Music and Mathematics— Creating the Sublime

The third mode of imagination is the abstract—the world shared by mathematics and music. Once held together in the ‘quadrivum’ of medieval liberal arts, they have now lost their obvious connection. This chapter explores their deeper commonalities, starting with Andrew Wiles’ proof of Fermat’s last theorem, and Shostakovich’s eighth string quartet, the shared role of number in rhythm, volume, and pitch leads to a deeper world of multi-layered structure and the unconscious imagination. The writing of, and writing about music of Robert Schumann, including a detailed examination of his Konzertstück for four horns and orchestra, is contrasted with writing about mathematical creativity by Hadamard. The collision of beauty, structure, and universality is illustrated by a close encounter with the Fluctuation–Dissipation Theorem. In both cases of mathematics and music, notation is explicitly displayed in an exploration of how it serves as an extension to imaginative thought.