Reflections on Euler (2009)

“Reflections on Euler” (2009) is a piece for string quartet in five movements, each inspired by one term of a famous formula named after Swiss mathematician Leonhard Euler. Euler’s Identity states that e^iπ + 1 = 0. This equation is remarkable for its simplicity and elegance as well as its comprehensiveness, as it connects key ideas from the fields of algebra, calculus, probability, geometry, and complex-number analysis. After proving the identity in a lecture, noted 19th century mathematician Benjamin Peirce said, “It is absolutely paradoxical; we cannot understand it, and we don’t know what it means, but we have proved it, and therefore we know it must be the truth.”

The first movement, e, is structured around an energetic theme that swells and grows, as the number e is used to calculate rates of growth. The second movement, i, is for the imaginary number, the square root of -1. This movement explores a mysterious web of interweaving violin melodies while the viola and cello provide a regular rhythmic base (inspired by the cyclic powers of i). The relationship between circles and lines informs the third movement, π: the cello and viola traverse long melodic lines while the violins pluck “circular” patterns around them. The fourth movement, + 1, is simply one of unstoppable expansion, and the final movement, = 0, explores motives from the previous four movements, playing them against one another in discordant ways until, from the chaos, we arrive at a place of order and harmony.