Mathematics Quotes

500+ Sourced quotes

Nicolaus Copernicus

Marston Morse

Richard Courant

Maria Mitchell

J. M. Coetzee

André Weil

Frank Capra

Not a few other very eminent and scholarly men made the same request, urging that I should no longer through fear refuse to give out my work for the common benefit of students of Mathematics.

Nicolaus Copernicus

But mathematics is the sister, as well as the servant, of the arts and is touched with the same madness and genius.

It is not of the essence of mathematics to be conversant with the ideas of number and quantity.

For the things of this world cannot be made known without a knowledge of mathematics.

The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future; and should analysis ever appear to be without or blemish, its perfection might only be that of death.

Eric Temple Bell

If scientific reasoning were limited to the logical processes of arithmetic, we should not get far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability. The abacus, with its beads strung on parallel wires, led the Arabs to positional numeration and the concept of zero many centuries before the rest of the world; and it was a useful tool — so useful that it still exists.

The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.

If in other sciences we should arrive at certainty without doubt and truth without error, it behoves us to place the foundations of knowledge in mathematics.

The so-called obvious was repeatedly scrutinized from every angle and was frequently found to be not obvious but false. "Obvious" is the most dangerous word in mathematics.

Eric Temple Bell

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning... The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.

The essence of mathematics lies entirely in its freedom.

I hope that seeing the excitement of solving this problem will make young mathematicians realize that there are lots and lots of other problems in mathematics which are going to be just as challenging in the future.

Film is one of the three universal languages, the other two: mathematics and music.

Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments. We also notice that, the farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separate branches of the science. So it happens that, with the extension of mathematics, its organic character is not lost but only manifests itself the more clearly.

It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences.

Eric Temple Bell

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.

Richard Courant

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

Richard Courant

In its conception the literature prize belongs to days when a writer could still be thought of as, by virtue of his or her occupation, a sage, someone with no institutional affiliations who could offer an authoritative word on our times as well as on our moral life. (It has always struck me as strange, by the way, that Alfred Nobel did not institute a philosophy prize, or for that matter that he instituted a physics prize but not a mathematics prize, to say nothing of a music prize - music is, after all, more universal than literature, which is bound to a particular language.) The idea of writer as sage is pretty much dead today. I would certainly feel very uncomfortable in the role.

The abstract analysis of the world by mathematics and physics rests on the concepts of space and time.

James J. Gibson

God exists since mathematics is consistent, and the Devil exists since we cannot prove it.

We especially need imagination in science. It is not all mathematics, nor all logic, but it is somewhat beauty and poetry. There will come with the greater love of science greater love to one another. Living more nearly to Nature is living farther from the world and from its follies, but nearer to the world's people; it is to be of them, with them, and for them, and especially for their improvement. We cannot see how impartially Nature gives of her riches to all, without loving all, and helping all; and if we cannot learn through Nature's laws the certainty of spiritual truths, we can at least learn to promote spiritual growth while we are together, and live in a trusting hope of a greater growth in the future.

God used beautiful mathematics in creating the world.

Applied to practice, it [mathematics] becomes an art, like RHETORIC. In both these arts the form is everything, the substance nothing. To mathematics it is indifferent whether it reckons pence or pounds; to RHETORIC, whether it defends truth or falsehood.

Johann Wolfgang von Goethe

The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it by God and which He revealed to us in the language of mathematics.

Johannes Kepler

I receive mathematics as the most sublime and useful science, so long as they are applied in their proper place; but I cannot commend the misuse of them in matters which do not belong to their sphere, and in which, noble science as they are, they seem to be mere nonsense.

Johann Wolfgang von Goethe