Best 1208 quotes in «math quotes» category

Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty and perfection.

Test scores aren't perfect, but having a test score for math or reading or other things that we can objectively measure is a meaningful component that makes a lot of sense.

Take a random group of 8-year-old American and Japanese kids, give them all a really, really hard math problem, and start a stopwatch. The American kids will give up after 30, 40 seconds. If you let the test run for 15 minutes, the Japanese kids will not have given up. You have to take it away.

That is the inescapable math of tragedy and the multiplication of grief. Too many good people die a little when they lose someone they love. One death begets two or twenty or one hundred. It's the same all over the world.

... that, in a few years, all great physical constants will have been approximately estimated, and that the only occupation which will be left to men of science will be to carry these measurements to another place of decimals.

Teaching is the royal road to learning.

That's all well and good in practice, but how does it work in theory?

The Advantage is that mathematics is a field in which one's blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil. It is a field which has often been compared with chess, but differs from the latter in that it is only one's best moments that count and not one's worst. A single inattention may lose a chess game, whereas a single successful approach to a problem, among many which have been relegated to the wastebasket, will make a mathematician's reputation.

The art of doing mathematics consists in finding that special case which contains all the germs of generality.

The arrogance of some of those who are so damned sure they are right is just astounding. Scientific witch hunts are often the worst kind, and have been since the secular authorities stopped enforcing the local bishop's decrees of anathema.

The best therapy for emotional blocks to math is the realization that the human race took centuries or millennia to see through the mist of difficulties and paradoxes which instructors now invite us to solve in a few minutes.

The best math lesson we can teach college students this year is to subtract a tuition increase and benefit from the dividends of higher education.

The clearer the teacher makes it, the worse it is for you. You must work things out for yourself and make the ideas your own.

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method

The bitter and the sweet come from the outside, the hard from within, from one's own efforts.

The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design.

The calculus is the greatest aid we have to the application of physical truth in the broadest sense of the word.

The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.

The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it by God and which He revealed to us in the language of mathematics.

The creator of the universe works in mysterious ways. But he uses a base ten counting system and likes round numbers.

The effort of the economist is to "see," to picture the interplay of economic elements. The more clearly cut these elements appear in his vision, the better; the more elements he can grasp and hold in his mind at once, the better. The economic world is a misty region. The first explorers used unaided vision. Mathematics is the lantern by which what before was dimly visible now looms up in firm, bold outlines. The old phantasmagoria disappear. We see better. We also see further.

The discovery in 1846 of the planet Neptune was a dramatic and spectacular achievement of mathematical astronomy. The very existence of this new member of the solar system, and its exact location, were demonstrated with pencil and paper; there was left to observers only the routine task of pointing their telescopes at the spot the mathematicians had marked.

The errors of definitions multiply themselves according as the reckoning proceeds; and lead men into absurdities, which at last they see but cannot avoid, without reckoning anew from the beginning.

The fact is there are few more popular subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune.

The fact that logic cannot satisfy us awakens an almost insatiable hunger for the irrational.

...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know

The first rule of discovery is to have brains and good luck. The second rule of discovery is to sit tight and wait till you get a bright idea.

The control of large numbers is possible, and like unto that of small numbers, if we subdivide them.

The excitement of learning separates youth from old age. As long as you're learning you're not old.

The fact that the same symbolic programming primitives work for those as work for math kinds of things, I think, really validates the idea of symbolic programming being something pretty general.

The financial crisis just made the hole deeper, which is why our stimulus needs to be both big and smart, both financially and educationally stimulating. It needs to be able to produce not only more shovel-ready jobs and shovel-ready workers, but more Google-ready jobs and Windows-ready and knowledge-ready workers.

The first book I ever wrote was in fourth grade and it was called 'Billy's Booger.' It was an autobiographical piece about a kid who was really bad at math.

The Good Lord made all the integers; the rest is man's doing.

The full beauty of the subject of generating functions emerges only from tuning in on both channels: the discrete and the continuous.

The grand thing is to be able to reason backwards.

The further a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science.

The greatest discoveries of science have always been those that forced us to rethink our beliefs about the universe and our place in it.

The historical resonances are sharp. [Louis] Brandeis is nominated on Jan. 28, 1916. Confirmed on June 1. Waits 125 days between nomination and confirmation, which remains an unbroken record, although Merrick Garland will surpass it in July, if my math is right. Anti-Semitism was definitely not the central reason for the opposition, which tended to focus more on his anti-corporate radicalism, but it was a theme.

The human mind has first to construct forms, independently, before we can find them in things.

The higher arithmetic presents us with an inexhaustible store of interesting truths - of truths, too, which are not isolated, but stand in a close internal connection, and between which, as our knowledge increases, we are continually discovering new and sometimes wholly unexpected ties.

The infinite! No other question has ever moved so profoundly the spirit of man.

The idea here, of course, is, you know, mathematics is the language of science, it's the way that we understand the natural world. And there's definitely been a push to sort of study advanced math and kind of reawaken the love of advanced math.

The infinite in mathematics is always unruly unless it is properly treated.

The investigation of mathematical truths accustoms the mind to method and correctness in reasoning, and is an employment peculiarly worthy of rational beings.

The introduction of the cipher 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps.

The introduction of numbers as coordinates by reference to the particular division scheme of the open one-dimensional continuum is an act of violence whose only practical vindication is the special calculatory manageability of the ordinary number continuum with its four basic operations.

The joy of suddenly learning a former secret and the joy of suddenly discovering a hitherto unknown truth are the same to me - both have the flash of enlightenment, the almost incredibly enhanced vision, and the ecstasy and euphoria of released tension.

Their Internet usage is growing very rapidly, and even they can do the math: If everyone in China needed an IPv4 address - just one - this country would use up one third of the entire public IP address space.

The great trick of regarding small departures from the truth as the truth itself - on which is founded the entire integral calculus - is also the basis of our witty speculations, where the whole thing would often collapse if we considered the departures with philosophical rigour.

The latest authors, like the most ancient, strove to subordinate the phenomena of nature to the laws of mathematics.