Quotes About Mathematics

Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.

. . . the membership relation for sets can often be replaced by the composition operation for functions. This leads to an alternative foundation for Mathematics upon categories -- specifically, on the category of all functions. Now much of Mathematics is dynamic, in that it deals with morphisms of an object into another object of the same kind. Such morphisms (like functions) form categories, and so the approach via categories fits well with the objective of organizing and understanding Mathematics. That, in truth, should be the goal of a proper philosophy of Mathematics.

Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course. There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology.

Mathematics is often defined as the science of space and number . . . it was not until the recent resonance of computers and mathematics that a more apt definition became fully evident: mathematics is the science of patterns.

I don't think that everyone should become a mathematician, but I do believe that many students don't give mathematics a real chance. I did poorly in math for a couple of years in middle school; I was just not interested in thinking about it. I can see that without being excited mathematics can look pointless and cold. The beauty of mathematics only shows itself to more patient followers.

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

The mathematics is the odd one, odd because I'm not sure how to measure its effect. It is so fundamental to my outlook on everything and yet I'm not even sure how. It must be because in my formative years it was everything to me, the single place of beauty in my life, and of breathtaking beauty at that. I still believe that pure mathematics is the most creative thing that humanity does, though I am no longer a part of it.

With the exception of the geometrical series, there does not exist in all of mathematics a single infinite series the sum of which has been rigorously determined. In other words, the things which are the most important in mathematics are also those which have the least foundation.

...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.

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.

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

Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.

Mathematics is the surest way to immortality. If you make a big discovery in mathematics, you will be remembered after everyone else will be forgotten

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.'

Mathematics, in the common lay view, is a static discipline based on formulas...But outside the public view, mathematics continues to grow at a rapid rate...the guid to this growth is not calculation and formulas, but an open ended search for pattern.

I do not think the division of the subject into two parts - into applied mathematics and experimental physics a good one, for natural philosophy without experiment is merely mathematical exercise, while experiment without mathematics will neither sufficiently discipline the mind or sufficiently extend our knowledge in a subject like physics.

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 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.

The mathematics clearly called for a set of underlying elementary objects-at that time we needed three types of them-elementary objects that could be combined three at a time in different ways to make all the heavy particles we knew. ... I needed a name for them and called them quarks, after the taunting cry of the gulls, "Three quarks for Muster mark," from Finnegan's Wake by the Irish writer James Joyce.

Women have a passion for mathematics. They divide their age in half, double the price of their clothes, and always add at least five years to the age of their best friend.

Everyone reads a different book. That's what's interesting. Everyone sees a different film, as well. We bring our past lives to whatever work of art we're experiencing at that moment, and that's what makes it interesting. It's not mathematics. There are different answers for different people.

Where mathematics and spirit join, where proof of the existence of mystery-salvific mystery-shimmers just below the surfaces of human perception, experience and the linguistic veil itself, Killarney Clary's new book-her best to date-dwells, plumbs, persuades and thrills.

Mathematics may be the only exception in the sciences that leaves no room for skepicism. But, if mathematical results are exact as no empirical law can ever be, philosophers have discovered that they are not absolutely novel - instead, they are tautological.

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

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

If I ever thought of directing again, I mean - I don't know, even the idea of directing a film is a strange one for me, because I feel kind of anti mathematics in a way in that sense. Anti - I don't like when things make sense, I prefer if they don't, so if I made a film, it wouldn't make any sense and no one would see it. So maybe I'll just make little films at home with my phone, never to be released.

All of mathematics is a tale about groups.

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.

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.

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.

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.

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.

By and large it is uniformly true in mathematics that there is a time lapse between a mathematical discovery and the moment when it is useful; and that this lapse of time can be anything from 30 to 100 years, in some cases even more; and that the whole system seems to function without any direction, without any reference to usefulness, and without any desire to do things which are useful.

Mathematics is a language

The economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth.

Just like a man grieving because he has recently lost in his dreams some thing that he had never had in reality, or hoping that tomorrow he would dream that he found it again. That is how mathematics is created; it has its fatal flaw.

Mathematics had never had more than a secondary interest for him ; and even logic he cared for chiefly as a means of clearing the ground of doctrines imagined to be proved, by showing that the evidence on which they were supposed to rest had no tendency to prove them. But he had been endeavouring to give a more active and positive help than this to the cause of what he deemed pure religion.

Although I am even now still a layman in the area of mathematics, and although I lack theoretical knowledge, the mathematicians, and in particular the crystallographers, have had considerable influence on my work of the last twenty years. The laws of the phenomena around us--order, regularity, cyclical repetition, and renewals--have assumed greater and greater importance for me. The awareness of their presence gives me peace and provides me with support. I try in my prints to testify that we live in a beautiful and orderly world, and not in a formless chaos, as it sometimes seems.

The advance and perfecting of mathematics are closely joined to the prosperity of the nation.

The fact that mathematics does such a good job of describing the Universe is a mystery that we don't understand. And a debt that we will probably never be able to repay.

Mathematics is the supreme nostalgia of our time.

Mathematics is the purest of the arts, as well as the most misunderstood.

Pure mathematics is, in its way, the poetry of logical ideas. ... [By seeking] logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.

Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruits of mathematics.

If you learn music, you'll learn history. If you learn music, you'll learn mathematics. If you learn music, you'll learn most all there is to learn.

I don't agree with mathematics; the sum total of zeros is a frightening figure.

I could never accept findings based almost exclusively on mathematics. It ain't ignorance that causes all the trouble in this world. It's the things people know that ain't so.