Quotes About Mathematics

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

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.

[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.

Gel'fand amazed me by talking of mathematics as though it were poetry. He once said about a long paper bristling with formulas that it contained the vague beginnings of an idea which could only hint at and which he had never managed to bring out more clearly. I had always thought of mathematics as being much more straightforward: a formula is a formula, and an algebra is an algebra, but Gel'fand found hedgehogs lurking in the rows of his spectral sequences!

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.

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.

Well, I was always... I used to get 100% in physics and chemistry and mathematics (well, maybe a couple of points off in mathematics), and that was in high school.

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

Mathematics my foot! Algorithms are mathematics too, and often more interesting and definitely more useful.

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.

In mathematics I can report no deficiency, except it be that men do not sufficiently understand the excellent use of Pure Mathematics.

Mathematics without natural history is sterile, but natural history without mathematics is muddled.

In mathematics we find the primitive source of rationality; and to mathematics must the biologists resort for means to carry out their researches.

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.'

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.

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.

Mathematics is one of the surest ways for a man to feel the power of thought and the magic of the spirit. Mathematics is one of the eternal truths and, as such, raises the spirit to the same level on which we feel the presence of God.

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then suchand such another proposition is true of that thing.... Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

The infinite in mathematics is always unruly unless it is properly treated.

Few realize that the world of modern mathematics is rich with vivid images and provocative ideas.

What would mathematics have amounted to without the imagination of its devotees-its giants and their followers? There never was a discovery made without the urge of imagination-of imagination which broke the roadway through the forest in order that cold logic might follow.

If there be some who, though ignorant of all mathematics . . . dare to reprove this work, because of some passage of Scripture, which they have miserably warped to their purpose, I regard them not, and even despise their rash judgement.

... though mathematics may teach a man how to build a bridge, it is what the Scotch Universities call the humanities, that teach him to be civil and sweet-tempered.

Programming is much much harder than doing mathematics.

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

I learnt to distrust all physical concepts as the basis for a theory. Instead one should put one's trust in a mathematical scheme, even if the scheme does not appear at first sight to be connected with physics. One should concentrate on getting interesting mathematics.

Logic and mathematics are nothing but specialised linguistic structures.

In no other branch of mathematics is it so easy for experts to blunder as in probability theory.

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.

Irrefragability, thy name is mathematics.

[Regarding mathematics,] there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy. This may be true; indeed it is probable, since the sensational triumphs of Einstein, that stellar astronomy and atomic physics are the only sciences which stand higher in popular estimation.

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.

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.

The highest form of pure thought is in mathematics.

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.

One would have to have completely forgotten the history of science so as to not remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics.

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.

Thus you see, most noble Sir, how this type of solution to the Königsberg bridge problem bears little relationship to mathematics, and I do not understand why you expect a mathematician to produce it, rather than anyone else, for the solution is based on reason alone, and its discovery does not depend on any mathematical principle.

And silence. She liked the silence most of all. The silence in which the body, senses, the instincts, are more alert, more powerful, more sensitized, live a more richly perfumed and intoxication life, instead of transmuting into thoughts, words, into exquisite abstractions, mathematics of emotion in place of violent impact, the volcanic eruptions of fever, lust and delight.

There are certainly lots of jobs in computer coding, but coding doesn't really require advanced mathematics. And engineering jobs, they vary widely in the amount of demand that we actually need. So, you know, the number of people for whom the job description includes Newton's calculus is not perhaps that high.

Science begins with the world we have to live in, accepting its data and trying to explain its laws. From there, it moves toward the imagination: it becomes a mental construct, a model of a possible way of interpreting experience. The further it goes in this direction, the more it tends to speak the language of mathematics, which is really one of the languages of the imagination, along with literature and music. Art, on the other hand, begins with the world we construct, not with the world we see. It starts with the imagination, and then works toward ordinary experience.

If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may give the youngsters the impression that mathematics consists in proving the most obvious things in the least obvious way.

[The] humanization of mathematical teaching, the bringing of the matter and the spirit of mathematics to bear not merely upon certain fragmentary faculties of the mind, but upon the whole mind, that this is the greatest desideratum is. I assume, beyond dispute.

Integers are the fountainhead of all mathematics.

Anyone who believes a growth rate in excess of 15% per annum over the long term is attainable should pursue a career in sales, but avoid one in mathematics.

It may be more important in the mathematics class how you teach than what you teach.

Mathematics is the key and door to the sciences.