To keep up the trend of making what are not actual posts, I give you a quotation I recently came across which I think well expresses the idea of what I call “the mathematical sublime.”
Mathematics, rightly viewed, possesses not only truth but supreme beauty — a beauty cold and austere, like that of a sculpture, without appeal to any part of our weaker nature, without the gorgeous trapping 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 in poetry.
— Bertrand Russell
This isn’t exactly the same as the scientific sublime I used a few weeks ago when discussing Andrew Bird, but it is related. There are two primary differences; first, science, while abstracted from humanity, still deals with the natural world, while mathematics is removed even from that, residing entirely in the realm of logic. This means that while the scientific sublime offers a way of looking at humans as cogs in a machine, the mathematical does not even offer the machine or the cogs — only the rules by which they would, in theory, operate, if they existed.
Second, unlike science, mathematics actually wrestles with infinity. People often go on about “infinity” when they just mean vastness; mathematics actually attempts to quantify the unquantifiable.
Few writers have a true feel for the mathematical sublime, I think (many more can grasp the scientific); the only positive example I can give is Jorge Luis Borges, many of whose stories offer excellent examples of it; see “The Library of Babel.”