literature and inductivism in scientific papers are simply the postures we choose to be seen in when the curtain goes up and the public sees us. The theatrical illusion is shattered if we ask what goes on behind the scenes. In real life discovery and justification are almost always different processes Picture Quote #1

In math, you could get 100 percent. It was very fair. That’s what I liked about math. You could figure it out, and the teacher couldn’t have a stupid opinion about it Picture Quote #1

Very often in mathematics the crucial problem is to recognize and discover what are the relevant concepts; once this is accomplished the job may be more than half done Picture Quote #1

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In the current era, more than prodigies in mathematics, science, athletics, or art, I believe we need prodigies of good character and integrity. People who have polished their character and integrity until they shine are the ones who can be the real heroes the world needs to solve its problems. I think that, when people have the correct understanding of the meaning of human character, there will be a solution Picture Quote #1

I got good grades in math, but I never really enjoyed it. My favorite part of math was algebra, but geometry was the worst Picture Quote #1

Gauss replied, when asked how soon he expected to reach certain mathematical conclusions, that he had them long ago, all he was worrying about was how to reach them! Picture Quote #1

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

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

I have the vagary of taking a lively interest in mathematical subjects only where I may anticipate ingenious association of ideas and results recommending themselves by elegance or generality Picture Quote #1

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My mother was an economics professor. I’m proficient in math, and statistics, game theory, symbolic logic and all of that 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

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

In my teenage years I was put off the idea of a career in flying, because I’d convinced myself that you had to be a boffin with degrees in maths and physics, which were my weakest subjects Picture Quote #1

My background is in math and science, and I thrive on complexity, and I think lots of people do. People love puzzles; it’s human nature to want to solve puzzles Picture Quote #1

I never failed in mathematics. Before I was fifteen I had mastered differential and integral calculus Picture Quote #1

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When something is beautiful in math, everything is just perfectly lined up, and you see through sheer thought that something really beautiful can take place Picture Quote #1

Perspective is a most subtle discovery in mathematical studies, for by means of lines it causes to appear distant that which is near, and large that which is small Picture Quote #1

If a child is poor in math but good at tennis, most people would hire a math tutor. I would rather hire a tennis coach Picture Quote #1

Some of the greatest advances in mathematics have been due to the invention of symbols, which it afterwards became necessary to explain; from the minus sign proceeded the whole theory of negative quantities Picture Quote #1

I’d like to take some calculus, too. I have absolutely no ability in that direction and not much interest, either, but there’s something going on in mathematics that I don’t understand, and I’d like to find out what it is Picture Quote #1

Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence Picture Quote #1

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Our species is the only creative species, and it has only one creative instrument, the individual mind and spirit of man. Nothing was ever created by two men. There are no good collaborations, whether in music, in art, in poetry, in mathematics, in philosophy. Once the miracle of creation has taken place, the group can build and extend it, but the group never invents anything. The preciousness lies in the lonely mind of a man 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

Unlike physics, for example, such parts of the bare bones of economic theory as are expressible in mathematical form are extremely easy compared with the economic interpretation of the complex and incompletely known facts of experience, and lead one a very little way towards establishing useful results 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

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

I was a bit of an introvert growing up, and I tended to do better in math and science at school, so I went with it Picture Quote #1

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Can the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesn’t make any sense since things follow from each other and, in principle, whoever knows the bases knows everything. All of the results of a mathematical theorem are in the axioms of mathematics in embryonic form, aren’t they? (In Math Quotes) Math is the beautiful, rich, joyful, playful, surprising, frustrating, humbling and creative art that speaks to something transcendental. It is worthy of much exploration and examination because it is intrinsically beautiful, nothing more to say. Why play the violin? Because it is beautiful! Why engage in math? Because it too is beautiful! (In Math Quotes) Logic leaves us no choice. In that sense, math always involves both invention and discovery: we invent the concepts but discover their consequences. … in mathematics our freedom lies in the questions we ask – and in how we pursue them – but not in the answers awaiting us (In Math Quotes) Deductivism in mathematical literature and inductivism in scientific papers are simply the postures we choose to be seen in when the curtain goes up and the public sees us. The theatrical illusion is shattered if we ask what goes on behind the scenes. In real life discovery and justification are almost always different processes (In Math Quotes) In math, you could get 100 percent. It was very fair. That’s what I liked about math. You could figure it out, and the teacher couldn’t have a stupid opinion about it (In Math Quotes) Very often in mathematics the crucial problem is to recognize and discover what are the relevant concepts; once this is accomplished the job may be more than half done (In Math Quotes) In the current era, more than prodigies in mathematics, science, athletics, or art, I believe we need prodigies of good character and integrity. People who have polished their character and integrity until they shine are the ones who can be the real heroes the world needs to solve its problems. I think that, when people have the correct understanding of the meaning of human character, there will be a solution (In Math Quotes) I got good grades in math, but I never really enjoyed it. My favorite part of math was algebra, but geometry was the worst (In Math Quotes) Gauss replied, when asked how soon he expected to reach certain mathematical conclusions, that he had them long ago, all he was worrying about was how to reach them! (In Math 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 (In Math 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 (In Math Quotes) I have the vagary of taking a lively interest in mathematical subjects only where I may anticipate ingenious association of ideas and results recommending themselves by elegance or generality (In Math Quotes) My mother was an economics professor. I’m proficient in math, and statistics, game theory, symbolic logic and all of that (In Math 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 (In Math 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 (In Math Quotes) In my teenage years I was put off the idea of a career in flying, because I’d convinced myself that you had to be a boffin with degrees in maths and physics, which were my weakest subjects (In Math Quotes) My background is in math and science, and I thrive on complexity, and I think lots of people do. People love puzzles; it’s human nature to want to solve puzzles (In Math Quotes) I never failed in mathematics. Before I was fifteen I had mastered differential and integral calculus (In Math Quotes) When something is beautiful in math, everything is just perfectly lined up, and you see through sheer thought that something really beautiful can take place (In Math Quotes) Perspective is a most subtle discovery in mathematical studies, for by means of lines it causes to appear distant that which is near, and large that which is small (In Math Quotes) If a child is poor in math but good at tennis, most people would hire a math tutor. I would rather hire a tennis coach (In Math Quotes) Some of the greatest advances in mathematics have been due to the invention of symbols, which it afterwards became necessary to explain; from the minus sign proceeded the whole theory of negative quantities (In Math Quotes) I’d like to take some calculus, too. I have absolutely no ability in that direction and not much interest, either, but there’s something going on in mathematics that I don’t understand, and I’d like to find out what it is (In Math Quotes) Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence (In Math Quotes) Our species is the only creative species, and it has only one creative instrument, the individual mind and spirit of man. Nothing was ever created by two men. There are no good collaborations, whether in music, in art, in poetry, in mathematics, in philosophy. Once the miracle of creation has taken place, the group can build and extend it, but the group never invents anything. The preciousness lies in the lonely mind of a man (In Math 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 (In Math Quotes) Unlike physics, for example, such parts of the bare bones of economic theory as are expressible in mathematical form are extremely easy compared with the economic interpretation of the complex and incompletely known facts of experience, and lead one a very little way towards establishing useful results (In Math 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 (In Math 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 (In Math Quotes) I was a bit of an introvert growing up, and I tended to do better in math and science at school, so I went with it (In Math Quotes)

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