Top 1200 Mathematics Quotes & Sayings - Page 20

We should teach kids how to question. Now having said that, of course, to be a productive adult, there are certain skills that are required - reading, writing, and, in the old-fashioned days, we used to say arithmetic. Now we say mathematics.

Sir Arthur Eddington deduces religion from the fact that atoms do not obey the laws of mathematics. Sir James Jeans deduces it from the fact that they do.

By keenly confronting the enigmas that surround us, and by considering and analyzing the observations that I had made, I ended up in the domain of mathematics. Although I am absolutely without training in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists.

To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.

If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper.

Why don't we want our children to learn to do mathematics? Is it that we don't trust them, that we think it's too hard? We seem to feel that they are capable of making arguments and coming to their own conclusions about Napoleon. Why not about triangles?

I learnt to distrust all physical concepts as the basis for a theory. Instead one should put one's trust in a mathematical scheme, even if the scheme does not appear at first sight to be connected with physics. One should concentrate on getting interesting mathematics.

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.

My first contact with game theory was a popular article in 'Fortune Magazine' which I read in my last high school year. I was immediately attracted to the subject matter, and when I studied mathematics, I found the fundamental book by von Neumann and Morgenstern in the library and studied it.

The Good Spirit never cared for the colleges, and though all men and boys were now drilled in Greek, Latin, and Mathematics, it had quite left these shells high on the beach, and was creating and feeding other matters [science] at other ends of the world.

Wherever Mathematics is mixed up with anything, which is outside its field, you will find attempts to demonstrate these merely conventional propositions a priori, and it will be your task to find out the false deduction in each case.

Football is not played on paper, it is played on a pitch. This game is not mathematics and in football, two plus two very rarely equals four - it's usually three or five.

Through music you can become sad, joyful, loving, you can learn. You can learn mathematics, touch, pacing... Oh my God! Ooh... Wow... You can see colors through music. Anything!

... mathematics is very much like poetry ... what makes a good poem -- a great poem -- is that there is a large amount of thought expressed in very few words. In this sense formulas like or are poems.

It has never been in my power to study anything, mathematics, ethics, metaphysics, gravitation, thermodynamics, optics, chemistry, comparative anatomy, astronomy, psychology, phonetics, economics, the history of science, whist, men and women, wine, metrology, except as a study of semeiotic .

The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism.

The most important single thing about string theory is that it's a highly mathematical theory, and the mathematics holds together in a very tight and consistent way. It contains in its basic structure both quantum mechanics and the theory of gravity. That's big news.

And then there is Pythagoras. The legend is that the founder of theoretical mathematics was so outraged when one of his students, the haplessly gifted Hippasus, discovered irrational numbers that he sent the poor fellow out on a raft to drown, initiating a venerable tradition of professors mistreating their graduate students.

In my own research when I'm working with equations, I never feel like I really understand what I'm doing if I'm solely relying on the mathematics for my understanding. I need to have a visual picture in my mind. I'm constantly translating from the math to some intuitive mind's-eye picture.

From the ages of five to twelve, I attended the Saint Laurence O'Toole elementary school in Lawrence, a city next to Methuen, and was taught by sisters of the Catholic order of Notre Dame de Namour. I enjoyed all my subjects there. I do not remember ever learning any science, except for mathematics.

I had an excellent math and physics teacher in high school named T.C. Patel, and in the university, I had truly dedicated professors in both physics and mathematics who gave me a sound foundation with which to pursue graduate studies.

. . . She knew only that if she did or said thus-and-so, men would unerringly respond with the complimentary thus-and-so. It was like a mathematical formula and no more difficult, for mathematics was the one subject that had come easy to Scarlett in her schooldays.

There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else - but persistent.

[Mathematics is] purely intellectual, a pure theory of forms, which has for its objects not the combination of quantities or their images, the numbers, but things of thought to which there could correspond effective objects or relations, even though such a correspondence is not necessary.

One of the strangest features of string theory is that it requires more than the three spatial dimensions that we see directly in the world around us. That sounds like science fiction, but it is an indisputable outcome of the mathematics of string theory.

The heart of mathematics consists of concrete examples and concrete problems. Big general theories are usually afterthoughts based on small but profound insights; the insights themselves come from concrete special cases.

I chose to deal with the science of cryptography. Cryptography began in mathematics. Codes were developed, even from Caesar's time, based on number theory and mathematical principles. I decided to use those principles and designed a work that is encoded.

We have such a great depth of human history in all of the arts, whether it's opera or mathematics or painting or classical music or jazz. There's so many things to study, new books to read, and certainly always ways to transform old ideas and to come up with new ones.

At the age of eleven, I began Euclid, with my brother as my tutor. This was one of the great events of my life, as dazzling as first love. I had not imagined there was anything so delicious in the world. From that moment until I was thirty-eight, mathematics was my chief interest and my chief source of happiness.

I earned my Ph.D. in philosophy, and one of my specializations was the logic and mathematics of game theory. I've also got a degree in drama, so I know about stories, characterizations, plot arcs, and the like. Lots of game designers can do one or the other: I've got the skills for both.

Logic leaves us no choice. In that sense, math always involves both invention and discovery: we invent the concepts but discover their consequences. … in mathematics our freedom lies in the questions we ask – and in how we pursue them – but not in the answers awaiting us.

I stayed away from mathematics not so much because I knew it would be hard work as because of the amount of time I knew it would take, hours spent in a field where I was not a natural.

At the beginning of the new millennium, we still do not know why mathematics is true and whether it is certain. But we know what we do not know in an immeasurably richer way than we did. And learning this has been a remarkable achievement-among the greatest and least-known of the modern era.

Whatever the course, whether the course was boring or interesting to me, whether I was talented in mathematics or not talented in languages, my parents expected A's.

Music is a science which should have definite rules; these rules should be drawn from an evident principle; and this principle cannot really be known to us without the aid of mathematics.

One would normally define a "religion" as a system of ideas that contain statements that cannot be logically or observationally demonstrated... Gödels theorem not only demonstrates that meathematics is a religion, but shows that mathematics is the only religion that proves itself to be one!

Films are not mathematics - that's the first thing you need to understand. At least, that's how I feel. They are not words on paper. Films are made with people, with teams and with individual bundles of creativity coming together to fulfill the vision of an individual who is the director of the film.

I was lucky to get into computers when it was a very young and idealistic industry. There weren't many degrees offered in computer science, so people in computers were brilliant people from mathematics, physics, music, zoology, whatever. They loved it, and no one was really in it for the money.

While physics and mathematics may tell us how the universe began, they are not much use in predicting human behavior because there are far too many equations to solve. I'm no better than anyone else at understanding what makes people tick, particularly women.

University President: Why is it that you physicists always require so much expensive equipment? Now the Department of Mathematics requires nothing but money for paper, pencils, and erasers . . . and the Department of Philosophy is better still. It doesn't even ask for erasers.

The two important variables for the policy formulation are projected inflation and the output gap. There is no clear hidebound mathematics that we must give 'X' weight to inflation and 'Y' weight to growth and form the associated policy.

As one reads mathematics, one needs to have an active mind, asking questions, forming mental connections between the current topic and other ideas from other contexts, so as to develop a sense of the structure, not just familiarity with a particular tour through the structure.

The student of mathematics must get rid of all arbitrary thinking and follow purely the demands of thought. In thinking in this way, the laws of the spiritual world flow into him. This regulated thinking leads to the most spiritual truths.

The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.

Very few people can communicate with one another. The only language that's not subject to interpretation is mathematics, chemistry, basic science, engineering principles, and applied agriculture. But other than that, many systems today are subject to interpretation.

I have been running maths clubs for children completely free. In my building in Bangalore, I conduct maths clubs for several months, and every child who attended the club was poor in mathematics and is now showing brilliant results.

[Adams] supposed that, except musicians, everyone thought Beethoven a bore, as every one except mathematicians thought mathematics a bore.

I am convinced that the act of thinking logically cannot possibly be natural to the human mind. If it were, then mathematics would be everybody's easiest course at school and our species would not have taken several millennia to figure out the scientific method.

I take after my mother more than my father in terms of personality. My mother's a worrier, and I'm a worrier. Both were very good with numbers and mathematics, so I kind of got that from both of them.

If there should chance to be any mathematicians who, ignorant in mathematics yet pretending to skill in that science, should dare, upon the authority of some passage of Scripture wrested to their purpose, to condemn and censure my hypothesis, I value them not, and scorn their inconsiderate judgement. De Revolutionibus Coelestibus

Do not trust financial market risk models. Despite the predilection of some analysts to model the financial markets using sophisticated mathematics, the markets are governed by behavioral science, not physical science.

If you help others, you will be helped, perhaps tomorrow, perhaps in one hundred years, but you will be helped. Nature must pay off the debt. It is a mathematical law and all life is mathematics.

Mathematics are the result of mysterious powers which no one understands, and which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty's sake and pulls it down to earth.

Nature's economy shall be the base for our own, for it is immutable, but ours is secondary. An economist without knowledge of nature is therefore like a physicist without knowledge of mathematics.

In studying mathematics or simply using a mathematical principle, if we get the wrong answer in sort of algebraic equation, we do not suddenly feel that there is an anti-mathematical principle that is luring us into the wrong answers.

The standard "foundation" for mathematics starts with sets and their elements. It is possible to start differently, by axiomatising not elements of sets but functions between sets. This can be done by using the language of categories and universal constructions.

Across a range of inferences involving not just language but mathematics, logic problems, and spatial reasoning, sleep has been shown to enhance the formation and understanding of abstract relations, so much so that people often wake having solved a problem that was unsolvable the night before.

Apart from two periods of intense study, of music between the ages of 12 and 14 and of mathematics between the ages of 14 and 16, I coasted, daydreaming, through most of my school years.

This book is about physics and its about physics and its relationship with mathematics and how they seem to be intimately related and to what extent can you explore this relationship and trust it.

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.