Quotes About Mathematics

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 alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don't happen to have all the data. In mathematics we have all the data, brought together in the full light of demonstration, and yet we don't understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.

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 fact is there are few more popular subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune.

People think that mathematics is complicated. Mathematics is the simple bit, it’s the stuff we CAN understand. It’s cats that are complicated.

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.

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.

I was fortunate to find an extraordinary mathematics and applied mathematics program in Toronto.

The proof of Fermat's Last Theorem underscores how stable mathematics is through the centuries - how mathematics is one of humanity's long continuous conversations with itself.

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.

Very few people realize the enormous bulk of contemporary mathematics. Probably it would be easier to learn all the languanges of the world than to master all mathematics at present known.

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.'

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

When the mathematician says that such and such a proposition is true of one thing, it may be interesting, and it is surely safe. But when he tries to extend his proposition to everything, though it is much more interesting, it is also much more dangerous. In the transition from one to all, from the specific to the general, mathematics has made its greatest progress, and suffered its most serious setbacks, of which the logical paradoxes constitute the most important part. For, if mathematics is to advance securely and confidently, it must first set its affairs in order at home.

Our teaching of mathematics revolves around a fundamental conflict. Rightly or wrongly, students are required to master a series of mathematical concepts and techniques, and anything that might divert them from doing so is deemed unnecessary. Putting mathematics into its cultural context, explaining what is has done for humanity, telling the story of its historical development, or pointing out the wealth of unsolved problems or even the existence of topics that do not make it into school textbooks leaves less time to prepare for the exam. So most of these things aren't discussed.

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.

The principles of logic and mathematics are true simply because we never allow them to be anything else. And the reason for this is that we cannot abandon them without contradicting ourselves, without sinning against the rules which govern the use of language, and so making our utterances self-stultifying. In other words, the truths of logic and mathematics are analytic propositions or tautologies.

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.

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

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

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

For mathematics, even to the logical forms in which it moves, is entirely dependent on the concept of natural number.

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

The development of mathematics toward greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules... One might therefore conjecture that these axioms and rules of inference are sufficient to decide any mathematical question that can at all be formally expressed in these systems. It will be shown below that this is not the case, that on the contrary there are in the two systems mentioned relatively simple problems in the theory of integers that cannot be decided on the basis of the axioms.

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.

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.

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.

Thinking - in particular abstract thinking, which most of us are introduced to through the study of mathematics and literature - helps us learn that we can become problem solvers.

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.

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.

Perhaps the most surprising thing about mathematics is that it is so surprising.

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

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

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 is fun if you don't let mathematicians push you around when you are doing it.

Combinatorics is an honest subject. No adèles, no sigma-algebras. You count balls in a box, and you either have the right number or you haven't. You get the feeling that the result you have discovered is forever, because it's concrete. Other branches of mathematics are not so clear-cut. Functional analysis of infinite-dimensional spaces is never fully convincing; you don't get a feeling of having done an honest day's work. Don't get the wrong idea - combinatorics is not just putting balls into boxes. Counting finite sets can be a highbrow undertaking, with sophisticated techniques.

At the age of eleven, I began Euclid, with my brother as my tutor. This was one of the great events of my life, as dazzling as first love. I had not imagined there was anything so delicious in the world. From that moment until I was thirty-eight, mathematics was my chief interest and my chief source of happiness.

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 did not have a very literary background. I came to poetry from the sciences and mathematics, and also through an interest in Japanese and Chinese poetry in translation.

The laws of nature are written by the hand of God in the language of mathematics.

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

He who does not understand the supreme certainty of mathematics is wallowing in confusion.

It is generally recognised that women are better than men at languages, personal relations and multi-tasking, but less good at map-reading and spatial awareness. It is therefore not unreasonable to suppose that women might be less good at mathematics and physics.

Our future rates of gain will fall far short of those achieved in the past. Berkshire's capital base is now simply too large to allow us to earn truly outsized returns. If you believe otherwise, you should consider a career in sales but avoid one in mathematics.

To understand the Universe, you must understand the language in which it's written, the language of Mathematics.

For existential mathematics, which does not exist, would probably propose this equation: the value of coincidence equals the degree of its improbability.