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Theorems Quotes

Young men should prove theorems, old men should write books Picture Quote #1

Economists often like startling theorems, results which seem to run counter to conventional wisdom Picture Quote #1

I have found a very great number of exceedingly beautiful theorems Picture Quote #1

Without computers we will be stuck only proving theorems that have short proofs Picture Quote #1

Response, when asked how he came upon his theorems Picture Quote #1

A mathematician is a device for turning coffee into theorems Picture Quote #1

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The product of mathematics is clarity and understanding. Not theorems, by themselves... In short, mathematics only exists in a living community of mathematicians that spreads understanding and breathes life into ideas both old and new Picture Quote #1

The theory of numbers, more than any other branch of mathematics, began by being an experimental science. Its most famous theorems have all been conjectured, sometimes a hundred years or more before they were proved; and they have been suggested by the evidence of a mass of computations Picture Quote #1

Humans like to think of themselves as unusual. We’ve got big brains that make it possible for us to think, and we think that we have free will and that our behavior can’t be described by some mechanistic set of theorems or ideas. But even in terms of much of our behavior, we really aren’t very different from other animals Picture Quote #1

Less depends upon the choice of words than upon this, that their introduction shall be justified by pregnant theorems Picture Quote #1

How many theorems in geometry which have seemed at first impracticable are in time successfully worked out! Picture Quote #1

I compare arithmetic with a tree that unfolds upwards in a multitude of techniques and theorems while the root drives into the depths Picture Quote #1

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There are infinitely many variations of the initial situation and therefore no doubt indefinitely many theorems of moral geometry Picture Quote #1

That’s the problem with false proofs of true theorems; it’s not easy to produce a counterexample Picture Quote #1

Math does come easily to me, but I was always much more interested in what theorems imply about the world than in proving them 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

He knew by heart every last minute crack on its surface. He had made maps of the ceiling and gone exploring on them; rivers, islands, and continents. He had made guessing games of it and discovered hidden objects; faces, birds, and fishes. He made mathematical calculations of it and rediscovered his childhood; theorems, angles, and triangles. There was practically nothing else he could do but look at it. He hated the sight of it Picture Quote #1

Mathematicians can and do fill in gaps, correct errors, and supply more detail and more careful scholarship when they are called on or motivated to do so. Our system is quite good at producing reliable theorems that can be solidly backed up. It’s just that the reliability does not primarily come from mathematicians formally checking formal arguments; it comes from mathematicians thinking carefully and critically about mathematical ideas Picture Quote #1

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A peculiarity of the higher arithmetic is the great difficulty which has often been experienced in proving simple general theorems which had been suggested quite naturally by numerical evidence Picture Quote #1

For what is important when we give children a theorem to use is not that they should memorize it. What matters most is that by growing up with a few very powerful theorems one comes to appreciate how certain ideas can be used as tools to think with over a lifetime. One learns to enjoy and to respect the power of powerful ideas. One learns that the most powerful idea of all is the idea of powerful ideas Picture Quote #1

The fundamental laws of the universe which correspond to the two fundamental theorems of the mechanical theory of heat.1. The energy of the universe is constant.2. The entropy of the universe tends to a maximum Picture Quote #1

I approached the bulk of my schoolwork as a chore rather than an intellectual adventure. The tedium was relieved by a few courses that seem to be qualitatively different. Geometry was the first exciting course I remember. Instead of memorizing facts, we were asked to think in clear, logical steps. Beginning from a few intuitive postulates, far reaching consequences could be derived, and I took immediately to the sport of proving theorems Picture Quote #1

If all sentient beings in the universe disappeared, there would remain a sense in which mathematical objects and theorems would continue to exist even though there would be no one around to write or talk about them. Huge prime numbers would continue to be prime, even if no one had proved them prime Picture Quote #1

You can learn to find unknowns in equations, draw equidistant lines and demonstrate theorems, but in real life there’s nothing to position, calculate, or guess Picture Quote #1

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When a truth is necessary, the reason for it can be found by analysis, that is, by resolving it into simpler ideas and truths until the primary ones are reached. It is this way that in mathematics speculative theorems and practical canons are reduced by analysis to definitions, axioms and postulates Picture Quote #1

There are three signs of senility. The first sign is that a man forgets his theorems. The second sign is that he forgets to zip up. The third sign is that he forgets to zip down Picture Quote #1

The pursuit of pretty formulas and neat theorems can no doubt quickly degenerate into a silly vice, but so can the quest for austere generalities which are so very general indeed that they are incapable of application to any particular Picture Quote #1

A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories Picture Quote #1

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Young men should prove theorems, old men should write books (Theorems Quotes) Economists often like startling theorems, results which seem to run counter to conventional wisdom (Theorems Quotes) I have found a very great number of exceedingly beautiful theorems (Theorems Quotes) Without computers we will be stuck only proving theorems that have short proofs (Theorems Quotes) Response, when asked how he came upon his theorems (Theorems Quotes) A mathematician is a device for turning coffee into theorems (Theorems Quotes) The product of mathematics is clarity and understanding. Not theorems, by themselves... In short, mathematics only exists in a living community of mathematicians that spreads understanding and breathes life into ideas both old and new (Theorems Quotes) The theory of numbers, more than any other branch of mathematics, began by being an experimental science. Its most famous theorems have all been conjectured, sometimes a hundred years or more before they were proved; and they have been suggested by the evidence of a mass of computations. (Theorems Quotes) Humans like to think of themselves as unusual. We’ve got big brains that make it possible for us to think, and we think that we have free will and that our behavior can’t be described by some mechanistic set of theorems or ideas. But even in terms of much of our behavior, we really aren’t very different from other animals. (Theorems Quotes) Less depends upon the choice of words than upon this, that their introduction shall be justified by pregnant theorems (Theorems Quotes) How many theorems in geometry which have seemed at first impracticable are in time successfully worked out! (Theorems Quotes) I compare arithmetic with a tree that unfolds upwards in a multitude of techniques and theorems while the root drives into the depths (Theorems Quotes) There are infinitely many variations of the initial situation and therefore no doubt indefinitely many theorems of moral geometry (Theorems Quotes) That’s the problem with false proofs of true theorems; it’s not easy to produce a counterexample (Theorems Quotes) Math does come easily to me, but I was always much more interested in what theorems imply about the world than in proving them (Theorems 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 (Theorems Quotes) He knew by heart every last minute crack on its surface. He had made maps of the ceiling and gone exploring on them; rivers, islands, and continents. He had made guessing games of it and discovered hidden objects; faces, birds, and fishes. He made mathematical calculations of it and rediscovered his childhood; theorems, angles, and triangles. There was practically nothing else he could do but look at it. He hated the sight of it (Theorems Quotes) Mathematicians can and do fill in gaps, correct errors, and supply more detail and more careful scholarship when they are called on or motivated to do so. Our system is quite good at producing reliable theorems that can be solidly backed up. It’s just that the reliability does not primarily come from mathematicians formally checking formal arguments; it comes from mathematicians thinking carefully and critically about mathematical ideas (Theorems Quotes) A peculiarity of the higher arithmetic is the great difficulty which has often been experienced in proving simple general theorems which had been suggested quite naturally by numerical evidence (Theorems Quotes) For what is important when we give children a theorem to use is not that they should memorize it. What matters most is that by growing up with a few very powerful theorems one comes to appreciate how certain ideas can be used as tools to think with over a lifetime. One learns to enjoy and to respect the power of powerful ideas. One learns that the most powerful idea of all is the idea of powerful ideas (Theorems Quotes) The fundamental laws of the universe which correspond to the two fundamental theorems of the mechanical theory of heat.1. The energy of the universe is constant.2. The entropy of the universe tends to a maximum (Theorems Quotes) I approached the bulk of my schoolwork as a chore rather than an intellectual adventure. The tedium was relieved by a few courses that seem to be qualitatively different. Geometry was the first exciting course I remember. Instead of memorizing facts, we were asked to think in clear, logical steps. Beginning from a few intuitive postulates, far reaching consequences could be derived, and I took immediately to the sport of proving theorems (Theorems Quotes) If all sentient beings in the universe disappeared, there would remain a sense in which mathematical objects and theorems would continue to exist even though there would be no one around to write or talk about them. Huge prime numbers would continue to be prime, even if no one had proved them prime (Theorems Quotes) You can learn to find unknowns in equations, draw equidistant lines and demonstrate theorems, but in real life there’s nothing to position, calculate, or guess (Theorems Quotes) When a truth is necessary, the reason for it can be found by analysis, that is, by resolving it into simpler ideas and truths until the primary ones are reached. It is this way that in mathematics speculative theorems and practical canons are reduced by analysis to definitions, axioms and postulates (Theorems Quotes) There are three signs of senility. The first sign is that a man forgets his theorems. The second sign is that he forgets to zip up. The third sign is that he forgets to zip down (Theorems Quotes) The pursuit of pretty formulas and neat theorems can no doubt quickly degenerate into a silly vice, but so can the quest for austere generalities which are so very general indeed that they are incapable of application to any particular (Theorems Quotes) A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories (Theorems Quotes)