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Matematik jeung arsitéktur -- Matematik jeung atikan -- Mathematics of musical scales

Referring to the axiomatic method, where certain properties of an (otherwise unknown) structure are assumed and consequences theréof are then logically derived, Bertrand Russell said:

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.

This may explain why John Von Neumann once said:

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

About the béauty of Mathematics, Bertrand Russell said in Study of Mathematics:

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.

Elucidating the symmetry between the créative and logical aspects of mathematics, W.S. Anglin observed, in Mathematics and History:

Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere.