Mathematics Quotes

It is impossible to be a mathematician without being a poet in soul.

I also require much time to ponder over the matters themselves, and particularly the principles of mechanics (as the very words: force, time, space, motion indicate) can occupy one severely enough; likewise, in mathematics, the meaning of imaginary quantities, of the infinitesimally small and infinitely large and similar matters.

In some parts of life, like mathematics and science, yeah, I was a genius. I would top all the top scores you could ever measure it by.

The origins of graph theory are humble, even frivolous.

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

Our minds are finite, and yet even in these circumstances of finitude we are surrounded by possibilities that are infinite, and the purpose of life is to grasp as much as we can out of that infinitude.

You know that I write slowly. This is chiefly because I am never satisfied until I have said as much as possible in a few words, and writing briefly takes far more time than writing at length.

Everyone engaged in research must have had the experience of working with feverish and prolonged intensity to write a paper which no one else will read or to solve a problem which no one else thinks important and which will bring no conceivable reward - which may only confirm a general opinion that the researcher is wasting his time on irrelevancies.

Nothing is done. Everything in the world remains to be done or done over. The greatest picture is not yet painted, the greatest play isn't written, the greatest poem is unsung. There isn't in all the world a perfect railroad, nor a good government, nor a sound law. Physics, mathematics, and especially the most advanced and exact of the sciences are being fundamentally revised. . . Psychology, economics, and sociology are awaiting a Darwin, whose work in turn is awaiting an Einstein.

Whoever despises the high wisdom of mathematics nourishes himself on delusion and will never still the sophistic sciences whose only product is an eternal uproar.

One man may have some special knowledge at first-hand about the character of a river or a spring, who otherwise knows only what everyone else knows. Yet to give currency to this shred of information, he will undertake to write on the whole science of physics. From this fault many great troubles spring.

The best of ideas is hurt by uncritical acceptance and thrives on critical examination.

The union of the mathematician with the poet, fervor with measure, passion with correctness, this surely is the ideal.

The world of ideas which it [mathematics] discloses or illuminates, the contemplation of divine beauty and order which it induces, the harmonious connexion of its parts, the infinite hierarchy and absolute evidence of the truths with which it is concerned, these, and such like, are the surest grounds of the title of mathematics to human regard, and would remain unimpeached and unimpaired were the plan of the universe unrolled like a map at our feet, and the mind of man qualified to take in the whole scheme of creation at a glance.

Mathematics is concerned with "all possible worlds."

We have a closed circle of consistency here: the laws of physics produce complex systems, and these complex systems lead to consciousness, which then produces mathematics, which can then encode in a succinct and inspiring way the very underlying laws of physics that gave rise to it.

Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.

Nixon's motto was, if two wrongs don't make a right, try three.

But actually a code is a language for translating one thing into another. And mathematics is the language of science. My big thesis is that although the world looks messy and chaotic, if you translate it into the world of numbers and shapes, patterns emerge and you start to understand why things are the way they are.

He who does not understand the supreme certainty of mathematics is wallowing in confusion.

Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.

[I]f in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics, in so far as disposed through it we are able to reach certainty in other sciences and truth by the exclusion of error.

Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, moulded and conformed. They are no exceptions to the rule that God always geometrizes. Their problems of form are in the first instance mathematical problems, their problems of growth are essentially physical problems, and the morphologist is, ipso facto, a student of physical science.

Among the minor, yet striking characteristics of mathematics, may be mentioned the fleshless and skeletal build of its propositions; the peculiar difficulty, complication, and stress of its reasonings; the perfect exactitude of its results; their broad universality; their practical infallibility.

Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.

Though this be madness, yet there is method in't.

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.

Arithmetic is numbers you squeeze from your head to your hand to your pencil to your paper till you get the answer.

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

Geometry is the archetype of the beauty of the world.

Every field has its taboos. In algebraic geometry the taboos are (1) writing a draft that can be followed by anyone but two or three of one's closest friends, (2) claiming that a result has applications, (3) mentioning the word 'combinatorial,' and (4) claiming that algebraic geometry existed before Grothendieck (only some handwaving references to 'the Italians' are allowed provided they are not supported by specific references).

The principle is so perfectly general that no particular application of it is possible.

When we talk about the impact inside mathematics, and applications in the sciences, [Mandelbrot] is one of the most important figures of the last 50 years.

My specific goal is to revolutionize the future of the species. Mathematics is just another way of predicting the future.

Now, in the development of our knowledge of the workings of Nature out of the tremendously complex assemblage of phenomena presented to the scientific inquirer, mathematics plays in some respects a very limited, in others a very important part. As regards the limitations, it is merely necessary to refer to the sciences connected with living matter, and to the ologies generally, to see that the facts and their connections are too indistinctly known to render mathematical analysis practicable, to say nothing of the complexity.

A chess problem is genuine mathematics, but it is in some way "trivial" mathematics. However, ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well as beautiful-"important" if you like, but the word is very ambiguous, and "serious" expresses what I mean much better.

Contrariwise, if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic.

In the last two months I have been very busy with my own mathematical speculations, which have cost me much time, without my having reached my original goal. Again and again I was enticed by the frequently interesting prospects from one direction to the other, sometimes even by will-o'-the-wisps, as is not rare in mathematic speculations.

What is best in mathematics deserves not merely to be learnt as a task, but to assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement.

Mathematics and art are quite different. We could not publish so many papers that used, repeatedly, the same idea and still command the respect of our colleagues.

At its heart, music is all higher mathematics.

It can be argued that the mathematics behind these images [of the orbit diagram for quadratic functions and the Mandelbrot set] is even prettier than the pictures themselves.

We have heard much about the poetry of mathematics, but very little of it has as yet been sung. The ancients had a juster notion of their poetic value than we. The most distinct and beautiful statements of any truth must take at last the mathematical form. We might so simplify the rules of moral philosophy, as well as of arithmetic, that one formula would express them both.

The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic.

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

You can see the meaning of the statement that "Literature is a living art" most easily and clearly, perhaps, by contrasting Science and Art at their two extremes - say Pure Mathematics and Acting. Science as a rule deals with things, Art with man's thought and emotion about things.

A surprising proportion of mathematicians are accomplished musicians. Is it because music and mathematics share patterns that are beautiful?

Physics is an otherworld thing, it requires a taste for things unseen, even unheard of- a high degree of abstraction... These faculties die off somehow when you grow up... profound curiosity happens when children are young. I think physicists are the Peter Pans of the human race... Once you are sophisticated, you know too much- far too much. Pauli once said to me, "I know a great deal. I know too much. I am a quantum ancient.".

There is nothing mysterious, as some have tried to maintain, about the applicability of mathematics. What we get by abstraction from something can be returned.

Mathematics would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude.