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Mathematics Quotes

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Mathematics Quotes

“I always believe in going hard at everything, whether it is Latin or mathematics, boxing or football, but at the same time I want to keep the sense of proportion. It is never worth while to absolutely exhaust one's self or to take big chances unless for an adequate object. I want you to keep in training the faculties which would make you, if the need arose, able to put your last ounce of pluck and strength into a contest. But I do not want you to squander these qualities.”

“When we find that God's ways always coincide with our own ways, it's time to question who we're really worshipping, God or ourselves. The latter moves the nature of godliness from the King to our servant to a slave, a deduction into the realm of selfhood and then the lower, slavehood. It's a spiritual mathematics in that men who need God in his godhood are humble yet strong and spiritually ambitious while men who need a slave in their selfhood are ultimately paralyzed and will remain paralyzed.”

“Three principles - the conformability of nature to herself, the applicability of the criterion of simplicity, and the utility of certain parts of mathematics in describing physical reality - are thus consequences of the underlying law of the elementary particles and their interactions. Those three principles need not be assumed as separate metaphysical postulates. Instead, they are emergent properties of the fundamental laws of physics.”

“Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understanding attuned to the principle of mathematical induction, as does Poincaré, or the primal intuition of Brouwer, or, finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot be compensated for by consistency proofs.”

“To arrive at the simplest truth, as Newton knew and practiced, requires years of contemplation. Not activity Not reasoning. Not calculating. Not busy behaviour of any kind. Not reading. Not talking. Not making an effort. Not thinking. Simply bearing in mind what it is one needs to know.”

“As for mathematicians themselves: don't expect too much help. Most of them are too far removed in their ivory towers to take up such challenges. And anyway, they are not competent. After all, they are just mathematicians-what we need is paramathematicians, like you... It is you who can be the welding force, between mathematicians and stories, in order to achieve the synthesis.”

“To create guilt, all that you need is a very simple thing: start calling mistakes, errors - sins. They are simply mistakes, human. Now, if somebody commits a mistake in mathematics - two plus two, and he concludes it makes five - you don`t say he has committed a sin. He is unalert, he is not paying attention to what he is doing. He is unprepared, he has not done his homework. He is certainly committing a mistake, but a mistake is not a sin. It can be corrected. A mistake does not make him feel guilty. At the most it makes him feel foolish.”

“Mathematicians need proofs to keep them honest. All technical areas of human activity need reality checks. It is not enough to believe that something works, that it is a good way to proceed, or even that it is true. We need to know why it's true. Otherwise, we won't know anything at all.”

“As one reads mathematics, one needs to have an active mind, asking questions, forming mental connections between the current topic and other ideas from other contexts, so as to develop a sense of the structure, not just familiarity with a particular tour through the structure.”

“I constantly meet people who are doubtful, generally without due reason, about their potential capacity [as mathematicians]. The first test is whether you got anything out of geometry. To have disliked or failed to get on with other [mathematical] subjects need mean nothing; much drill and drudgery is unavoidable before they can get started, and bad teaching can make them unintelligible even to a born mathematician.”

“I didn't want to teach my kid how to read, so I used to read to him at night and close the book at the most interesting part. He said, “What happened then, daddy?” I said, “If you learn to read, you can find out. I'm too tired to read. I'll read to you tomorrow.” So, he had a need to want to learn how to read. Don't teach children how to read. Don't teach them mathematics. Give them a reason to want it. In school, they're working ass-backwards.”

“Mathematics is a logical method. . . . Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.”

“...mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics. Every other science, even logic, especially in its early stages, is in danger of evaporating into airy nothingness, degenerating, as the Germans say, into an arachnoid film, spun from the stuff that dreams are made of. There is no such danger for pure mathematics; for that is precisely what mathematics ought to be.”

“Man is full of desires: he loves only those who can satisfy them all. "This man is a good mathematician," someone will say. But I have no concern for mathematics; he would take me for a proposition. "That one is a good soldier." He would take me for a besieged town. I need, that is to say, a decent man who can accommodate himself to all my desires in a general sort of way.”

“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?”

“Like a stool which needs three legs to be stable, mathematics education needs three components: good problems, with many of them being multi-step ones, a lot of technical skill, and then a broader view which contains the abstract nature of mathematics and proofs. One does not get all of these at once, but a good mathematics program has them as goals and makes incremental steps toward them at all levels.”

“Four circles to the kissing come, The smaller are the benter. The bend is just the inverse of The distance from the centre. Though their intrigue left Euclid dumb There's now no need for rule of thumb. Since zero bend's a dead straight line And concave bends have minus sign, The sum of squares of all four bends Is half the square of their sum.”

“You can only hear clearly when you sit quietly, when you give your attention. Nor can you have order if you are not free to watch, if you are not free to listen, if you are not free to be considerate. This problem of freedom and order is one of the most difficult and urgent problems in life. It is a very complex problem. It needs to be thought over much more than mathematics, geography, or history.”

“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.”

“Essentially all civilizations that rose to the level of possessing an urban culture had need for two forms of science-related technology, namely, mathematics for land measurements and commerce and astronomy for time-keeping in agriculture and aspects of religious rituals.”