Quotes About Mathematics

Like a stool which needs three legs to be stable, mathematics education needs three components: good problems, with many of them being multi-step ones, a lot of technical skill, and then a broader view which contains the abstract nature of mathematics and proofs. One does not get all of these at once, but a good mathematics program has them as goals and makes incremental steps toward them at all levels.

Music is mathematics, the mathematics of listening, mathematics for the ears.

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.

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.

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

Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems-general and specific statements-can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences.

Just by studying mathematics we can hope to make a guess at the kind of mathematics that will come into the physics of the future... If someone can hit on the right lines along which to make this development, it may lead to a future advance in which people will first discover the equations and then, after examining them, gradually learn how to apply them... My own belief is that this is a more likely line of progress than trying to guess at physical pictures.

Pi is not merely the ubiquitous factor in high school geometry problems; it is stitched across the whole tapestry of mathematics, not just geometry's little corner of it. Pi occupies a key place in trigonometry too. It is intimately related to e, and to imaginary numbers. Pi even shows up in the mathematics of probability

Of these austerer virtues the love of truth is the chief, and in mathematics, more than elsewhere, the love of truth may find encouragement for waning faith. Every great study is not only an end in itself, but also a means of creating and sustaining a lofty habit of mind; and this purpose should be kept always in view throughout the teaching and learning of mathematics.

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

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.

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.

Where mathematics and spirit join, where proof of the existence of mystery-salvific mystery-shimmers just below the surfaces of human perception, experience and the linguistic veil itself, Killarney Clary's new book-her best to date-dwells, plumbs, persuades and thrills.

The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience.

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.

I went to Princeton from Amherst, where I split my interests between mathematics and philosophy.

... You get surreal numbers by playing games. I used to feel guilty in Cambridge that I spent all day playing games, while I was supposed to be doing mathematics. Then, when I discovered surreal numbers, I realized that playing games IS math.

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

The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience

... 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.

Our species is the only creative species, and it has only one creative instrument, the individual mind and spirit of man. Nothing was ever created by two men. There are no good collaborations, whether in music, in art, in poetry, in mathematics, in philosophy. Once the miracle of creation has taken place, the group can build and extend it, but the group never invents anything. The preciousness lies in the lonely mind of a man.

Proofs exist only in mathematics and logic, not in science.

For most people, the major hurdle in grasping modern insights into the nature of the universe is that these developments are usually phrased using mathematics.

Mathematics is a collection of cheap tricks and dirty jokes.

Mathematics is one of the deepest and most powerful expressions of pure human reason, and, at the same time, the most fundamental resource for description and analysis of the experiential world.

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

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.

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

It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.

We're progressing on a lot of fronts, but on the aspect of your responsibility - just the very basics of how we treat each other - before we learn mathematics and computers and science in school, and languages and all of this, the basis of it: What is it to be a human? What responsibility do you have?

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.

Man is full of desires: he loves only those who can satisfy them all. "This man is a good mathematician," someone will say. But I have no concern for mathematics; he would take me for a proposition. "That one is a good soldier." He would take me for a besieged town. I need, that is to say, a decent man who can accommodate himself to all my desires in a general sort of way.

A formal manipulator in mathematics often experiences the discomforting feeling that his pencil surpasses him in intelligence.

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.

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.

Now ... the basic principle of modern mathematics is to achieve a complete fusion [of] 'geometric' and 'analytic' ideas.

Mathematics allows for no hypocrisy and no vagueness.

Sex is mathematics. Individuality no longer an issue. What does intelligence signify? Define reason. Desire - meaningless. Intellect is not a cure. Justice is dead.

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.

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.

The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.

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.

Yet things are knowable! They are knowable, because, being from one, things correspond. There is a scale: and the correspondence of heaven to earth, of matter to mind, of the part to the whole, is our guide. As there is a science of stars, called astronomy; and science of quantities, called mathematics; a science of qualities, called chemistry; so there is a science of sciences,--I call it Dialectic,--which is the Intellect discriminating the false and the true.

Our faith in Mathematics is not likely to wane if we openly acknowledge that the personalities of even the greatest mathematicians may be as flawed as those of anyone else.

There is no place for [the Bantu] in the European community above the level of certain forms of labour ... What is the use of teaching the Bantu child mathematics when it cannot use it in practice? That is quite absurd. Education must train people in accordance with their opportunities in life, according to the sphere in which they live.

Anyone who cannot cope with mathematics is not fully human. At best, he is a tolerable subhuman who has learned to wear his shoes, bathe, and not make messes in the house.