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.

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.

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.

Statistics is, or should be, about scientific investigation and how to do it better, but many statisticians believe it is a branch of mathematics. Now I agree that the physicist, the chemist, the engineer, and the statistician can never know too much mathematics, but their objectives should be better physics, better chemistry, better engineering, and in the case of statistics, better scientific investigation. Whether in any given study this implies more or less mathematics is incidental.

I would say, if you like, that the party is like an out-moded mathematics...that is to say, the mathematics of Euclid. We need to invent a non-Euclidian mathematics with respect to political discipline.

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 the queen of science, and arithmetic the queen of mathematics.

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 error in the teaching of mathematics is that] mathematics is expected either to be immediately attractive to students on its own merits or to be accepted by students solely on the basis of the teacher's assurance that it will be helpful in later life. [And yet,] mathematlcs is the key to understanding and mastering our physical, social and biological worlds.

Let me also remind you that zero, like all of mathematics, is fictional and an idealization. It is impossible to reach absolute zero temperature or to get perfect vacuum. Luckily, mathematics is a fairyland where ideal and fictional objects are possible.

Mathematics and logic have been proved to be one; a fact from which it seems to follow that mathematics may successfully deal with non-quantitative problems in a much broader sense than was suspected to be possible.

I never could do anything with figures, never had any talent for mathematics, never accomplished anything in my efforts at that rugged study, and to-day the only mathematics I know is multiplication, and the minute I get away up in that, as soon as I reach nine times seven- [He lapsed into deep thought, trying to figure nine times seven. Mr. McKelway whispered the answer to him.] I've got it now. It's eighty-four. Well, I can get that far all right with a little hesitation. After that I am uncertain, and I can't manage a statistic.

Though determinants and matrices received a great deal of attention in the nineteenth century and thousands of papers were written on these subjects, they do not constitute great innovations in mathematics.... Neither determinants nor matrices have influenced deeply the course of mathematics despite their utility as compact expressions and despite the suggestiveness of matrices as concrete groups for the discernment of general theorems of group theory.

Well, I was always... I used to get 100% in physics and chemistry and mathematics (well, maybe a couple of points off in mathematics), and that was in high school.

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

For me, rhythm is a type of divine mathematics in a way. No matter where you're from, we can all understand the mathematics of rhythm. I try to apply this mathematical thinking to my playing.

Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity-- to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs-- you deny them mathematics itself.

Except in mathematics, the shortest distance between point A and point B is seldom a straight line. I don't believe in mathematics.

I'm sorry to say that the subject I most disliked was mathematics. I have thought about it. I think the reason was that mathematics leaves no room for argument. If you made a mistake, that was all there was to it.

I do not think the division of the subject into two parts - into applied mathematics and experimental physics a good one, for natural philosophy without experiment is merely mathematical exercise, while experiment without mathematics will neither sufficiently discipline the mind or sufficiently extend our knowledge in a subject like physics.

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.

I am ever more intrigued by the correspondence between mathematics and physical facts. The adaptability of mathematics to the description of physical phenomena is uncanny.

The study of mathematics is apt to commence in disappointment.

Education is like a diamond with many facets: It includes the basic mastery of numbers and letters that give us access to the treasury of human knowledge, accumulated and refined through the ages; it includes technical and vocational training as well as instruction in science, higher mathematics, and humane letters.

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.

Mathematics, even in its present and most abstract state, is not detached from life. It is just the ideal handling of the problems of life.

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method-more daring than anything that the history of philosophy records-of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.

Logic and mathematics are nothing but specialised linguistic structures.

In my family, as in most middle-class Indian families I knew when I was growing up, science and mathematics were held in awe.

If you refuse to study anatomy, the arts of drawing and perspective, the mathematics of aesthetics, and the science of color, let me tell you that this is more a sign of laziness than of genius.

[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.

The mathematics are distinguished by a particular privilege, that is, in the course of ages, they may always advance and can never recede.

Mathematics - the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human affairs.

There are certainly lots of jobs in computer coding, but coding doesn't really require advanced mathematics. And engineering jobs, they vary widely in the amount of demand that we actually need. So, you know, the number of people for whom the job description includes Newton's calculus is not perhaps that high.

By and large it is uniformly true in mathematics that there is a time lapse between a mathematical discovery and the moment when it is useful; and that this lapse of time can be anything from 30 to 100 years, in some cases even more; and that the whole system seems to function without any direction, without any reference to usefulness, and without any desire to do things which are useful.

The conception of objective reality ... has thus evaporated ... into the transparent clarity of mathematics that represents no longer the behavior of particles but rather our knowledge of this behavior.

If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may give the youngsters the impression that mathematics consists in proving the most obvious things in the least obvious way.

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.

Mathematics directs the flow of the universe, lurks behind its shapes and curves, holds the reins of everything from tiny atoms to the biggest stars.

We chose to do this work mathematically, which has the advantage of precision but is not always appreciated by readers. It is perhaps for this reason that anthropologists have not shown much interest in these models, unlike economists, for example, for whom the use of mathematics poses no problem. However, one could reach the same conclusions by using just a bit of common sense.

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.

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.

The truth is that you can divide your heart in all sorts of interesting ways - a little here, a little there, most banked at home, some of it coined out for a flutter. But love cleaves through the mind's mathematics. Love's lengthways splits the heart in two - the heart where you are, the heart where you want to be. How will you heal your heart when love has split it in two?

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.

Mathematics is the purest of the arts, as well as the most misunderstood.

My early education was in the public school system of Omaha, where, retrospectively, I realize that my high school training served me in good stead for the basic subjects of mathematics, English, foreign languages and history.

Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruits of mathematics.

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.