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Mathematics is one of the essential emanations of the human spirit, a thing to be valued in and for itself, like art or poetry.
--
Bulletin of the American Mathematical Society, Volume 30 (1924), p. 289

 

Oswald Veblen

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Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true ... If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.

 

Bertrand Russell

 

In time of the crises of the spirit, we are aware of all of need, our need for each other and our need for ourselves. We call up our fullness; we turn, and act. We begin to be aware of correspondences, of the acknowledgement in us of necessity, and of the lands.
And poetry, among all this — where is there a place for poetry?
If poetry as it comes to us through action were all we had, it would be very much. For the dense and crucial moments, spoken under the stress of realization, full-bodied and compelling in their imagery, arrive with music, with our many kinds of theatre, and in the great prose. If we had these only, we would be open to the same influences, however diluted and applied. For these ways in which poetry reaches past the barriers set up by our culture, reaching toward those who refuse it in essential presence, are various, many-meaning, and certainly — in this period — more acceptable. They stand in the same relation to poetry as applied science to pure science.

 

Muriel Rukeyser

 

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 gorgeous 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 highest excellence, is to be found in mathematics as surely as in poetry.

 

Bertrand Russell

 

I know that any discussion of the relation of this poem to its historical materials is, in one perspective, irrelevant to its value; and it could be totally accurate as history and still not worth a dime as a poem. I am trying to write a poem, not a history, and therefore have no compunction about tampering with non-essential facts. But poetry is more than fantasy and is committed to the obligation of trying to say something, however obliquely, about the human condition. Therefore, a poem dealing with history is no more at liberty to violate what the writer takes to be the spirit of his history than it is at liberty to violate what he takes to be the nature of the human heart. What he takes those things to be is, of course, his ultimate gamble.

 

Robert Penn Warren

 

The science of pure mathematics, in its modern developments, may claim to be the most original creation of the human spirit.

 

Alfred North Whitehead