Best 579 quotes in «mathematics quotes» category

Schools were started to train human talents... The Guild... emphasizes almost pure mathematics. Bene Gesserit performs... politics. The original Bene Gesserit school was directed by those who saw the need of a thread of continuity in human affairs. They saw there count be no such continuity without separating human stock from animal stock - for breeding purposes.

Scientists and inventors of the USA (especially in the so-called "blue state" that voted overwhelmingly against Trump) have to think long and hard whether they want to continue research that will help their government remain the world's superpower. All the scientists who worked in and for Germany in the 1930s lived to regret that they directly helped a sociopath like Hitler harm millions of people. Let us not repeat the same mistakes over and over again.

She, like many, had always thought that mathematics did not derive its meaning from the universe, but rather imposed some meaning onto the universe.

She would not have cared to confess how infinitely she preferred the exactitude, the star-like impersonality, of figures to the confusion, agitation, and vagueness of the finest prose.

Simplicio: Are you really trying to claim that mathematics offers no useful or practical applications to society? Salviati: Of course not. I'm merely suggesting that just because something happens to have practical consequences, doesn't mean that's what it is about. Music can lead armies into battle, but that's not why people write symphonies. Michelangelo decorated a ceiling, but I'm sure he had loftier things on his mind.

Simple problems are hard to solve, Because they need common sense. Simple problems are made complex. Complex things are solved using patterns. Coefficient is introduced along with variable to create a pattern, But coefficient is a constant. To find coefficient, We again use complex patterns to make it look constant.

Soon after I began working for the Professor, I realized that he talked about numbers whenever he was unsure of what to say or do. Numbers were also his way of reaching out to the world. They were safe, a source of comfort.

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.

Someone. Everyone. Anyone. No-one. One. One can't be everyone, but there isn't more than one everyone, at the same time. And at the same time no-one can't be someone, but anyone can be one, and also anyone can be a no-one. To sum up - everyone is someone, and any-one becomes a no-one if you divide the one part long enough by every part of every-one, so in conclusion, I have no idea what I’m talking about, basically.

Take this neat little equation here. It tells me all the ways an electron can make itself comfortable in or around an atom. That's the logic of it. The poetry of it is that the equation tells me how shiny gold is, how come rocks are hard, what makes grass green, and why you can't see the wind. And a million other things besides, about the way nature works.

Taking responsibility in choosing our own math materials is better than getting struck with resources which we don't find particularly useful.

Teaching Ramanujan was like writing on a blackboard covered with excerpts from a more interesting lecture.

Teaching mathematics, like teaching any art, requires the ability to inspire the student. Inspiration requires marketing, and marketing requires stirring communication.

Tengo's lectures took on uncommon warmth, and the students found themselves swept up in his eloquence. He taught them how to practically and effectively solve mathematical problems while simultaneously presenting a spectacular display of the romance concealed in the questions it posed. Tengo saw admiration in the eyes of several of his female students, and he realized that he was seducing these seventeen- or eighteen-year-olds through mathematics. His eloquence was a kind of intellectual foreplay. Mathematical functions stroked their backs; theorems sent warm breath into their ears.

The astonishing fact is that similar mathematics applies so well to planets and to clocks. It needn’t have been this way. We didn’t impose it on the Universe. That’s the way the Universe is. If this is reductionism, so be it.

The appearance of Professor Benjamin Peirce, whose long gray hair, straggling grizzled beard and unusually bright eyes sparkling under a soft felt hat, as he walked briskly but rather ungracefully across the college yard, fitted very well with the opinion current among us that we were looking upon a real live genius, who had a touch of the prophet in his make-up.

... That little narrative is an example of the mathematician’s art: asking simple and elegant questions about our imaginary creations, and crafting satisfying and beautiful explanations. There is really nothing else quite like this realm of pure idea; it’s fascinating, it’s fun, and it’s free!

The acknowledgement of mathematics as a creative, exploratory and a faillible human endeavor is not fatalistic.

The beauty of a mathematical theorem depends a great deal on its seriousness, as even in poetry the beauty of a line may depend to some extent on the significance of the ideas which it contains.

The deep study of nature is the most fruitful source of mathematical discoveries. By offering to research a definite end, this study has the advantage of excluding vague questions and useless calculations; besides it is a sure means of forming analysis itself and of discovering the elements which it most concerns us to know, and which natural science ought always to conserve.

The certainty of mathematics depends on its complete abstract generality.

The consequence model, the logical one, the amoral one, the one which refuses any divine intervention, is a problem really for just the (hypothetical) logician. You see, towards God I would rather be grateful for Heaven (which I do not deserve) than angry about Hell (which I do deserve). By this the logician within must choose either atheism or theism, but he cannot possibly through good reason choose anti-theism. For his friend in this case is not at all mathematical law: the law in that 'this equation, this path will consequently direct me to a specific point'; over the alternative and the one he denies, 'God will send me wherever and do it strictly for his own sovereign amusement.' The consequence model, the former, seeks the absence of God, which orders he cannot save one from one's inevitable consequences; hence the angry anti-theist within, 'the logical one', the one who wants to be master of his own fate, can only contradict himself - I do not think it wise to be angry at math.

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.

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

The focus of history and philosophy of science scholar Arthur Miller’s (2010) "137: Jung and Pauli and the Pursuit of Scientific Obsession" is Jung and Pauli’s mutual effort to discover the cosmic number or fine structure constant, which is a fundamental physical constant dealing with electromagnetism, or, from a different perspective, could be considered the philosopher’s stone of the mathematical universe. This was indeed one of Pauli and Jung’s collaborative passions, but it was not the only concentration of their relationship. Quantum physics could be seen as the natural progression from ancient alchemy, through chemistry, culminating in the abstract world of subatomic particles, wave functions, and mathematics. [Ancient Egypt and Modern Psychotherapy]

[The golden proportion] is a scale of proportions which makes the bad difficult [to produce] and the good easy.

The Golden Number is a mathematical definition of a proportional function which all of nature obeys, whether it be a mollusk shell, the leaves of plants, the proportions of the animal body, the human skeleton, or the ages of growth in man.

The Golden Ratio defines the squaring of a circle. Stated in mathematical terms, this says: Given a square of known perimeter, create a circle of equal circumference. According to some, in ancient Egypt, this mathematical mystery was encoded in the measurements of the Great Pyramid of Giza.

The Golden Proportion, sometimes called the Divine Proportion, has come down to us from the beginning of creation. The harmony of this ancient proportion, built into the very structure of creation, can be unlocked with the 'key' ... 528, opening to us its marvelous beauty. Plato called it the most binding of all mathematical relations, and the key to the physics of the cosmos.

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.

The impulse to all movement and all form is given by [the golden ratio], since it is the proportion that summarizes in itself the additive and the geometric, or logarithmic, series.

The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated ... The importance of this invention is more readily appreciated when one considers that it was beyod the two greatest men of antiquity, Archimedes and Apollonius.

The Intelligence of Mathematics existed first before the Intelligence of the Mind.

The integrals which we have obtained are not only general expressions which satisfy the differential equation, they represent in the most distinct manner the natural effect which is the object of the phenomenon... when this condition is fulfilled, the integral is, properly speaking, the equation of the phenomenon; it expresses clearly the character and progress of it, in the same manner as the finite equation of a line or curved surface makes known all the properties of those forms.

The language of mathematics differs from that of everyday life, because it is essentially a rationally planned language. The languages of size have no place for private sentiment, either of the individual or of the nation. They are international languages like the binomial nomenclature of natural history. In dealing with the immense complexity of his social life man has not yet begun to apply inventiveness to the rational planning of ordinary language when describing different kinds of institutions and human behavior. The language of everyday life is clogged with sentiment, and the science of human nature has not advanced so far that we can describe individual sentiment in a clear way. So constructive thought about human society is hampered by the same conservatism as embarrassed the earlier naturalists. Nowadays people do not differ about what sort of animal is meant by Cimex or Pediculus, because these words are used only by people who use them in one way. They still can and often do mean a lot of different things when they say that a mattress is infested with bugs or lice. The study of a man's social life has not yet brought forth a Linnaeus. So an argument about the 'withering away of the State' may disclose a difference about the use of the dictionary when no real difference about the use of the policeman is involved. Curiously enough, people who are most sensible about the need for planning other social amenities in a reasonable way are often slow to see the need for creating a rational and international language.

The language of mathematics, scientific observations, and our perceptivity together knit the window to reality.

The person who wishes to attain human perfection should study logic first, next mathematics, then physics, and, lastly, metaphysics.

The mathematical theory of continuity is based, not on intuition, but on the logically developed theories of number and sets of points.

The philosophers make still another objection: "What you gain in rigour," they say, "you lose in objectivity. You can rise toward your logical ideal only by cutting the bonds which attach you to reality. Your science is infallible, but it can only remain so by imprisoning itself in an ivory tower and renouncing all relation with the external world. From this seclusion it must go out when it would attempt the slightest application.

The letter is susceptible of operations which enables one to transform literal expressions and thus to paraphrase any statement into a number of equivalent forms. It is this power of transformation that lifts algebra above the level of a convenient shorthand.

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

There are other reasons we use math in physics. Besides keeping us honest, math is also the most economical and unambiguous terminology that we know of. Language is malleable; it depends on context and interpretation. But math doesn’t care about culture or history. If a thousand people read a book, they read a thousand different books. But if a thousand people read an equation, they read the same equation.

The probability of an event is the reason we have to believe that it has taken place, or that it will take place. The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible.

There is a mathematics to all his relationships, underlying each and every one. He wants it to all add up in his head and he wants to do the adding. And should someone step outside his ciphers, the circle his mind has drawn, his trust evaporates.

There are two kinds of people in life: those who like crude dualities and those who do not.

There is no great religion without a great schism. All of them have it. And that's because you're dealing with something called faith. And faith is not something you can prove; faith is personal opinion. Uh, when you're dealing with something with certainty, like, y'know, science or logic, you don't have the--there's no wiggle room; that's why history is not filled with warring math cults, y'know, because you can settle the issue; you can prove something to be right or wrong, and that's the end of the argument: next case. Whereas, when you're dealing with faith, you can forever argue your point, or another point, because you're dealing with intangibles. Personally, I think, faith is what you ask of somebody when you don't have the goods to prove your point.

There is no logical necessity for the existence of a unique direction of total time; whether there is only one time direction, or whether time directions alternate, depends on the shape of the entropy curve plotted by the universe.

The spectacular thing about Johnny [von Neumann] was not his power as a mathematician, which was great, or his insight and his clarity, but his rapidity; he was very, very fast. And like the modern computer, which no longer bothers to retrieve the logarithm of 11 from its memory (but, instead, computes the logarithm of 11 each time it is needed), Johnny didn't bother to remember things. He computed them. You asked him a question, and if he didn't know the answer, he thought for three seconds and would produce and answer.

There was yet another disadvantage attaching to the whole of Newton’s physical inquiries, ... the want of an appropriate notation for expressing the conditions of a dynamical problem, and the general principles by which its solution must be obtained. By the labours of LaGrange, the motions of a disturbed planet are reduced with all their complication and variety to a purely mathematical question. It then ceases to be a physical problem; the disturbed and disturbing planet are alike vanished: the ideas of time and force are at an end; the very elements of the orbit have disappeared, or only exist as arbitrary characters in a mathematical formula.

These estimates may well be enhanced by one from F. Klein (1849-1925), the leading German mathematician of the last quarter of the nineteenth century. 'Mathematics in general is fundamentally the science of self-evident things.' ... If mathematics is indeed the science of self-evident things, mathematicians are a phenomenally stupid lot to waste the tons of good paper they do in proving the fact. Mathematics is abstract and it is hard, and any assertion that it is simple is true only in a severely technical sense—that of the modern postulational method which, as a matter of fact, was exploited by Euclid. The assumptions from which mathematics starts are simple; the rest is not.