Quotes About Mathematics

Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.

The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. . . . Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.

But there is another reason for the high repute of mathematics: it is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain.

Life is good for only two things, discovering mathematics and teaching mathematics.

One of the high points of my life was when I suddenly realized that this dream I had in my late adolescence of combining pure mathematics, very pure mathematics with very hard things which had been long a nuisance to scientists and to engineers, that this combination was possible and I put together this new geometry of nature, the fractal geometry of nature.

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.

Pure mathematics is on the whole distinctly more useful than applied... For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.

It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.

You have this world of mathematics, which is very real and which contains all kinds of wonderful stuff. And then we also have the world of nature, which is real, too. And that, by some miracle, the language that nature speaks is the same language that we invented for mathematics. That's just an amazing piece of luck, which we don't understand.

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.

As I considered the matter carefully it gradually came to light that all those matters only were referred to mathematics in which order and measurements are investigated, and that it makes no difference whether it be in numbers, figures, stars, sounds or any other object that the question of measurement arises. I saw consequently that there must be some general science to explain that element as a whole which gives rise to problems about order and measurement, restricted as these are to no special subject matter. This, I perceived was called 'universal mathematics'.

Theology, Mr. Fortune found, is a more accommodating subject than mathematics; its technique of exposition allows greater latitude. For instance when you are gravelled for matter there is always the moral to fall back upon. Comparisons too may be drawn, leading cases cited, types and antetypes analysed and anecdotes introduced. Except for Archimedes mathematics is singularly naked of anecdotes.

Mathematics is not just a language. Mathematics is a language plus reasoning.

Poincaré was a vigorous opponent of the theory that all mathematics can be rewritten in terms of the most elementary notions of classical logic; something more than logic, he believed, makes mathematics what it is.

Mathematical economics is old enough to be respectable, but not all economists respect it. It has powerful supporters and impressive testimonials, yet many capable economists deny that mathematics, except as a shorthand or expository device, can be applied to economic reasoning. There have even been rumors that mathematics is used in economics (and in other social sciences) either for the deliberate purpose of mystification or to confer dignity upon common places as French was once used in diplomatic communications.

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.

All the sciences have a relation, greater or less, to human nature; and...however wide any of them may seem to run from it, they still return back by one passage or another. Even Mathematics, Natural Philosophy, and Natural Religion, are in some measure dependent on the science of MAN; since they lie under the cognizance of men, and are judged of by their powers and faculties.

There are things which seem incredible to most men who have not studied Mathematics.

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

Nature imitates mathematics.

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.

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!

My brain doesn't work very well, in terms of mathematics. I'm not one of those people who can just spout off numbers for things, if numbers are thrown at me.

Increasingly, the mathematics will demand the courage to face its implications.

There are fields of scientific work...which have been explored from the different sides of pure mathematics, statistics, electrical engineering, and neurophysiology...in which every single notion receives a separate and different name from each group, and in which important work has been triplicated or quadruplicated, while still other important work is delayed by the unavailability in one field of results that may have already become classical in the next field.

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.

Mathematics, however, is, as it were, its own explanation; this, although it may seem hard to accept, is nevertheless true, for the recognition that a fact is so is the cause upon which we base the proof.

The power of mathematics is often to change one thing into another, to change geometry into language.

In any case, do you really think kids even want something that is relevant to their daily lives? You think something practical like compound interest is going to get them excited? People enjoy fantasy, and that is just what mathematics can provide - a relief from daily life, an anodyne to the practical workaday world.

[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.

Even when I was studying mathematics, physics, and computer science, it always seemed that the problem of consciousness was about the most interesting problem out there for science to come to grips with.

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.

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection.

Just like a man grieving because he has recently lost in his dreams some thing that he had never had in reality, or hoping that tomorrow he would dream that he found it again. That is how mathematics is created; it has its fatal flaw.

Every education system on Earth has the same hierarchy of subjects: at the top are mathematics and languages, then the humanities, and the bottom are the arts.

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.

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.

I want to get young girls excited in science, tech, engineering mathematics, art, design - and how they come together. We've got this Choose Science campaign. Once women are there, though, we have to retain them. When I look at universities, it's not enough to have role models, we need to have champions. We need to have more women in senior leadership positions. There are issues about work-life balance. Women go to have children and then who keeps the lab running? There are many challenges.

Consequently he who wishes to attain to human perfection, must therefore first study Logic, next the various branches of Mathematics in their proper order, then Physics, and lastly Metaphysics.

Many of the proofs in mathematics are very long and intricate. Others, though not long, are very ingeniously constructed.

Mathematics is the supreme judge; from its decisions there is no appeal.

The more progress physical sciences make, the more they tend to enter the domain of mathematics, which is a kind of centre to which they all converge. We may even judge the degree of perfection to which a science has arrived by the facility with which it may be submitted to calculation.

The question for the ultimate foundations and the ultimate meaning of mathematics remains open; we do not know in which direction it will find its final solution nor even whether a final objective answer can be expected at all. "Mathematizing" may well be a creative activity of man, like language or music, of primary originality, whose historical decisions defy complete objective rationalization.

The writing in mathematics text is not only laconic to a fault; it is cold, monotonous, dry, dull, and even ungrammatical... The books are not only printed by machines; they are written by machines.

As the existence of a corps of professors of mathematics is peculiar to our navy, as well as an apparent, perhaps a real, anomaly, some account of it may be of interest.

Children, as well as grown-ups, in their individual, glorified, drudgery-proof homes of Labrador, the tropics, the Orient, or where you will, to which they can pass with pleasure and expedition by means of ever-improving transportation, will be able to tune in their television and radio to the moving picture lecture of, let us say, President Lowell of Harvard; the professor of Mathematics of Oxford; of the doctor of Indian antiquities of Delhi, etc.

Mathematics is a body of knowledge, but it contains no truths.

Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold.