Quotes About Mathematics

[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing - one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.

Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity

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.

I would say, if you like, that the party is like an out-moded mathematics...that is to say, the mathematics of Euclid. We need to invent a non-Euclidian mathematics with respect to political discipline.

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 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.

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.

To create a language all of a piece which would be a women's language, that I find quite insane. There does not exist a mathematics which is only a women's mathematics, or a feminine science.

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

For me, rhythm is a type of divine mathematics in a way. No matter where you're from, we can all understand the mathematics of rhythm. I try to apply this mathematical thinking to my playing.

Theology, Mr. Fortune found, is a more accommodating subject than mathematics; its technique of exposition allows greater latitude. For instance when you are gravelled for matter there is always the moral to fall back upon. Comparisons too may be drawn, leading cases cited, types and antetypes analysed and anecdotes introduced. Except for Archimedes mathematics is singularly naked of anecdotes.

Mathematics is really an art, not a science. You could say science also is an art. So I would say the difference is something you can't really describe - you can only recognize. You hear somebody playing the violin, and it was Fritz Kreisler or it was somebody else, and you can tell the difference. It is so in almost every art. We just don't understand why it is that there are just a few people who are just completely off the scale and the rest of them are just mediocre. And we don't know why. But I say it's certainly true of mathematics.

We sometimes think of being good at mathematics as an innate ability. You either have "it" or you don't. But to Schoenfeld, it's not so much ability as attitude. You master mathematics if you are willing to try.

I'm not the sort of person who does my mathematics writing on paper. I do that at the last stage of the game. I do my mathematics in my head. I sit down for a hard day's work and I write nothing all day. I just think. And I walk up and down because that helps keep me awake, it keeps the blood circulating, and I think and think.

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

The product of mathematics is clarity and understanding. Not theorems, by themselves. ... In short, mathematics only exists in a living community of mathematicians that spreads understanding and breathes life into ideas both old and new.

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.

The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method.

Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems-general and specific statements-can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences.

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.

Mathematical economics is old enough to be respectable, but not all economists respect it. It has powerful supporters and impressive testimonials, yet many capable economists deny that mathematics, except as a shorthand or expository device, can be applied to economic reasoning. There have even been rumors that mathematics is used in economics (and in other social sciences) either for the deliberate purpose of mystification or to confer dignity upon common places as French was once used in diplomatic communications.

It was as though applied mathematics was my spouse, and pure mathematics was my secret lover.

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.

Thus metaphysics and mathematics are, among all the sciences that belong to reason, those in which imagination has the greatest role. I beg pardon of those delicate spirits who are detractors of mathematics for saying this . . . . The imagination in a mathematician who creates makes no less difference than in a poet who invents. . . . Of all the great men of antiquity, Archimedes may be the one who most deserves to be placed beside Homer.

Mathematics is a language. We want scientists to be able to read it, speak it, and write it. But we are are not training them to be grammarians.

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

In mathematics we do not appeal to authority, but rather you are responsible for what you believe.

I assert that, in any particular natural science, one encounters genuine scientific substance only to the extent that mathematics is present.

Mathematics is written for mathematicians.

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.

All the sciences have a relation, greater or less, to human nature; and...however wide any of them may seem to run from it, they still return back by one passage or another. Even Mathematics, Natural Philosophy, and Natural Religion, are in some measure dependent on the science of MAN; since they lie under the cognizance of men, and are judged of by their powers and faculties.

We the undersigned, intend to establish an instruction and training institution which differs from the common elementary schools principally in that it will embrace, outside of (in addition to) the general and elementary curriculum, all branches of the classical high school, which are necessary for a true Christian and scientific education, such as: Religion, the Latin, Greek, Hebrew, German, French and English languages; History, Geography, Mathematics, Physics, natural history, Introduction to Philosophy, Music, and Drawing.

I read one or two other books which gave me a background in mathematics other than logic.

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.

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

... we should not be disappointed that everyday language does not work any longer at the apex of our little theory. It is natural; like poetry, the very reason for the existence of mathematics is that it expresses thoughts and feelings which we cannot express in mundane everyday language.

The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience

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.

Irrefragability, thy name is mathematics.

In my family, as in most middle-class Indian families I knew when I was growing up, science and mathematics were held in awe.

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.

The power of mathematics is often to change one thing into another, to change geometry into language.

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.

Mathematics is the science of patterns, and nature exploits just about every pattern that there is.

When, therefore, I had long considered this uncertainty of traditional mathematics, it began to weary me that no more definite explanation of the movement of the world-machine established in our behalf by the best and most systematic builder of all, existed among the philosophers who had studied so exactly in other respects the minutest details in regard to the sphere.

Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos [mathematics], where pure thought can dwell in its natural home.

In my schooling through high school, I excelled mainly in chemistry, physics and mathematics.

Even when I was studying mathematics, physics, and computer science, it always seemed that the problem of consciousness was about the most interesting problem out there for science to come to grips with.