Works of art have value not only as entertainment and aesthetic expression -- they also externalize features of human cognition that would often otherwise remain hidden. A musical example from the 19th century is a striking case in point. In 1819, Austrian music publisher, editor, and composer Anton Diabelli invited fifty-one of Austria's most prominent musicians to submit one variation on a waltz theme he had created. Among those solicited was Ludwig van Beethoven. Though imperfect and no doubt unintentional, Diabelli's project created a real-world experiment -- fifty-one minds tackling the same creative problem. While every other composer submitted a single variation, Beethoven sent Diabelli thirty-three. Widely regarded as one of the greatest piano works of 19th century Europe, Beethoven's Diabelli Variations represent a peerless display of divergent thinking. A cognitive investigation contrasting Beethoven's approach with the practices of his contemporaries is highly revealing about the creative process, with implications for future research, educational practice, and artificial intelligence.