The ideas expressed via the arts are malleable, sometimes good or bad but not essential to a given art. Poetry, for example, is more about how something is said than what it means. Mathematics, conversely, deals solely in ideas.

Educated people understand that mathematics has beauty and that, like all beauty, it’s hard to define. Some dismiss this aesthetic value as unimportant, yet millions of chess players understand at once the beauty of an elegant move, and chess is essentially mathematical. Chess and other puzzle-like games owe their wide appeal to the underlying math that gives solving them an “intellectual ‘kick.’”

Most math has no practical consequences, and that which does usually has little aesthetic value. The value of a math theorem lies in its seriousness, which, in turn, depends on its “significance”—its ability to say something important within a large region of mathematical concepts and perhaps to improve that area and the sciences connected to it.

William Shakespeare is great not because of his impact on the English language but because of the beauty of his writing. That beauty includes the ways that his verse presents ideas, but this is only a part of its success and not the main cause of it.