(2015) O Austere Mathematics

As an impressionable student in my final year of high school, I was introduced to Hegel’s theory of dialectics in a course on European history. Of course, at the time, we learned the concept by its most easily-comprehensible model: a triad in which a thesis and its antithesis act against one another to produce a new idea, a synthesis of the two. What immediately struck me, and has fascinated me since, was the remarkable overlap between this simplified model of Hegelian dialectics and the dramatic arch of sonata-allegro form—all the more interesting when a deeper understanding of dialectics is applied.

One of the most critical stipulations of Hegel’s theory not covered in the high school primer on dialectics was the substantially more difficult idea that the perceived initial opposition between thesis and antithesis was basically illusion, for all things in this view are in effect imbued with their opposites. O Austere Mathematics relentlessly pursues this slightly modified model of thematic relationships in the sonata-allegro form: through a process of elision, the “principal” and “subordinate” themes are eventually revealed to be one and the same.