Quotes About Mathematics

Mathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt to draw absolute conclusions. All mathematical truths are relative, conditional. In E. T. Bell Men of Mathematics, New York: Simona and Schuster, 1937.

What, after all, is mathematics but the poetry of the mind, and what is poetry but the mathematics of the heart?

Can the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesn't make any sense since things follow from each other and, in principle, whoever knows the bases knows everything. All of the results of a mathematical theorem are in the axioms of mathematics in embryonic form, aren't they?

The propositions of mathematics have, therefore, the same unquestionable certainty which is typical of such propositions as "All bachelors are unmarried," but they also share the complete lack of empirical content which is associated with that certainty: The propositions of mathematics are devoid of all factual content; they convey no information whatever on any empirical subject matter.

You have this world of mathematics, which is very real and which contains all kinds of wonderful stuff. And then we also have the world of nature, which is real, too. And that, by some miracle, the language that nature speaks is the same language that we invented for mathematics. That's just an amazing piece of luck, which we don't understand.

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.

An Arab activist can take pride in the Arab heritage of mathematics and science or he can take pride in his religion, and there's pride to be taken in both. But one of them could be exploited much more easily and has been in the context of world conflict. And the other is very difficult to do on the grounds that science and literature and mathematics have been among the uniting factors in the history of the world.

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

Blindness to the aesthetic element in mathematics is widespread and can account for a feeling that mathematics is dry as dust, as exciting as a telephone book... Contrariwise, appreciation of this element makes the subject live in a wonderful manner and burn as no other creation of the human mind seems to do.

When the world is mad, a mathematician may find in mathematics an incomparable anodyne. For mathematics is, of all the arts and sciences, the most austere and the most remote, and a mathematician should be of all men the one who can most easily take refuge where, as Bertrand Russell says, "one at least of our nobler impulses can best escape from the dreary exile of the actual world."

If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy.

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

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

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

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'm sorry to say that the subject I most disliked was mathematics. I have thought about it. I think the reason was that mathematics leaves no room for argument. If you made a mistake, that was all there was to it.

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

A first fact should surprise us, or rather would surprise us if we were not used to it. How does it happen there are people who do not understand mathematics? If mathematics invokes only the rules of logic, such as are accepted by all normal minds...how does it come about that so many persons are here refractory?

I didn't feel comfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of everything and explore the world.

Applied mathematics will always need pure mathematics just as anteaters will always need ants.

Mathematics expresses values that reflect the cosmos, including orderliness, balance, harmony, logic, and abstract beauty.

Pure mathematics, may it never be of any use to anyone.

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.

You can not apply mathematics as long as words still becloud reality.

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.

The Good Spirit never cared for the colleges, and though all men and boys were now drilled in Greek, Latin, and Mathematics, it had quite left these shells high on the beach, and was creating and feeding other matters [science] at other ends of the world.

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 is the art of giving the same name to different things.

The power of equations lies in the philosophically difficult correspondence between mathematics, a collective creation of human minds, and an external physical reality. Equations model deep patterns in the outside world. By learning to value equations, and to read the stories they tell, we can uncover vital features of the world around us.

Outside of mathematics and logic, there are common sense truths, such as that it is snowing that normal observers, in a specified context can agree on, subject to vagueness considerations, and theoretical truths, such as that snow is crystallised water vapour, and maybe in-between truths.

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.

One of my colleagues likes to say that, mathematics is the - he thinks about the only subject that he knows in academia or in the real world where if two people disagree about something - if people are studying some mathematical object and there's supposed to be a proof and they disagree about whether this proof or not, the will go into a room, sit down and talk about it and fairly quickly or at the end of the day one of them will admit they're wrong.

That sometimes clear ... and sometimes vague stuff ... which is ... mathematics.

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 an independent world created out of pure intelligence.

When a branch of mathematics ceases to interest any but the specialists, it is very near its death, or at any rate dangerously close to a paralysis, from which it can be rescued only by being plunged back into the vivifying source of the science.

The word "mathematics" is a Greek word and, by origin, it means "something that has been learned or understood," or perhaps "acquired knowledge," or perhaps even, somewhat against grammar, "acquirable knowledge," that is, "learnable knowledge," that is, "knowledge acquirable by learning."

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

Proofs exist only in mathematics and logic, not in science.

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.

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.

Mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics.

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.

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.

Mathematics is the only true metaphysics.

It is a monstrous thing to force a child to learn Latin or Greek or mathematics on the ground that they are an indispensable gymnastic for the mental powers. It would be monstrous even if it were true.

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.