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.

To criticize mathematics for its abstraction is to miss the point entirely. Abstraction is what makes mathematics work. If you concentrate too closely on too limited an application of a mathematical idea, you rob the mathematician of his most important tools: analogy, generality, and simplicity. Mathematics is the ultimate in technology transfer.

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.

Mathematics never reveals man to the degree, never expresses him in the way, that any other field of human endeavour does: the extent of the negation of man's corporeal self that mathematics achieves cannot be compared with anything. Whoever is interested in this subject I refer to my articles. Here I will say only that the world injected its patterns into human language at the very inception of that language; mathematics sleeps in every utterance, and can only be discovered, never invented.

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.

No one really understood music unless he was a scientist, her father had declared, and not just a scientist, either, oh, no, only the real ones, the theoreticians, whose language was mathematics. She had not understood mathematics until he had explained to her that it was the symbolic language of relationships. "And relationships," he had told her, "contained the essential meaning of life."

Mathematics is the queen of science, and arithmetic the queen of mathematics.

The fact is there are few more popular subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune.

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.

If you want to be a physicist, you must do three things-first, study mathematics, second, study more mathematics, and third, do the same.

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.

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.

The proof of Fermat's Last Theorem underscores how stable mathematics is through the centuries - how mathematics is one of humanity's long continuous conversations with itself.

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.

Mathematics, rightly viewed, possesses not only truth, but supreme beauty a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the georgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.

Except in mathematics, the shortest distance between point A and point B is seldom a straight line. I don't believe in mathematics.

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?

One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That's so unlike the true nature of mathematics.

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.

Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.

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

The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience.

Education is like a diamond with many facets: It includes the basic mastery of numbers and letters that give us access to the treasury of human knowledge, accumulated and refined through the ages; it includes technical and vocational training as well as instruction in science, higher mathematics, and humane letters.

Probably no branch of mathematics has experienced a more surprising growth than has... topology... Considered as a most specialized and abstract subject in the early 1920's, it is today [1938] an indispensable equipment for the investigation of modern mathematical theories.

We are servants rather than masters in mathematics.

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.

Beauty means a lot of different things to a lot of different people. A lot of different ways in which things can be beautiful. But this really has a very specific meaning and which is more along the lines of elegance which is that we say an idea is beautiful or elegant in mathematics or physics if a very simple principle or a very simple idea, or simple set of ideas, turns out to be very powerful and leads to all sort of unexpected structure and unexpected predictions.

One can understand nature only when one has learned the language and the signs in which it speaks to us; but this language is mathematics and these signs are methematical figures.

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.

The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism.

If there is one thing in mathematics that fascinates me more than anything else (and doubtless always has), it is neither "number" nor "size", but always form. And among the thousand-and-one faces whereby form chooses to reveal itself to us, the one that fascinates me more than any other and continues to fascinate me, is the structure hidden in mathematical things.

The heart of mathematics is its problems.

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.

There are fields of scientific work...which have been explored from the different sides of pure mathematics, statistics, electrical engineering, and neurophysiology...in which every single notion receives a separate and different name from each group, and in which important work has been triplicated or quadruplicated, while still other important work is delayed by the unavailability in one field of results that may have already become classical in the next field.

Perhaps the most surprising thing about mathematics is that it is so surprising.

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.

One thing that definitely did calculate properly for me was the mathematics that makes sense every day, no matter how I look at it, I can't get around it. I try to get around it, I keep trying to find one plus one is not two, somehow. I can't. People can talk about string theory, parallel realities, different dimensions, it's still one plus one is two, baby.

Poetry is a form of mathematics, a highly rigorous relationship with words.

The highest form of pure thought is in mathematics.

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.

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.

How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?

I would not dare to say that there is a direct relation between mathematics and madness, but there is no doubt that great mathematicians suffer from maniacal characteristics, delirium and symptoms of schizophrenia.

And then there is Pythagoras. The legend is that the founder of theoretical mathematics was so outraged when one of his students, the haplessly gifted Hippasus, discovered irrational numbers that he sent the poor fellow out on a raft to drown, initiating a venerable tradition of professors mistreating their graduate students.

As one reads mathematics, one needs to have an active mind, asking questions, forming mental connections between the current topic and other ideas from other contexts, so as to develop a sense of the structure, not just familiarity with a particular tour through the structure.

Now ... the basic principle of modern mathematics is to achieve a complete fusion [of] 'geometric' and 'analytic' ideas.

Mathematics allows for no hypocrisy and no vagueness.