Quotes About Mathematics

Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.

May not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life.

The history of mathematics, lacking the guidance of philosophy, [is] blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the history of mathematics, is empty.

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.

The main duty of the historian of mathematics, as well as his fondest privilege, is to explain the humanity of mathematics, to illustrate its greatness, beauty and dignity, and to describe how the incessant efforts and accumulated genius of many generations have built up that magnificent monument, the object of our most legitimate pride as men, and of our wonder, humility and thankfulness, as individuals. The study of the history of mathematics will not make better mathematicians but gentler ones, it will enrich their minds, mellow their hearts, and bring out their finer qualities.

...mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics. Every other science, even logic, especially in its early stages, is in danger of evaporating into airy nothingness, degenerating, as the Germans say, into an arachnoid film, spun from the stuff that dreams are made of. There is no such danger for pure mathematics; for that is precisely what mathematics ought to be.

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 mathematics is the odd one, odd because I'm not sure how to measure its effect. It is so fundamental to my outlook on everything and yet I'm not even sure how. It must be because in my formative years it was everything to me, the single place of beauty in my life, and of breathtaking beauty at that. I still believe that pure mathematics is the most creative thing that humanity does, though I am no longer a part of it.

It is indubitable that a 50-year-old mathematician knows the mathematics he learned at 20 or 30, but has only notions, often rather vague, of the mathematics of his epoch, i.e. the period of time when he is 50.

The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things.

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.

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.

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

Thers is this wonderful iconoclast at Rutgers, Doron Zeilberger, who says that our mathematics is the result of a random walk, by which he means what WE call mathematics. Likewise, I think, for the sciences.

I tell you that studying humanities in high school is more important than mathematics - mathematics is too sharp an instrument, no good for kids.

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then suchand such another proposition is true of that thing.... Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself.

Applied mathematics will always need pure mathematics just as anteaters will always need ants.

Mathematics is a language. We want scientists to be able to read it, speak it, and write it. But we are are not training them to be grammarians.

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.

All mathematicians share... a sense of amazement over the infinite depth and the mysterious beauty and usefulness of mathematics.

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.

Standard mathematics has recently been rendered obsolete by the discovery that for years we have been writing the numeral five backward. This has led to reevaluation of counting as a method of getting from one to ten. Students are taught advanced concepts of Boolean algebra, and formerly unsolvable equations are dealt with by threats of reprisals.

The power of equations lies in the philosophically difficult correspondence between mathematics, a collective creation of human minds, and an external physical reality. Equations model deep patterns in the outside world. By learning to value equations, and to read the stories they tell, we can uncover vital features of the world around us.

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.

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.

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.

This splendid subject [mathematics], queen of all exact sciences, and the ideal and norm of all careful thinking.

It seems to me now that mathematics is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the number of people who feel it, to that of music, but because it gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect and yet true.

It is perplexing to see the flexibility of the so-called 'exact sciences' which by cast-iron laws of logic and by the infallible help of mathematics can lead to conclusions which are diametrically opposite to one another.

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.

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.

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.

Combinatorics is an honest subject. No adèles, no sigma-algebras. You count balls in a box, and you either have the right number or you haven't. You get the feeling that the result you have discovered is forever, because it's concrete. Other branches of mathematics are not so clear-cut. Functional analysis of infinite-dimensional spaces is never fully convincing; you don't get a feeling of having done an honest day's work. Don't get the wrong idea - combinatorics is not just putting balls into boxes. Counting finite sets can be a highbrow undertaking, with sophisticated techniques.

[All phenomena] are equally susceptible of being calculated, and all that is necessary, to reduce the whole of nature to laws similar to those which Newton discovered with the aid of the calculus, is to have a sufficient number of observations and a mathematics that is complex enough.

In my youth it was said that what was too silly to be said may be sung. In modern economics it may be put into mathematics.

Mathematics is the key and door to the sciences.

Mathematics is, in many ways, the most precious response that the human spirit has made to the call of the infinite.

There are two generic and invariable features that characterize utopias. One is the content: the authors of utopias paint what they consider to be ideal societies; translating this into the language of mathematics, we might say that utopias bear a + sign. The other feature, organically growing out of the content, is to be found in the form: a utopia is always static; it is always descriptive and has no, of almost no, plot dynamics.

The scientists from Franklin to Morse were clear thinkers and did not produce erroneous theories. The scientists of today think deeply instead of clearly. One must be sane to think clearly, but one can think deeply and be quite insane. Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.

I finally reached the conclusion that mathematics was the study I was best fitted to follow, though I did not clearly see in what way I should turn the subject to account.

Mathematics is the supreme nostalgia of our time.

I hated science in high school. Technology? Engineering? Math? Why would I ever need this? Little did I realize that music was also about science, technology, engineering and mathematics, all rolled into one.

The merit of painting lies in the exactness of reproduction. Painting is a science and all sciences are based on mathematics. No human inquiry can be a science unless it pursues its path through mathematical exposition and demonstration.

Perhaps there will be prattlers who, although completely ignorant of mathematics, nevertheless take it upon themselves to pass judgment on mathematical questions, and on account of some passage in Scripture, badly distorted to their purpose, will dare to censure and assail what I have presented here.