Most successful art creates a coherent internal context by which it operates and with which it can be interpreted according to the patterns that it itself establishes. Among the most well-known examples of this context-making is the opening of the first movement of Beethoven's Symphony No. 5. This movement is largely built upon the short-short-short-long motive with which it starts (a motive popularly interpreted as "Fate knocking at the door"). Without listeners' recognition and remembrance of this fundamental pattern - this atomic musical unit - the work would lose much of its power and intensity. After all, if we ignore the organizing power of this motive, the movement becomes merely a fast, chaotic, and rather ugly mass and mess of notes. In the realm of visual art, consider, for example, the work of M. C. Escher, in which patterns shift and morph from one region of a work to the next. The meaning and interest of such a work reside precisely in our recognition of such patterns and the ways in which they change.

But is all of this really mathematical? Well, yes and no. It is mathematical in the sense that math is, at its heart, symbolic reasoning and manipulation. In this sense, any endeavor that relies on the combination, mutation, and permutation of symbols or patterns is mathematical. But, truth be told, the mathematics in most (though not all) art is fairly elementary. In the 20th and 21st centuries, however, mathematically-literate artists (including M. C. Escher) have begun to incorporate mathematics more explicitly into their work. This merging - at times wonderful, at times dreadful - has been largely confined to the academic realms of art and art criticism. In general, though, the visual arts have proven more amenable to mathematicization than has music. Think, for example, of the very effective CGI imagery in many a blockbuster film - imagery that could not have been created without quite a lot of mathematical and computational horsepower.

In conclusion, I would observe that it is usually more profitable to consider the internal structure of a work of art in general rather than to search (and stretch) for an explicitly mathematical interpretation.

Learn more about this author, Nathan Davis.
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