Quotes About Mathematics

One cannot inquire into the foundations and nature of mathematics without delving into the question of the operations by which the mathematical activity of the mind is conducted. If one failed to take that into account, then one would be left studying only the language in which mathematics is represented rather than the essence of mathematics.

The first and foremost duty of the high school in teaching mathematics is to emphasize methodical work in problem solving...The teacher who wishes to serve equally all his students, future users and nonusers of mathematics, should teach problem solving so that it is about one-third mathematics and two-thirds common sense.

If you want to be a physicist, you must do three things-first, study mathematics, second, study more mathematics, and third, do the same.

I was fortunate to find an extraordinary mathematics and applied mathematics program in Toronto.

It has been a fortunate fact in the modern history of physical science that the scientist constructing a new theoretical system has nearly always found that the mathematics. . . required. . . had already been worked out by pure mathematicians for their own amusement. . . . The moral for statesmen would seem to be that, for proper scientific "planning", pure mathematics should be endowed fifty years ahead of scientists.

There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics (mathematicians conceived of black holes long before astronomers actually found any), and allows more freedom of expression than poetry, art, or music (which depends heavily on properties of the physical universe). Mathematics is the purest of the arts, as well as the most misunderstood.

It seems that every practitioner of physics has had to wonder at some point why mathematics and physics have come to be so closely entwined. Opinions vary on the answer. ..Bertrand Russell acknowledged..'Physics is mathematical not because we know so much about the physical world, but because we know so little.' ..Mathematics may be indispensable to physics, but it obviously does not constitute physics.

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.

General Systems Theory is a name which has come into use to describe a level of theoretical model-building which lies somewhere between the highly generalized constructions of pure mathematics and the specific theories of the specialized disciplines. Mathematics attempts to organize highly general relationships into a coherent system, a system however which does not have any necessary connections with the "real" world around us. It studies all thinkable relationships abstracted from any concrete situation or body of empirical knowledge.

I didn't feel comfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of everything and explore the world.

Mathematics is being lazy. Mathematics is letting the principles do the work for you so that you do not have to do the work for yourself

The problem is that modern fundamental physics is so far from you and me. The mathematics has become so much more complicated that you need at least 10 years to understand it. Fundamental physics has advanced so far from the understanding of most people that there is really a big disconnect.

Mathematics is written for mathematicians.

If all of mathematics disappeared, physics would be set back by exactly one week.

There are only two kinds of certain knowledge: Awareness of our own existence and the truths of mathematics.

Mathematical study and research are very suggestive of mountaineering. Whymper made several efforts before he climbed the Matterhorn in the 1860's and even then it cost the life of four of his party. Now, however, any tourist can be hauled up for a small cost, and perhaps does not appreciate the difficulty of the original ascent. So in mathematics, it may be found hard to realise the great initial difficulty of making a little step which now seems so natural and obvious, and it may not be surprising if such a step has been found and lost again.

When a branch of mathematics ceases to interest any but the specialists, it is very near its death, or at any rate dangerously close to a paralysis, from which it can be rescued only by being plunged back into the vivifying source of the science.

... geometry became a symbol for human relations, except that it was better, because in geometry things never go bad. If certain things occur, if certain lines meet, an angle is born. You cannot fail. It's not going to fail; it is eternal. I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total. Thus, I'm able to avoid or manipulate or process pain.

[Regarding mathematics,] there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy. This may be true; indeed it is probable, since the sensational triumphs of Einstein, that stellar astronomy and atomic physics are the only sciences which stand higher in popular estimation.

Cryptography shifts the balance of power from those with a monopoly on violence to those who comprehend mathematics and security design.

The mathematics of rhythm are universal. They don't belong to any particular culture.

I think the biggest misconception is that everybody has to learn mathematics. That seems to be a complete mistake.

And silence. She liked the silence most of all. The silence in which the body, senses, the instincts, are more alert, more powerful, more sensitized, live a more richly perfumed and intoxication life, instead of transmuting into thoughts, words, into exquisite abstractions, mathematics of emotion in place of violent impact, the volcanic eruptions of fever, lust and delight.

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.

Mathematics is the most beautiful and most powerful creation of the human spirit.

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 would not dare to say that there is a direct relation between mathematics and madness, but there is no doubt that great mathematicians suffer from maniacal characteristics, delirium and symptoms of schizophrenia.

I did not have a very literary background. I came to poetry from the sciences and mathematics, and also through an interest in Japanese and Chinese poetry in translation.

The laws of nature are written by the hand of God in the language of mathematics.

There have been many authorities who have asserted that the basis of science lies in counting or measuring, i.e. in the use of mathematics. Neither counting nor measuring can however be the most fundamental processes in our study of the material universe-before you can do either to any purpose you must first select what you propose to count or measure, which presupposes a classification.

The best result of mathematics is to be able to do without it.

Mathematics is not a separate entity. It owes a great deal of its power and its beauty to other disciplines.

It can be argued that the mathematics behind these images [of the orbit diagram for quadratic functions and the Mandelbrot set] is even prettier than the pictures themselves.

Because of mathematics precise, formal character, mathematical arguments remain sound even when they are long and complex. In contast, common sense arguments can generally be trusted only if they remain short; even moderately long nonmathematical arguments rapidly becomes farfetched an dubious.

Although I am even now still a layman in the area of mathematics, and although I lack theoretical knowledge, the mathematicians, and in particular the crystallographers, have had considerable influence on my work of the last twenty years. The laws of the phenomena around us--order, regularity, cyclical repetition, and renewals--have assumed greater and greater importance for me. The awareness of their presence gives me peace and provides me with support. I try in my prints to testify that we live in a beautiful and orderly world, and not in a formless chaos, as it sometimes seems.

Almost everything about the universe is astounding. I think the most amazing thing is how gifted we are - we are only monkeys who came down from the trees just recently. We have these amazing gifts of music and mathematics and painting and Olympic running.

Modern mathematics, that most astounding of intellectual creations, has projected the mind's eye through infinite time and the mind's hand into boundless space.

I wasn't actually very naturally good at economics. My brain doesn't work very well, in terms of mathematics.

Pure mathematics is, in its way, the poetry of logical ideas. ... [By seeking] logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.

Logic issues in tautologies, mathematics in identities, philosophy in definitions; all trivial, but all part of the vital work of clarifying and organising our thought.

Questions that pertain to the foundations of mathematics, although treated by many in recent times, still lack a satisfactory solution. Ambiguity of language is philosophy's main source of problems. That is why it is of the utmost importance to examine attentively the very words we use.

This is an extremely ambitious book. In addition to science and mathematics, Byers brings to bear insights from literature, philosophy, religion, history, anthropology, medicine, and psychology. The Blind Spot breaks new ground, and represents a major step forward in the philosophy of science. The book is also a page-turner, which is rare for this topic.

Why do children dread mathematics? Because of the wrong approach. Because it is looked at as a subject.

In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug.

I still can't figure out what inspired me to do physics. But since I was nine or ten years old, I wanted to be like [Albert] Einstein. He was my hero. I knew no physicists. I knew no scientists. I had nobody around me. And I went to a convent that didn't even have higher mathematics and physics. I taught myself these subjects in order to get into university.

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.

Mathematics may humbly help in the market-place, but it also reaches to the stars.

The use of mathematics has brought rigor to economics. Unfortunately, it has also brought mortis.