Quotes About Mathematics

If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.

May not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life.

On foundations we believe in the reality of mathematics, but of course, when philosophers attack us with their paradoxes, we rush to hide behind formalism and say 'mathematics is just a combination of meaningless symbols,'... Finally we are left in peace to go back to our mathematics and do it as we have always done, with the feeling each mathematician has that he is working with something real. The sensation is probably an illusion, but it is very convenient.

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 first and foremost duty of the high school in teaching mathematics is to emphasize methodical work in problem solving...The teacher who wishes to serve equally all his students, future users and nonusers of mathematics, should teach problem solving so that it is about one-third mathematics and two-thirds common sense.

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.

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

Men are constantly attracted and deluded by two opposite charms: the charm of competence which is engendered by mathematics and everything akin to mathematics, and the charm of humble awe, which is engendered by meditation on the human soul and its experiences. Philosophy is characterized by the gentle, if firm, refusal to succumb to either charm.

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.

What, after all, is mathematics but the poetry of the mind, and what is poetry but the mathematics of the heart?

...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.

Mathematics, rightly viewed, possesses not only truth, but supreme beauty a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the georgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. 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 in poetry.

We know that nature is described by the best of all possible mathematics because God created it. So there is a chance that the best of all possible mathematics will be created out of physicists' attempts to describe nature.

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 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.

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.

If a man's wit be wandering, let him study the mathematics.

The study of mathematics is apt to commence in disappointment.

Pure mathematics, may it never be of any use to anyone.

Mathematics is an obscure field, an abstruse science, complicated and exact; yet so many have attained perfection in it that we might conclude almost anyone who seriously applied himself would achieve a measure of success.

White folks was in the caves while we [blacks] was building empires ... We built pyramids before Donald Trump ever knew what architecture was ... we taught philosophy and astrology and mathematics before Socrates and them Greek homos ever got around to it.

Mathematics should be mixed not only with physics but with ethics.

One can understand nature only when one has learned the language and the signs in which it speaks to us; but this language is mathematics and these signs are methematical figures.

In the realm of ideas, of mental objects, those ideas whose properties are reproducible are called mathematical objects, and the study of mental objects with reproducible properties is called mathematics.

Outside of mathematics and logic, there are common sense truths, such as that it is snowing that normal observers, in a specified context can agree on, subject to vagueness considerations, and theoretical truths, such as that snow is crystallised water vapour, and maybe in-between truths.

A mathematician either has a feeling for equations and an understanding and delight in it, not only in the purity of it, but in its beauty as well. I don't think that's something that you learn at school. I think you can get better in mathematics on a school level, but when you're talking about being a mathematician, I think that's definitely a gift of genes or whatever, you know? Whatever your pool is.

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.

Perhaps the best reason for regarding mathematics as an art is not so much that it affords an outlet for creative activity as that it provides spiritual values. It puts man in touch with the highest aspirations and lofiest goals. It offers intellectual delight and the exultation of resolving the mysteries of the universe.

Logic and mathematics are nothing but specialised linguistic structures.

In high school I was good at math and everybody wanted me to do something with that - mathematics or engineering - which was a nightmare scenario for me. Meeting other artists and going to punk rock shows at that age, there was a feeling of freedom and community that I wanted to partake in.

... 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.

Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.

Mathematics as we know it and as it has come to shape modern science could never have come into being without some disregard for the dangers of the infinite.

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.

By simple mathematics giving is key to the world you seek to live in. If I take I alone gain. If I give or share then two at least are enriched.

One thing that definitely did calculate properly for me was the mathematics that makes sense every day, no matter how I look at it, I can't get around it. I try to get around it, I keep trying to find one plus one is not two, somehow. I can't. People can talk about string theory, parallel realities, different dimensions, it's still one plus one is two, baby.

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.

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

Mathematics is concerned only with the enumeration and comparison of relations.

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.

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?

The only reason psychology students don't have to do more and harder mathematics than physics students is because the mathematicians haven't yet discovered ways of dealing with problems as hard as those in psychology.

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.

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.

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

Mathematics is, in many ways, the most precious response that the human spirit has made to the call of the infinite.