Open Questions: Mathematical Quotations

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Many people who have never had occasion to learn what mathematics is confuse it with arithmetic and consider it a dry and arid science. In actual fact it is the science which demands the utmost imagination. One of the foremost mathematicians of our century says very justly that it is impossible to be a mathematician without also being a poet in spirit... It seems to me that the poet must see what others do not see, must see more deeply than other people. And the mathematician must do the same.
Sofya Kovalevskaya, 1890

The mathematician does not dig for lost artifacts of a vanished civilization but for the fundamental patterns that undergird the universe, and like the archaeologist we usually find only small fragments.
David M. Bressoud

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.
Bertrand Russell

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 the highest excellence, is to be found in mathematics as surely as poetry.
Bertrand Russell

In mathematics you don't understand things. You just get used to them.
John Von Neumann


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