Quotes About Mathematics

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.

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.

Mathematics never reveals man to the degree, never expresses him in the way, that any other field of human endeavour does: the extent of the negation of man's corporeal self that mathematics achieves cannot be compared with anything. Whoever is interested in this subject I refer to my articles. Here I will say only that the world injected its patterns into human language at the very inception of that language; mathematics sleeps in every utterance, and can only be discovered, never invented.

...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.

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

Mathematics... is a bit like discovering oil. ... But mathematics has one great advantage over oil, in that no one has yet ... found a way that you can keep using the same oil forever.

[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.

The propositions of mathematics have, therefore, the same unquestionable certainty which is typical of such propositions as "All bachelors are unmarried," but they also share the complete lack of empirical content which is associated with that certainty: The propositions of mathematics are devoid of all factual content; they convey no information whatever on any empirical subject matter.

An Arab activist can take pride in the Arab heritage of mathematics and science or he can take pride in his religion, and there's pride to be taken in both. But one of them could be exploited much more easily and has been in the context of world conflict. And the other is very difficult to do on the grounds that science and literature and mathematics have been among the uniting factors in the history of the world.

One of the chief triumphs of modern mathematics consists in having discovered what mathematics really is.

Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent to a pair of ears. Mathematics can only be "seen" with the "eyes of the mind". It is as if we had no sense of hearing, so that only someone able to sight read music would be able to appreciate its patterns and harmonies.

To exist (in mathematics), said Henri Poincaré, is to be free from contradiction. But mere existence does not guarantee survival. To survive in mathematics requires a kind of vitality that cannot be described in purely logical terms.

The most rewarding part of my work is the "Aha" moment, the excitement of discovery and enjoyment of understanding something new - the feeling of being on top of a hill and having a clear view. But most of the time, doing mathematics for me is like being on a long hike with no trail and no end in sight. I find discussing mathematics with colleagues of different backgrounds one of the most productive ways of making progress.

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.

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.

A Noah's Ark of mathematicians, their lives, loves, hard times, and madnesses, Loving and Hating Mathematics shows our community with all its warts as well as its triumphs. I especially liked the chapter on much-hated school mathematics, 'Almost All Children Left Behind.'

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.

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.

Given the brief - and generally misleading - exposure most people have to mathematics at school, raising the public awareness of mathematics will always be an uphill battle.

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

In mathematics we do not appeal to authority, but rather you are responsible for what you believe.

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.

I assert that, in any particular natural science, one encounters genuine scientific substance only to the extent that mathematics is present.

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.

The Good Spirit never cared for the colleges, and though all men and boys were now drilled in Greek, Latin, and Mathematics, it had quite left these shells high on the beach, and was creating and feeding other matters [science] at other ends of the world.

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.

Programming is much much harder than doing mathematics.

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.

[Mathematics] is an independent world created out of pure intelligence.

But I simply can't stand a view limited to this earth, I feel life is so small unless it has windows into other worlds...I like mathematics largely because it is not human.

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.

Journalists say that when a dog bites a man, that is not news, but when a man bites a dog, that is news ... Thanks to the mathematics of combinatorics, we will never run out of news.

It is insufficient to protect ourselves with laws; we need to protect ourselves with mathematics.

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.

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.

I think the biggest misconception is that everybody has to learn mathematics. That seems to be a complete mistake.

Mathematics is the science of patterns, and nature exploits just about every pattern that there is.

The Advantage is that mathematics is a field in which one's blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil. It is a field which has often been compared with chess, but differs from the latter in that it is only one's best moments that count and not one's worst. A single inattention may lose a chess game, whereas a single successful approach to a problem, among many which have been relegated to the wastebasket, will make a mathematician's reputation.

Only in mathematics and physics was I, through self-study, far beyond the school curriculum, and also with regard to philosophy as it was taught in the school curriculum.

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

Mathematics is a field which has often been compared with chess, but differs from the latter in that it is only one's best moments that count and not one's worst.

The best result of mathematics is to be able to do without it.

There was a transition going on - Baghdad being the intellectual capital of the world where major advances were made in agriculture and mathematics and engineering and medicine and astronomy, and then that all sort of collapsed. And I was trying to understand how such a intellectually fertile environment can lose its compass bearing. Because I think about the creative centers today - countries, or even regions. Will Silicon Valley always be as innovative? Will the United States be innovative, or will we become complacent?

The rejection of all abstract formalism. Materialism reminds every science of its real source: the world men transform. No science can, whether in its history or its object, grasp its own origins within itself or constitute itself as a closed world, exhaustively defined by internal rules. Materialism refers every science and every activity to the reality they depend on, even if this dependence is masked by a great many abstract mediations: mathematics as well as logic, aesthetics as well as ethics and politics.

Mathematics had never had more than a secondary interest for him ; and even logic he cared for chiefly as a means of clearing the ground of doctrines imagined to be proved, by showing that the evidence on which they were supposed to rest had no tendency to prove them. But he had been endeavouring to give a more active and positive help than this to the cause of what he deemed pure religion.

As an exercise of the reasoning faculties, pure mathematics is an admirable exercise, because it consists of reasoning alone and does not encumber the student with any exercise of judgment.

[Georg Cantor was the first to prove that there could be a series of infinities; that infinities come in an infinite number of sizes.] Thus Cantor's Absolute is a perfect image for what we experience of God. When I speak of a Big Enough God I am not merely thinking of an Infinite God, but the God of infinities, the Absolute, which either chooses to reveal itself or remains veiled in mystery. Modern mathematics does begin to feel like the language that God talks.

For many parts of Nature can neither be invented with sufficient subtlety, nor demonstrated with sufficient perspicuity, nor accommodated unto use with sufficient dexterity, without the aid and intervening of the mathematics, of which sort are perspective, music, astronomy, cosmography, architecture, engineery, and divers others.