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.

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

Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33, like Riemann before him. Working in total isolation from the main currents of his field, he was able to rederive 100 years' worth of Western mathematics on his own. The tragedy of his life is that much of his work was wasted rediscovering known mathematics.

Some people think that mathematics is a serious business that must always be cold and dry; but we think mathematics is fun, and we aren't ashamed to admit the fact. Why should a strict boundary line be drawn between work and play? Concrete mathematics is full of appealing patterns; the manipulations are not always easy, but the answers can be astonishingly attractive.

The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. . . . Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.

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.

The history of mathematics, lacking the guidance of philosophy, [is] blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the history of mathematics, is empty.

But there is another reason for the high repute of mathematics: it is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain.

[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.

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.

A Christian boy or girl can learn mathematics, for example, from a teacher who is not a Christian; and truth is truth however learned. But while truth is truth however learned, the bearing of truth, the meaning of truth, the purpose of truth, even in the sphere of mathematics, seem entirely different to the Christian from that which they seem to the non-Christian; and that is why a truly Christian education is possible only when Christian conviction underlies not a part but all, of the curriculum of the school.

The tool which serves as intermediary between theory and practice, between thought and observation, is mathematics; it is mathematics which builds the linking bridges and gives the ever more reliable forms.

We can... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics.

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.

Mathematics was born and nurtured in a cultural environment. Without the perspective which the cultural background affords, a proper appreciation of the content and state of present-day mathematics is hardly possible.

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.

Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting.

I tell you that studying humanities in high school is more important than mathematics - mathematics is too sharp an instrument, no good for kids.

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.

[P]olitical and social and scientific values ... should be correlated in some relation of movement that could be expressed in mathematics, nor did one care in the least that all the world said it could not be done, or that one knew not enough mathematics even to figure a formula beyond the schoolboy s=(1/2)gt2. If Kepler and Newton could take liberties with the sun and moon, an obscure person ... could take liberties with Congress, and venture to multiply its attraction into the square of its time. He had only to find a value, even infinitesimal, for its attraction.

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.

Mathematicians care no more for logic than logicians for mathematics.

In short, if we adhere to the standard of perfection in all our endeavors, we are left with nothing but mathematics and the White Album.

White folks was in the caves while we [blacks] was building empires ... We built pyramids before Donald Trump ever knew what architecture was ... we taught philosophy and astrology and mathematics before Socrates and them Greek homos ever got around to it.

In mathematics, two angles that are said to coincide fit together perfectly. The word "coincidence" does not describe luck or mistakes. It describes that which fits together perfectly.

In the realm of ideas, of mental objects, those ideas whose properties are reproducible are called mathematical objects, and the study of mental objects with reproducible properties is called mathematics.

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.

The progress of mathematics can be viewed as progress from the infinite to the finite.

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

I have long admired Ron Whitehead. He is crazy as nine loons, and his poetry is a dazzling mix of folk wisdom and pure mathematics

But I simply can't stand a view limited to this earth, I feel life is so small unless it has windows into other worlds...I like mathematics largely because it is not human.

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.

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

I merely say that all reading for pleasure is escape, whether it be Greek, mathematics, astronomy, Benedetto Croce, or The Diary of the Forgotten Man. To say otherwise is to be an intellectual snob, and a juvenile at the art of living.

I have a true aversion to teaching. The perennial business of a professor of mathematics is only to teach the ABC of his science; most of the few pupils who go a step further, and usually to keep the metaphor, remain in the process of gathering information, become only Halbwisser [one who has superficial knowledge of the subject], for the rarer talents do not want to have themselves educated by lecture courses, but train themselves. And with this thankless work the professor loses his precious time.

Mathematics is like draughts in being suitable for the young, not too difficult, amusing, and without peril to the state.

This is not mathematics; this is theology.

All of mathematics is a tale about groups.

The Babylonian and Assyrian civilizations have perished; Hammurabi, Sargon and Nebuchadnezzar are empty names; yet Babylonian mathematics is still interesting, and the Babylonian scale of 60 is still used in Astronomy.

Mathematics, however, is, as it were, its own explanation; this, although it may seem hard to accept, is nevertheless true, for the recognition that a fact is so is the cause upon which we base the proof.

Mathematics - the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human affairs.

Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of constraint and freedom that is the very essence of human nature.

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.

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.

A formal manipulator in mathematics often experiences the discomforting feeling that his pencil surpasses him in intelligence.

The conception of objective reality ... has thus evaporated ... into the transparent clarity of mathematics that represents no longer the behavior of particles but rather our knowledge of this behavior.

Mathematics is the most beautiful and most powerful creation of the human spirit.