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.

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.

One cannot inquire into the foundations and nature of mathematics without delving into the question of the operations by which the mathematical activity of the mind is conducted. If one failed to take that into account, then one would be left studying only the language in which mathematics is represented rather than the essence of mathematics.

This is a wonderful book, unique and engaging. Diaconis and Graham manage to convey the awe and marvels of mathematics, and of magic tricks, especially those that depend fundamentally on mathematical ideas. They range over many delicious topics, giving us an enchanting personal view of the history and practice of magic, of mathematics, and of the fascinating connection between the two cultures. Magical Mathematics will have an utterly devoted readership.

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.

It is indubitable that a 50-year-old mathematician knows the mathematics he learned at 20 or 30, but has only notions, often rather vague, of the mathematics of his epoch, i.e. the period of time when he is 50.

... the word "theory" ... was originally an Orphic word, which Cornford interprets as "passionate sympathetic contemplation" ... For Pythagoras, the "passionate sympathetic contemplation" was intellectual, and issued in mathematical knowledge ... To those who have reluctantly learnt a little mathematics in school this may seem strange; but to those who have experienced the intoxicating delight of sudden understanding that mathematics gives, from time to time, to those who love it, the Pythagorean view will seem completely natural.

On all levels primary, and secondary and undergraduate - mathematics is taught as an isolated subject with few, if any, ties to the real world. To students, mathematics appears to deal almost entirely with things whlch are of no concern at all to man.

Mathematics is so much easier than words mathematics makes things clear that words merely muddle and confuse and mess up.

The research reported on in our book "A=B", has moved a whole active field of mathematics from the province of human thought to the realm of computer-fodder. It is quite exciting to think about what other fields of pure mathematics, hitherto thought to be reserved to human intelligence, might be moved to that realm next. The goal is to put ourselves out of business completely, and the work is well underway.

Pi is not merely the ubiquitous factor in high school geometry problems; it is stitched across the whole tapestry of mathematics, not just geometry's little corner of it. Pi occupies a key place in trigonometry too. It is intimately related to e, and to imaginary numbers. Pi even shows up in the mathematics of probability

The problem is that modern fundamental physics is so far from you and me. The mathematics has become so much more complicated that you need at least 10 years to understand it. Fundamental physics has advanced so far from the understanding of most people that there is really a big disconnect.

Strange as it may sound, the power of mathematics rests on its evasion of all unnecessary thought and on its wonderful saving of mental operations.

Mathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with concepts introduced previously by means of precise definitions.

I doubt not, but from self-evident Propositions, by necessary Consequences, as incontestable as those in Mathematics, the measures of right and wrong might be made out.

Mathematics may be compared to a mill of exquisite workmanship, which grinds you stuff of any degree of fineness; but, nevertheless, what you get out depends upon what you put in; and as the grandest mill in the world will not extract wheat-flour from peascods, so pages of formulae will not get a definite result out of loose data.

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

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.

Mathematics does not grow through a monotonous increase of the number of indubitably established theorems but through the incessant improvement of guesses by speculation and criticism, by the logic of proofs and refutations.

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

Mathematics is as much an aspect of culture as it is a collection of algorithms.

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.

Increasingly, the mathematics will demand the courage to face its implications.

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.

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

Beauty is startling. She wears a gold shawl in the summer and sells seven kinds of honey at the flea market. She is young and old at once, my daughter and my grandmother. In school she excelled in mathematics and poetry. . . Beauty will dance with anyone who is brave enough to ask her.

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.

It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.

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.

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.

The theory of numbers, more than any other branch of mathematics, began by being an experimental science. Its most famous theorems have all been conjectured, sometimes a hundred years or more before they were proved; and they have been suggested by the evidence of a mass of computations.

Being exposed to theory, stimulated by a basic love of concepts and mathematics, was a marvelous experience.

You can only hear clearly when you sit quietly, when you give your attention. Nor can you have order if you are not free to watch, if you are not free to listen, if you are not free to be considerate. This problem of freedom and order is one of the most difficult and urgent problems in life. It is a very complex problem. It needs to be thought over much more than mathematics, geography, or history.

Because of mathematics precise, formal character, mathematical arguments remain sound even when they are long and complex. In contast, common sense arguments can generally be trusted only if they remain short; even moderately long nonmathematical arguments rapidly becomes farfetched an dubious.

[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.

Logic issues in tautologies, mathematics in identities, philosophy in definitions; all trivial, but all part of the vital work of clarifying and organising our thought.

Mathematics has beauty and romance. It's not a boring place to be, the mathematical world. It's an extraordinary place; it's worth spending time there.

Creativity is essential to particle physics, cosmology, and to mathematics, and to other fields of science, just as it is to its more widely acknowledged beneficiaries - the arts and humanities.

While there is such a thing as correctness in ethics, in interpretation, in mathematics, the way to understand that is not by trying to model it on the ways in which we get things right in physics.

In mathematics our role is more that of servant than master.

Perhaps the greatest paradox of all is that there are paradoxes in mathematics.

Mathematics as a science, commenced when first someone, probably a Greek, proved propositions about "any" things or about "some" things, without specifications of definite particular things.