Polynomials In Mathematics Quotes

The study of mathematics is apt to commence in disappointment ... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it. ~ Alfred North Whitehead

Earlier traditions usually formulated their theories in terms of stories. Modern science uses mathematics. ~ Yuval Noah Harari

The applications of knowledge, especially mathematics, reveal the unity of all knowledge. In a new situation almost anything and everything you ever learned might be applicable, and the artificial divisions seem to vanish. ~ Richard Hamming

This relationship, often called the Golden mean, has been discovered and rediscovered at various times in history as a unique proportion believed to have both aesthetic and mystic significance. That the Egyptians knew of it and used it seems certain. ~ John Pile

What about the inside of the earth? A great deal is known about the speed of
earthquake waves through the earth and the density of distribution of the earth.
However, physicists have been unable to get a good theory as to how dense a
substance should be at the pressures that would be expected at the center of the
earth. In other words, we cannot figure out the properties of matter very well in
these circumstances. We do much less well with the earth than we do with the
conditions of matter in the stars. The mathematics involved seems a little too
difficult, so far, but perhaps it will not be too long before someone realizes that
it is an important problem, and really work it out. The other aspect, of course, is
that even if we did know the density, we cannot figure out the circulating currents.
Nor can we really work out the properties of rocks at high pressure. We cannot
tell how fast the rocks should "give"; that must all be worked out by experiment. ~ Richard P. Feynman

Look you wanna know the truth? I don't really care about the
stats or the cup or the trophy or anything like that. In fact even the games aren't that important to me. What matters to me is the perfect throw, making the perfect catch, the perfect step and block. Perfection. That's what it's about. It's those moments. When you can feel the perfection of creation. The beauty the physics you know the wonder of mathematics. The elations of action and reaction and that is the kind of perfection that I want to be connected to. ~ Samuel Anders

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

To Learn is to create. Learning- whether it is programming, mathematics, art, music, poetry, biology, or chemistry- is all about breaking down walls and freeing the one thing that kept us alive: knowledge.

Knowledge expands freedom in all its forms. Knowledge breaks down walls. It liberates the oppressed. We are committed to knowledge. Knowledge as a hammer against classism, against sexism, against racism, against gender discrimination, against slavery, against bigotry, against war, against hatred. If there is darkness in the world, we will light it up. ~ Leopoldo Gout

I'm obviously attuned to pick up mathematics whenever I can see it. But in Mozart there is a lot of conscious use of mathematical symbolism and numbers in order to try and give messages. ~ Marcus Du Sautoy

Man is a fantastic animal; he was born of fantasy, he is the son of "the mad woman of the house." And universal history is the gigantic and thousand-year effort to go on putting order into that huge, disorderly, anti-animal fantasy. What we call reason is no more than fantasy put into shape. Is there anything in the world more fantastic than that which is the most rational? Is there anything more fantastic than the mathematical point, and the infinite line, and, in general, all mathematics and all physics? Is there a more fantastic fancy than what we call "justice" and the other thing that we call "happiness"? ~ Jose Ortega Y Gasset

We are not told, or not told early enough so that it sinks in, that mathematics is a language, and that we can learn it like any other, including our own. We have to learn our own language twice, first when we learn to speak it, second when we learn to read it. Fortunately, mathematics has to be learned only once, since it is almost wholly a written language. ~ Mortimer J. Adler

Whenever I meet in Laplace with the words 'Thus it plainly appears', I am sure that hours and perhaps days, of hard study will alone enable me to discover how it plainly appears. ~ Nathaniel Bowditch

The only reason psychology students don't have to do more and harder mathematics than physics students is because the mathematicians haven't yet discovered ways of dealing with problems as hard as those in psychology. ~ John G. Kemeny

The golden section was discovered by the Egyptians, and has been used in art and architecture, most commonly, during the classical ages of Egypt and Greece. ~ Steven L. Griffing

In terms of it being a first screenplay, literally, my hat is off to him [Wally Pfister]. I didn't see any virgin blather in screen direction, or anything like that. It was just a wonderfully executed piece, and a complicated one. The mathematics involved in putting this film together, between Jack and Wally, and the great support of Alcon, it was not a easy little operetta. ~ Johnny Depp

I abandoned the assigned problems in standard calculus textbooks and followed my curiosity. Wherever I happened to be
a Vegas casino, Disneyland, surfing in Hawaii, or sweating on the elliptical in Boesel's Green Microgym
I asked myself, Where is the calculus in this experience? ~ Jennifer Ouellette

Young man, in mathematics you don't understand things. You just get used to them. ~ John Von Neumann

Another explanation for the failure of logic and observation alone to advance medicine is that unlike, say, physics, which uses a form of logic - mathematics - as its natural language, biology does not lend itself to logic. Leo Szilard, a prominent physicist, made this point when he complained that after switching from physics to biology he never had a peaceful bath again. As a physicist he would soak in the warmth of a bathtub and contemplate a problem, turn it in his mind, reason his way through it. But once he became a biologist, he constantly had to climb out of the bathtub to look up a fact. ~ John M Barry

The definition of a limit is essentially his [Cauchy's] creation and is as much of a miracle as those fantastic Swiss clocks of the period in which hundreds of gleaming cogs are made to celebrate not only the time and date but the phases of the moon. ~ David Berlinski

There is no thing as a man who does not create mathematics and yet is a fine mathematics teacher. Textbooks, course material-these do not approach in importance the communication of what mathematics is really about, of where it is going, and of where it currently stands with respect to the specific branch of it being taught. What really matters is the communication of the spirit of mathematics. It is a spirit that is active rather than contemplative-a spirit of disciplined search for adventures of the intellect. Only as adventurer can really tell of adventures. ~ Alfred Adler

Mathematical theories have sometimes been used to predict phenomena that were not confirmed until years later. For example, Maxwell's equations, named after physicist James Clerk Maxwell, predicted radio waves. Einstein's field equations suggested that gravity would bend light and that the universe is expanding. Physicist Paul Dirac once noted that the abstract mathematics we study now gives us a glimpse of physics in the future. In fact, his equations predicted the existence of antimatter, which was subsequently discovered. Similarly, mathematician Nikolai Lobachevsky said that "there is no branch of mathematics, however abstract, which may not someday be applied to the phenomena of the real world. ~ Clifford A. Pickover

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. ~ Jiddu Krishnamurti

The Ludolphian number is fixed in eternity - not a digit out of place, all characters in their proper order, an endless sentence written to the end of the world by the division of the circle's diameter into its circumference. ~ Richard Preston

Immortality is often ridiculous or cruel: few of us would have chosen to be Og or Ananias or Gallio. Even in mathematics, history sometimes plays strange tricks; Rolle figures in the textbooks of elementary calculus as if he had been a mathematician like Newton; Farey is immortal because he failed to understand a theorem which Haros had proved perfectly fourteen years before; the names of five worthy Norwegians still stand in Abel's Life, just for one act of conscientious imbecility, dutifully performed at the expense of their country's greatest man. But on the whole the history of science is fair, and this is particularly true in mathematics. No other subject has such clear-cut or unanimously accepted standards, and the men who are remembered are almost always the men who merit it. Mathematical fame, if you have the cash to pay for it, is one of the soundest and steadiest of investments. ~ G.H. Hardy

I thought. I thought of the slow yellow autumn in the swamp and the high honey sun of spring and the eternal silence of the marshes, and the shivering light on them, and the whisper of the spartina and sweet grass in the wind and the little liquid splashes of who-knew-what secret creatures entering that strange old place of blood-warm half earth, half water. I thought of the song of all the birds that I knew, and the soft singsong of the coffee-skinned women who sold their coiled sweet-grass baskets in the market and on Meeting Street. I thought of the glittering sun on the morning harbor and the spicy, somehow oriental smells from the dark old shops, and the rioting flowers everywhere, heavy tropical and exotic. I thought of the clop of horses' feet on cobblestones and the soft, sulking, wallowing surf of Sullivan's Island in August, and the countless small vistas of grace and charm wherever the eye fell; a garden door, a peeling old wall, an entire symmetrical world caught in a windowpane. Charlestone simply could not manage to offend the eye. I thought of the candy colors of the old houses in the sunset, and the dark secret churchyards with their tumbled stones, and the puresweet bells of Saint Michael's in the Sunday morning stillness. I thought of my tottering piles of books in the study at Belleau and the nights before the fire when my father told me of stars and butterflies and voyages, and the silver music of mathematics. I thought of hot, milky sweet coffee in the mo ~ Anne Rivers Siddons

Mathematics is the surest way to immortality. If you make a big discovery in mathematics, you will be remembered after everyone else will be forgotten ~ Paul Erdos

I accept no principles of physics which are not also accepted in mathematics. ~ Rene Descartes

Here we see that models, despite their reputation for impartiality, reflect goals and ideology. When I removed the possibility of eating Pop-Tarts at every meal, I was imposing my ideology on the meals model. It's something we do without a second thought. Our own values and desires influence our choices, from the data we choose to collect to the questions we ask. Models are opinions embedded in mathematics. ~ Cathy O'Neil

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. ~ Norbert Wiener

In science, technology, engineering and mathematics, men far outnumber women in the classroom and the boardroom. ~ Weili Dai

Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room and it's dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly, it's all illuminated and you can see exactly where you were. Then you enter the next dark room ... ~ Andrew Wiles

But my relief that David Auburn's Proof is less about its ballyhooed higher mathematics than the fragility of life and love was matched by my delight in his fine and tender play. ( ... ) Proof surprises us with its aliveness and intelligent modesty, and we have not met these characters before. ~ John Heilpern

Nature's great book is written in mathematics. ~ Galileo Galilei

My occupation is an open question. I was once an assistant professor of mathematics. Since then, I have spent time living in the woods of Montana. ~ Theodore Kaczynski

The research reported on in our book "A=B", has moved a whole active field of mathematics from the province of human thought to the realm of computer-fodder. It is quite exciting to think about what other fields of pure mathematics, hitherto thought to be reserved to human intelligence, might be moved to that realm next. The goal is to put ourselves out of business completely, and the work is well underway. ~ Herbert Wilf

Do you know why I love mathematics?"
"Because it blew your mind for free when you couldn't get drugs?"
Eccles snorted in surprise. "Well, yes, but there's another reason. ~ Brendan Halpin

The mathematical giant [Gauss], who from his lofty heights embraces in one view the stars and the abysses ... ~ Farkas Bolyai

Economics is haunted by more fallacies than any other study known to man. This is no accident. The inherent difficulties of the subject would be great enough in any case, but they are multiplied a thousandfold by a factor that is insignificant in, say, physics, mathematics or medicine - the special pleading of selfish interests. ~ Henry Hazlitt

What is the proper justification of a mathematician's life? My answers will be, for the most part, such as are expected from a mathematician: I think that it is worthwhile, that there is ample justification. But I should say at once that my defense of mathematics will be a defense of myself, and that my apology is bound to be to some extent egotistical. I should not think it worth while to apologize for my subject if I regarded myself as one of its failures. Some egotism of this sort is inevitable, and I do not feel that it really needs justification. Good work is no done by "humble" men. It is one of the first duties of a professor, for example, in any subject, to exaggerate a little both the importance of his subject and his own importance in it. A man who is always asking "Is what I do worth while?" and "Am I the right person to do it?" will always be ineffective himself and a discouragement to others. He must shut his eyes a little and think a little more of his subject and himself than they deserve. This is not too difficult: it is harder not to make his subject and himself ridiculous by shutting his eyes too tightly. ~ G.H. Hardy

In mathematics there are no true controversies. ~ Carl Friedrich Gauss

This success permits us to hope that after thirty or forty years of observation on the new Planet [Neptune], we may employ it, in its turn, for the discovery of the one following it in its order of distances from the Sun. Thus, at least, we should unhappily soon fall among bodies invisible by reason of their immense distance, but whose orbits might yet be traced in a succession of ages, with the greatest exactness, by the theory of Secular Inequalities.
[Following the success of the confirmation of the existence of the planet Neptune, he considered the possibility of the discovery of a yet further planet.] ~ Urbain Le Verrier

But many, many stories were told; from what could be gathered, all fifty of the mine's inhabitants had reacted on each other, two by two, as in combinatorial analysis, that is to say, everyone with all the others, and especially every man with all the women, old maids or married, and every woman with all the men. All I had to do was to select two names at random, better if different sex, and ask a third person, "What happened with those two?" and lo and behold, a splendid story was unfolded for me, since everyone knew the story of everyone else. ~ Primo Levi

There is an old debate," Erdos liked to say, "about whether you create mathematics or just discover it. In other words, are the truths already there, even if we don't yet know them?" Erdos had a clear answer to this question: Mathematical truths are there among the list of absolute truths, and we just rediscover them. Random graph theory, so elegant and simple, seemed to him to belong to the eternal truths. Yet today we know that random networks played little role in assembling our universe. Instead, nature resorted to a few fundamental laws, which will be revealed in the coming chapters. Erdos himself created mathematical truths and an alternative view of our world by developing random graph theory. Not privy to nature's laws in creating the brain and society, Erdos hazarded his best guess in assuming that God enjoys playing dice. His friend Albert Einstein, at Princeton, was convinced of the opposite: "God does not play dice with the universe. ~ Albert Laszlo Barabasi

Einstein and the Quantum is delightful to read, with numerous historical details that were new to me and cham1ing vignettes of Einstein and his colleagues. By avoiding mathematics, Stone makes his book accessible to general readers, but even physicists who are well versed in Einstein and his physics are likely to find new insights into the most remarkable mind of the modern era. ~ Daniel Kleppner

The golden ratio, as well as the Great Pyramid as an expression of it, is an important key to our universe containing the Earth and the Moon. ... The ratio between the Earth and the Moon is in fact the basis for the mathematical concept of 'squaring the circle' ... ~ Willem Witteveen

There is a slam-dunk case for extending foreign language teaching to children aged five. Just as some people have taken a perverse pride in not understanding mathematics, so we have taken a perverse pride in the fact that we do not speak foreign languages, and we just need to speak louder in English. ~ Michael Gove

We can ... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics. ~ Hans Reichenbach

Write as you like, use the rhythms that come out, try different instruments, sit at the piano, destroy the metric, shout instead of singing, blow your guitar and ring the horn. Hate mathematics, and love eddies. Creation is a bird without a flight plan, that will never fly in a straight line. ~ Violeta Parra