Quotable Mathematics

"A poem therefore is to be defined as a structure of words whose sound constitutes a rhythmical unity, complete in itself, irrefragable...

"The true mathematician is always a great deal of an artist, an architect, yes, of a poet. Beyond the real world, though perceptibly co...

"Poetry is the universal art of the spirit which has become free in itself and which is not tied down for its realization to external s...

"One of the central problems studied by mankind is the problem of the succession of form. Whatever is the ultimate nature of reality (a...

"The philosopher who is really useful to the cause of science, is he who, uniting to a fertile imagination, a rigid severity in investi...

"The sciences bring into play the imagination, the building of images in which the reality, of the past is blended with the ideals for ...

"This is the greatest degree of impoverishment; the [mental] image, deprived little by little of its own characteristics, is nothing mo...

"It is in fact wonderful how physics - as soon as it is concerned not with technical purposes but with general results - without knowin...

"Anything worth discovering in mathematics does not need proof; it needs only to be seen or understood."  (Scott Buchanan, "P...

"Genius and science have burst the limits of space, and few observations, explained by just reasoning, have unveiled the mechanism of t...

"The most ordinary things are to philosophy a source of insoluble puzzles. In order to explain our perceptions it constructs the concep...

"Our science, in contrast with others, is not founded on a single period of human history, but has accompanied the development of cultu...

"Poetry is a sort of inspired mathematics, which gives us equations, not for abstract figures, triangles, squares, and the like, but fo...

"It is of our very nature to see the universe as a place that we can talk about. In particular, you will remember, the brain tends to c...

"Number theory is revealed in its entire simplicity and natural beauty when the field of arithmetic is extended to the imaginary number...

"The whole history of the development of mathematics has been a history of the destruction of old definitions, old hobbies, old idols....

"[W]hatsoever the Philosopher saith should be done, [the poet] gives a perfect picture of it by some one, by who he presupposeth it was...

"Poetry is not the proper antithesis to prose, but to science. Poetry is opposed to science, and prose to metre. The proper and immedia...

"The imagination […] that reconciling and mediatory power, which incorporating the reason in images of the sense and organizing (as it ...

"Metaphor consists in giving the thing a name that belongs to something else; the transference being either from genus to species, or f...