Best 1208 quotes in «math quotes» category

The will of man is by his reason swayed.

The tantalizing and compelling pursuit of mathematical problems offers mental absorption, peace of mind amid endless challenges, repose in activity, battle without conflict, refuge from the goading urgency of contingent happenings, and the sort of beauty changeless mountains present to senses tried by the present day kaleidoscope of events.

[The works of Archimedes] are without exception, monuments of mathematical exposition; the gradual revelation of the plan of attack, the masterly ordering of the propositions, the stern elimination of everything not immediately relevant to the purpose, the finish of the whole, are so impressive in their perfection as to create a feeling akin to awe in the mind of the reader.

They look at what's more important, like subjects to help with the SAT's, etc. They miss that music is vital. It offers a break from a stressful day of science and math and it's different.

Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent to a pair of ears. Mathematics can only be "seen" with the "eyes of the mind". It is as if we had no sense of hearing, so that only someone able to sight read music would be able to appreciate its patterns and harmonies.

This much I'm sure of. Chances for winning = 1 - (# of math students playing)/ (# of math students cheering). That's a fraction.

Those who write against vanity want the glory of having written well, and their readers the glory of reading well, and I who write this have the same desire, as perhaps those who read this have also.

Throughout the 1960s and 1970s devoted Beckett readers greeted each successively shorter volume from the master with a mixture of awe and apprehensiveness; it was like watching a great mathematician wielding an infinitesimal calculus, his equations approaching nearer and still nearer to the null point.

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the "logic piano" imagined by Stanley Jevons; or, if you choose, a machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.

Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.

Time was when all the parts of the subject were dissevered, when algebra, geometry, and arithmetic either lived apart or kept up cold relations of acquaintance confined to occasional calls upon one another; but that is now at an end; they are drawn together and are constantly becoming more and more intimately related and connected by a thousand fresh ties, and we may confidently look forward to a time when they shall form but one body with one soul.

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.

To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess.

To be sure, mathematics can be extended to any branch of knowledge, including economics, provided the concepts are so clearly defined as to permit accurate symbolic representation. That is only another way of saying that in some branches of discourse it is desirable to know what you are talking about.

...to characterize the import of pure geometry, we might use the standard form of a movie-disclaimer: No portrayal of the characteristics of geometrical figures or of the spatial properties of relationships of actual bodies is intended, and any similarities between the primitive concepts and their customary geometrical connotations are purely coincidental.

Today I said to the calculus students, "I know, you're looking at this series and you don't see what I'm warning you about. You look and it and you think, 'I trust this series. I would take candy from this series. I would get in a car with this series.' But I'm going to warn you, this series is out to get you. Always remember: The harmonic series diverges. Never forget it.

Today, it is not only that our kings do not know mathematics, but our philosophers do not know mathematics and - to go a step further - our mathematicians do not know mathematics.

Today, more than ever before, science holds the key to our survival as a planet and our security and prosperity as a nation. It's time we once again put science at the top of our agenda and work to restore America's place as the world leader in science and technology.

Today, over half of China's undergraduate degrees are in math, science technology and engineering, yet only 16 percent of America's undergraduates pursue these schools.

To deny, to believe, and to doubt well, are to a man what the race is to a horse.

To divide a cube into two other cubes, a fourth power, or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.

To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion − not because it makes no sense to you, but because you gave it sense and you still don't understand what your creation is up to.

To isolate mathematics from the practical demands of the sciences is to invite the sterility of a cow shut away from the bulls.

To speak algebraically, Mr. M. is execrable, but Mr. G. is (x + 1)- ecrable.

To Thales the primary question was not what do we know, but how do we know it.

To teach effectively a teacher must develop a feeling for his subject; he cannot make his students sense its vitality if he does not sense it himself. He cannot share his enthusiasm when he has no enthusiasm to share. How he makes his point may be as important as the point he makes; he must personally feel it to be important.

To the wise, life is a problem; to the fool, a solution.

To think I have spent my life on absolute muck.

To the pure geometer the radius of curvature is an incidental characteristic - like the grin of the Cheshire cat. To the physicist it is an indispensable characteristic. It would be going too far to say that to the physicist the cat is merely incidental to the grin. Physics is concerned with interrelatedness such as the interrelatedness of cats and grins. In this case the "cat without a grin" and the "grin without a cat" are equally set aside as purely mathematical phantasies.

To the extent math refers to reality, we are not certain to the extent we are certain, math does not refer to reality.

To throw in a fair game at Hazards only three-spots, when something great is at stake, or some business is the hazard, is a natural occurrence and deserves to be so deemed; and even when they come up the same way for a second time if the throw be repeated. If the third and fourth plays are the same, surely there is occasion for suspicion on the part of a prudent man.

To think deeply of simple things.

Trust me, there is no formula for most things that are not math.

To understand this for sense it is not required that a man should be a geometrician or a logician, but that he should be mad.

Twice two makes four seems to me simply a piece of insolence. Twice two makes four is a pert coxcomb who stands with arms akimbo barring your path and spitting. I admit that twice two makes four is an excellent thing, but if we are to give everything its due, twice two makes five is sometimes a very charming thing too.

Uneven numbers are the gods' delight.

Unfortunately I have never been good in math. Numbers simply do not interest me or seem as real to me as words.

Upon the whole, I am inclined to think that the far greater part, if not all, of those difficulties which have hitherto amused philosophers, and blocked up the way to knowledge, are entirely owing to our selves. That we have first raised a dust, and then complain, we cannot see.

USA Today has come out with a new survey - apparently, three out of every four people make up 75% of the population.

Very few people realize the enormous bulk of contemporary mathematics. Probably it would be easier to learn all the languanges of the world than to master all mathematics at present known.

War can protect; it cannot create.

We all know that there are these exemplars who can take the toughest students, and they'll teach them two-and-a-half years of math in a single year.

We are justified in calling numbers a free creation of the human mind.

We are so presumptuous that we should like to be known all over the world, even by people who will only come when we are no more. Such is our vanity that the good opinion of half a dozen of the people around us gives us pleasure and satisfaction.

Two wrongs don't make a right.

We believed we could prepare our kids for a more competitive world. And today, our younger students have earned the highest math and reading scores on record. Our high school graduation rate has hit an all-time high. And more Americans finish college than ever before.

We can and should place special emphasis on developing in our youth constructive incentives — a love of science, engineering, and math, so that they will want to take advanced scientific courses and thereby help meet the needs of our times.

We come now to the question: what is a priori certain or necessary, respectively in geometry (doctrine of space) or its foundations? Formerly we thought everything; nowadays we think nothing. Already the distance-concept is logically arbitrary; there need be no things that correspond to it, even approximately.

We cheated on our math tests, we carved some dirty words on the desk.

We could use up two Eternities in learning all that is to be learned about our own world and the thousands of nations that have arisen and flourished and vanished from it. Mathematics alone would occupy me eight million years.