Quotes About Mathematics

It is almost as hard to define mathematics as it is to define economics, and one is tempted to fall back on the famous old definition attributed to Jacob Viner, "Economics is what economists do," and say that mathematics is what mathematicians do. A large part of mathematics deals with the formal relations of quantities or numbers.

The broader the chess player you are, the easier it is to be competitive, and the same seems to be true of mathematics - if you can find links between different branches of mathematics, it can help you resolve problems. In both mathematics and chess, you study existing theory and use that to go forward.

Mathematics is a logical method. . . . Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.

Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand... So Greek mathematics is 'permanent', more permanent even than Greek literature.

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.

Yes, I share your concern: how to program well -though a teachable topic- is hardly taught. The situation is similar to that in mathematics, where the explicit curriculum is confined to mathematical results; how to do mathematics is something the student must absorb by osmosis, so to speak. One reason for preferring symbol-manipulating, calculating arguments is that their design is much better teachable than the design of verbal/pictorial arguments. Large-scale introduction of courses on such calculational methodology, however, would encounter unsurmoutable political problems.

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.

One of the biggest problems of mathematics is to explain to everyone else what it is all about. The technical trappings of the subject, its symbolism and formality, its baffling terminology, its apparent delight in lengthy calculations: these tend to obscure its real nature. A musician would be horrified if his art were to be summed up as "a lot of tadpoles drawn on a row of lines"; but that"s all that the untrained eye can see in a page of sheet music... In the same way, the symbolism of mathematics is merely its coded form, not its substance.

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.

Doing research in mathematics is frustrating and if being frustrated is something you cannot get used to, then mathematics may not be an ideal occupation for you.

Compare mathematics and the political sciences - it's quite striking. In mathematics, in physics, people are concerned with what you say, not with your certification. But in order to speak about social reality, you must have the proper credentials, particularly if you depart from the accepted framework of thinking. Generally speaking, it seems fair to say that the richer the intellectual substance of a field, the less there is a concern for credentials, and the greater is the concern for content.

For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?

The product of mathematics is clarity and understanding. Not theorems, by themselves. ... In short, mathematics only exists in a living community of mathematicians that spreads understanding and breathes life into ideas both old and new.

The world is colors and motion, feelings and thoughts and what does math have to do with it? Not much, if 'math' means being bored in high school, but in truth mathematics is the one universal science. Mathematics is the study of pure pattern and everything in the cosmos is a kind of pattern.

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.

Being a language, mathematics may be used not only to inform but also, among other things, to seduce.

The study of mathematics is apt to commence in disappointment.

Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.

You can not apply mathematics as long as words still becloud reality.

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.

Mathematics is a dangerous profession; an appreciable proportion of us go mad.

Mathematics-a wonderful science, but it hasn't yet come up with a way to divide one tricycle between three small boys.

In the company of friends, writers can discuss their books, economists the state of the economy, lawyers their latest cases, and businessmen their latest acquisitions, but mathematicians cannot discuss their mathematics at all. And the more profound their work, the less understandable it is.

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.

These days people are much more aware that mathematics is a communal endeavor: even the most brilliant idea gets meaning only from its relation to the whole.

The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism.

What humans do with the language of mathematics is to describe patterns.

The importance of the "New Mathematics" lies mainly in the fact that it has taught us the difference between the disc and the circle.

I have long admired Ron Whitehead. He is crazy as nine loons, and his poetry is a dazzling mix of folk wisdom and pure mathematics

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.

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

Here, where we reach the sphere of mathematics, we are among processes which seem to some the most inhuman of all human activities and the most remote from poetry. Yet it is here that the artist has the fullest scope of his imagination.

Mathematics is like draughts in being suitable for the young, not too difficult, amusing, and without peril to the state.

What is especially striking and remarkable is that in fundamental physics, a beautiful or elegant theory is more likely to be right than a theory that is inelegant. A theory appears to be beautiful or elegant (or simple, if you prefer) when it can be expressed concisely in terms of mathematics we already have. Symmetry exhibits the simplicity. The Foundamental Law is such that the different skins of the onion resemble one another and therefore the math for one skin allows you to express beautifully and simply the phenomenon of the next skin.

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.

Unless the chemist learns the language of mathematics, he will become a provincial and the higher branches of chemical work, that require reason as well as skill, will gradually pass out of his hands.

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.

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.

How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?

Mathematics - this may surprise or shock some - is never deductive in creation.

My interest in the sciences started with mathematics in the very beginning, and later with chemistry in early high school and the proverbial home chemistry set.

Mathematics is the only true metaphysics.

Modern bodybuilding is ritual, religion, sport, art, and science, awash in Western chemistry and mathematics. Defying nature, it surpasses it.

We have these amazing gifts of music and mathematics and painting and Olympic running. I mean, we're the animal that is best of all the animals at long-distance running. Why? It is quite amazing. Superfluous gifts you don't really need to survive.

At present, when the prevailing forms of society have become hindrances to the free expression of human powers, it is precisely the abstract branches of science, mathematics and theoretical physics, which ... offer a less distorted form of knowledge than other branches of science which are interwoven with the pattern of daily life, and the practicality of which seemingly testifies to their realistic character.

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.

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.