Quotes About Mathematics

To criticize mathematics for its abstraction is to miss the point entirely. Abstraction is what makes mathematics work. If you concentrate too closely on too limited an application of a mathematical idea, you rob the mathematician of his most important tools: analogy, generality, and simplicity. Mathematics is the ultimate in technology transfer.

All our surest statements about the nature of the world are mathematical statements, yet we do not know what mathematics "is"... and so we find that we have adapted a religion strikingly similar to many traditional faiths. Change "mathematics" to "God" and little else might seem to change. The problem of human contact with some spiritual realm, of timelessness, of our inability to capture all with language and symbol-all have their counterparts in the quest for the nature of Platonic mathematics.

It is almost as hard to define mathematics as it is to define economics, and one is tempted to fall back on the famous old definition attributed to Jacob Viner, "Economics is what economists do," and say that mathematics is what mathematicians do. A large part of mathematics deals with the formal relations of quantities or numbers.

Mathematical thinking is not the same as doing mathematics - at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box - a valuable ability in today's world.

It is impossible to overstate the imporance of problems in mathematics. It is by means of problems that mathematics develops and actually lifts itself by its own bootstraps... Every new discovery in mathematics, results from an attempt to solve some problem.

Mathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt to draw absolute conclusions. All mathematical truths are relative, conditional. In E. T. Bell Men of Mathematics, New York: Simona and Schuster, 1937.

Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.

People think that mathematics is complicated. Mathematics is the simple bit, it’s the stuff we CAN understand. It’s cats that are complicated.

... the word "theory" ... was originally an Orphic word, which Cornford interprets as "passionate sympathetic contemplation" ... For Pythagoras, the "passionate sympathetic contemplation" was intellectual, and issued in mathematical knowledge ... To those who have reluctantly learnt a little mathematics in school this may seem strange; but to those who have experienced the intoxicating delight of sudden understanding that mathematics gives, from time to time, to those who love it, the Pythagorean view will seem completely natural.

There are four great sciences, without which the other sciences cannot be known nor a knowledge of things secured ... Of these sciences the gate and key is mathematics ... He who is ignorant of this [mathematics] cannot know the other sciences nor the affairs of this world.

Without mathematics, there’s nothing you can do. Everything around you is mathematics. Everything around you is numbers.

Mathematics is ordinarily considered as producing precise and dependable results; but in the stock market the more elaborate and abstruse the mathematics the more uncertain and speculative are the conclusions we draw there from. Whenever calculus is brought in, or higher algebra, you could take it as a warning that the operator was trying to substitute theory for experience, and usually also to give to speculation the deceptive guise of investment.

Mathematics without natural history is sterile, but natural history without mathematics is muddled.

In mathematics we find the primitive source of rationality; and to mathematics must the biologists resort for means to carry out their researches.

Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.

When the mathematician says that such and such a proposition is true of one thing, it may be interesting, and it is surely safe. But when he tries to extend his proposition to everything, though it is much more interesting, it is also much more dangerous. In the transition from one to all, from the specific to the general, mathematics has made its greatest progress, and suffered its most serious setbacks, of which the logical paradoxes constitute the most important part. For, if mathematics is to advance securely and confidently, it must first set its affairs in order at home.

Mathematics is one of the surest ways for a man to feel the power of thought and the magic of the spirit. Mathematics is one of the eternal truths and, as such, raises the spirit to the same level on which we feel the presence of God.

Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning.

God exists since mathematics is consistent, and the Devil exists since we cannot prove it.

Mathematics expresses values that reflect the cosmos, including orderliness, balance, harmony, logic, and abstract beauty.

Combinatorial analysis, in the trivial sense of manipulating binomial and multinomial coefficients, and formally expanding powers of infinite series by applications ad libitum and ad nauseamque of the multinomial theorem, represented the best that academic mathematics could do in the Germany of the late 18th century.

Mathematics is the handwriting on the human consciousness of the very Spirit of Life itself.

Few realize that the world of modern mathematics is rich with vivid images and provocative ideas.

Beauty means a lot of different things to a lot of different people. A lot of different ways in which things can be beautiful. But this really has a very specific meaning and which is more along the lines of elegance which is that we say an idea is beautiful or elegant in mathematics or physics if a very simple principle or a very simple idea, or simple set of ideas, turns out to be very powerful and leads to all sort of unexpected structure and unexpected predictions.

We the undersigned, intend to establish an instruction and training institution which differs from the common elementary schools principally in that it will embrace, outside of (in addition to) the general and elementary curriculum, all branches of the classical high school, which are necessary for a true Christian and scientific education, such as: Religion, the Latin, Greek, Hebrew, German, French and English languages; History, Geography, Mathematics, Physics, natural history, Introduction to Philosophy, Music, and Drawing.

These days people are much more aware that mathematics is a communal endeavor: even the most brilliant idea gets meaning only from its relation to the whole.

I read one or two other books which gave me a background in mathematics other than logic.

If there is one thing in mathematics that fascinates me more than anything else (and doubtless always has), it is neither "number" nor "size", but always form. And among the thousand-and-one faces whereby form chooses to reveal itself to us, the one that fascinates me more than any other and continues to fascinate me, is the structure hidden in mathematical things.

The importance of the "New Mathematics" lies mainly in the fact that it has taught us the difference between the disc and the circle.

As a kid, I dreamt of becoming a writer. My most exciting pastime was reading novels; in fact, I would read anything I could find. I never thought I would pursue mathematics until my last year in high school. I grew up in a family with three siblings. My parents were always very supportive and encouraging. It was important for them that we have meaningful and satisfying professions, but they didn't care as much about success and achievement.

Perhaps the best reason for regarding mathematics as an art is not so much that it affords an outlet for creative activity as that it provides spiritual values. It puts man in touch with the highest aspirations and lofiest goals. It offers intellectual delight and the exultation of resolving the mysteries of the universe.

Thinking - in particular abstract thinking, which most of us are introduced to through the study of mathematics and literature - helps us learn that we can become problem solvers.

Here, where we reach the sphere of mathematics, we are among processes which seem to some the most inhuman of all human activities and the most remote from poetry. Yet it is here that the artist has the fullest scope of his imagination.

[In mathematics] There are two kinds of mistakes. There are fatal mistakes that destroy a theory, but there are also contingent ones, which are useful in testing the stability of a theory.

Now do you not see that the eye embraces the beauty of the whole world? It counsels and corrects all the arts of mankind... it is the prince of mathematics, and the sciences founded on it are absolutely certain. It has measured the distances and sizes of the stars it has discovered the elements and their location... it has given birth to architecture and to perspective and to the divine art of painting.

Mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics.

The so-called mysteries of quantum mechanics are in its philosophical interpretation, not in its mathematics.

Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.

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.

I suppose you are two fathoms deep in mathematics, and if you are, then God help you. For so am I, only with this difference: I stick fast in the mud at the bottom, and there I shall remain.

Being exposed to theory, stimulated by a basic love of concepts and mathematics, was a marvelous experience.

[The] humanization of mathematical teaching, the bringing of the matter and the spirit of mathematics to bear not merely upon certain fragmentary faculties of the mind, but upon the whole mind, that this is the greatest desideratum is. I assume, beyond dispute.

Regarding the fundamental investigations of mathematics, there is no final ending ... no first beginning.

Anyone who believes a growth rate in excess of 15% per annum over the long term is attainable should pursue a career in sales, but avoid one in mathematics.

If we ever establish contact with intelligent aliens living on a planet around a distant star ... They would be made of similar atoms to us. They could trace their origins back to the big bang 13.7 billion years ago, and they would share with us the universe's future. However, the surest common culture would be mathematics.

I can only play the sport for so long, I have mathematics for the rest of my life.

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.

Essentially all civilizations that rose to the level of possessing an urban culture had need for two forms of science-related technology, namely, mathematics for land measurements and commerce and astronomy for time-keeping in agriculture and aspects of religious rituals.