Mathematics Quotes - Page 6

Its a mathematical fact that two negatives make a positive so even under adverse circumstances think positively.

The first successes were such that one might suppose all the difficulties of science overcome in advance, and believe that the mathematician, without being longer occupied in the elaboration of pure mathematics, could turn his thoughts exclusively to the study of natural laws.

It seems to me that the poet has only to perceive that which others do not perceive, to look deeper than others look. And the mathematician must do the same thing.

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.

Essentially, all models are wrong, but some are useful

I do not think the division of the subject into two parts - into applied mathematics and experimental physics a good one, for natural philosophy without experiment is merely mathematical exercise, while experiment without mathematics will neither sufficiently discipline the mind or sufficiently extend our knowledge in a subject like physics.

Histories make men wise; poets, witty; the mathematics, subtle; natural philosophy, deep; moral, grave; logic and rhetoric, able to contend.

I'm sorry to say that the subject I most disliked was mathematics. I have thought about it. I think the reason was that mathematics leaves no room for argument. If you made a mistake, that was all there was to it.

The spirit of mathematics is not captured by spending 3 hours solving 20 look-alike homework problems. Mathematics is thinking, comparing, analyzing, inventing, and understanding. The main point is not quantity or speed—the main point is quality of thought.The spirit of mathematics is not captured by spending 3 hours solving 20 look-alike homework problems. Mathematics is thinking, comparing, analyzing, inventing, and understanding. The main point is not quantity or speed—the main point is quality of thought.

Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold.

Mathematics should be studied if only for that it puts the mind in order.

Mr Baley", said Quemot, "you can't treat human emotions as though they were built about a positronic brain"."I'm not saying you can. Robotics is a deductive science and sociology an inductive one. But mathematics can be made to apply in either case.

Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity

You’re probably better at math than I am, because pretty much everyone’s better at math than I am, but it’s okay, I’m fine with it. See, I excel at other, more important things—guitar, sex, and consistently disappointing my dad, to name a few.

Making mathematics accessible to the educated layman, while keeping high scientific standards, has always been considered a treacherous navigation between the Scylla of professional contempt and the Charybdis of public misunderstanding.

And, most important of all," added the Mathemagician, "here is your own magic staff. Use it well and there is nothing it cannot do for you."He placed in Milo's breast pocket a small gleaming pencil which, except for the size, was much like his own.

Children must be taught mathematics well in anywhere under every condition at every age and so we can have more rational, more logical societies!

Logic, n. The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding. The basic of logic is the syllogism, consisting of a major and a minor premise and a conclusion - thus:Major Premise: Sixty men can do a piece of work sixty times as quickly as one man.Minor Premise: One man can dig a post-hole in sixty seconds; Therefore-Conclusion: Sixty men can dig a post-hole in one second.This may be called syllogism arithmetical, in which, by combining logic and mathematics, we obtain a double certainty and are twice blessed.

In the Principia Mathematica, Bertrand Russell and Alfred Whitehead attempted to give a rigorous foundation to mathematics using formal logic as their basis. They began with what they considered to be axioms, and used those to derive theorems of increasing complexity. By page 362, they had established enough to prove "1 + 1 = 2.

He possesses the minimum sensibility necessary for his intelligence not to be merely mathematical, the minimum a human being needs so that it can be proven with a thermometer that he's not dead.

His ironing seemed highly rational, with a constant speed that allowed him to get the best results, with the least effort; all the economy and elegance of his mathematical proofs performed right there on the ironing board. The Professor was definitely the best man for this job, we had to admit, since the tablecloth was made of delicate lace.

How do you quantify love? Can you weigh it, measure it, pin it down with equations? If the sum of all experiences is really just the interaction of a finite soup of chemicals copulating in nerve endings, how did this even dare articulate the infinite?Mathematicians will tell you there are different types of infinities. Some are countable, some are not. We can love someone more and more; we can stop loving. But we can never guess how much all this is. Love has no units.

...it would not be quite right to say that the problem is unsolvable in principle; only so complicated that it is not worth anybody’s time to think about it. So what do we do?In probability theory there is a very clever trick for handling a problem that becomes too difficult. We just solve it anyway by:(1)  making it still harder;(2)  redefining what we mean by ‘solving’ it, so that it becomes something we can do;(3)  inventing a dignified and technical-sounding word to describe this procedure, which has the psychological effect of concealing the real nature of what we have done, and making it appear respectable.

In a Sense, we all are Time Travelers! We are Surviving each and every Active Time-Point in this Timeline.......

Mathematics education is much more complicated than you expected, even though you expected it to be more complicated than you expected.

There is the potential for a particle of matter to be located where we expect it to be or to be located anywhere in the physical world. So it is with our lives – our very next moment can occur along the most probable path or it can occur on a path entirely discontinuous with the expectations that others have for us, but more likely in line with the expectations that we have for ourselves.

The golden era of the golden number was the Italian renaissance. The expression divine proportion was coined by the great mathematician Luca Pacioli in his book 'De divina proportione', written in 1509.

When the time is ripe for certain things, these things appear in different places in the manner of violets coming to light in early spring.

Every formula which expresses a law of nature is a hymn of praise to God.

I had a polynomial once. My doctor removed it.

Infinity...is used in physics simply as a shorthand for "a very big number.

Last period of the day. Charles had decided that morning that he would talk about tessellations. Last period, they should have been covering sines and cosines. They should have been starting to graph, but he just didn't have it in him. Tessellations were his favorite.

The algebraic sum of all the transformations occurring in a cyclical process can only be positive, or, as an extreme case, equal to no

So [in mathematics] we get to play and imagine whatever we want and make patterns and ask questions about them. But how do we answer these questions? It’s not at all like science. There’s no experiment I can do ... The only way to get at the truth about our imaginations is to use our imaginations, and that is hard work.

the theorem of incompleteness . . . [shows] there is nothing on this level of existence that can fully explain this level of existence.

Mathematics began to seem too much like puzzle solving. Physics is puzzle solving, too, but of puzzles created by nature, not by the mind of man.

The Planeswalker knowYOu take the card from the libraryAnd bury it when you're done.On the path, you face history.Walk the path, do the math:Start with the prime numbers under 100Whose digits give you 10.Choose the happy median.Add it to: The square root of The cube of five divided byThe sum of 3 and 2.

As the several items can be exchanged, they must be equal; but in what terms? Not in pounds, yards, or hours; they are equal in value. Then what is wanted is a unit of value to reckon by.

Plenty of mathematicians, Hardy knew, could follow a step-by-step discursus unflaggingly—yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan he gave 100.

And I'll go even further and say that mathematics, this art of abstract pattern-making — even more than storytelling, painting, or music - is our most quintessentially human art form. This is what our brains do, whether we like it or not. We are biochemical pattern-recognition machines and mathematics is nothing less than the distilled essence of who we are.

No doubt there are some who, when confronted with a line of mathematical symbols, however simply presented, can only see the face of a stern parent or teacher who tried to force into them a non-comprehending parrot-like apparent competence--a duty and a duty alone--and no hint of magic or beauty of the subject might be allowed to come through.

Maths is at only one remove from magic.

What would it be like, a world without snow? I cannot imagine such a place. It would be like a world devoid of numbers. Every snowflake, unique as every number, tells us something about complexity. Perhaps that is why we will never tire of its wonder.

Mathematics brought rigor to economics. Unfortunately it also brought mortis.

Mathematics is the art of explanation.

Eternal truths are ultimately invisible, and you won't find them in material things or natural phenomena, or even in human emotions. Mathematics, however, can illuminate them, can give them expression - in fact, nothing can prevent it from doing so.

Yes," I continued, "I discovered this model recently and her style never fails to be mathematically perfect. She seems to come by it naturally. As if she were born resonant. I notice Japanese models tend to do this. Like I said, they seem to have resonance somewhere deep in their culture. But Yuri Nakagawa, she's the best I've ever seen. The best model, with the most powerful resonance. I need her to probe deeper into this profound mathematical instinct, which I call resonance.

The distance between your Dreams and Reality is inversely proportional to your Efforts.

Logic, it is often said, is the study of valid arguments. It is a systematic attempt to distinguish valid arguments from invalid arguments.

Although some of her passages seek to persuade the reader of the meaninglessness and marginalization of the mathematics, Hayles is content to use mathematics as a means for understanding Borges, perhaps in the same way a sponge riddled with holes is useful in sopping up fluid reality.

Outside the port, the slashed rock of the unnamed asteroid tumbled and spun in dynamics known only to the gods of chaos mathematics.

...I guess I can put two and two together.""Sometimes the answer's four," I said, "and sometimes it's twenty-two...

Infinite is a meaningless word: except – it states / The mind is capable of performing / an endless process of addition.

It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians who, like Einstein, are philosophers.

The thing I want you especially to understand is this feeling of divine revelation. I feel that this structure was "out there" all along I just couldn't see it. And now I can! This is really what keeps me in the math game-- the chance that I might glimpse some kind of secret underlying truth, some sort of message from the gods.

What is it, in fact, that we are supposed to abstract from, in order to get, for example, from the moon to the number 1? By abstraction we do indeed get certain concepts, viz. satellite of the Earth, satellite of a planet, non-self-luminous heavenly body, heavenly body, body, object. But in this series 1 is not to be met with; for it is no concept that the moon could fall under. In the case of 0, we have simply no object at all from which to start our process of abstracting. It is no good objecting that 0 and 1 are not numbers in the same sense as 2 and 3. What answers the question How many? is number, and if we ask, for example, "How many moons has this planet?", we are quite as much prepared for the answer 0 or 1 as for 2 or 3, and that without having to understand the question differently. No doubt there is something unique about 0, and about 1000; but the same is true in principle of every whole number, only the bigger the number the less obvious it is. To make out of this a difference in kind is utterly arbitrary. What will not work with 0 and 1 cannot be essential to the concept of number.

It seems that mathematical ideas are arranged somehow in strata, the ideas in each stratum being linked by a complex of relations both among themselves and with those above and below. The lower the stratum, the deeper (and in general more difficult) the idea. Thus the idea of an ‘irrational’ is deeper than that of an integer; and Pythagoras’s theorem is, for that reason, deeper than Euclid’s.

Only dead mathematics can be taught where competition prevails: living mathematics must always be a communal possession.

The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.

Just as all things speak about God to those that know Him, and reveal Him to those that love Him, they also hide Him from all those that neither seek nor know Him.