Since the dawn of time, if not earlier, mathematicians have been fascinated by prime numbers. Euclid, Eratosthenes and other ancient thinkers rigorously studied the primes, yet these enigmatic integers defy our understanding even in the twenty-first century. Another ancient number theory pioneer, Pythagoras, also pioneered modern music theory. He found pleasing-sounding chords and melodies to be related to whole number ratios of waveforms on vibrating strings. These musical experiments of Pythagoras resonate throughout the mathematical sciences, from applications of Fourier series to the mysteries of quantum physics and string theory. One of the most famous open problems in all of mathematics, the Riemann Hypothesis, suggests beautiful waveform-like behavior in the distribution of prime numbers among the integers, which some authors poetically liken to “music of the primes.”
But this is a talk about actual music. We will discuss and hear new directions in composition that explore prime numbers through the superposition of sound waves and rhythms, such as the experimental “Dream House” installation by composer La Monte Young, and somewhat less far-out pieces by the speaker.
Robert Schneider is a number theorist and lecturer at the University of Georgia (Athens), having received his Ph.D. in 2018 from Emory University under the supervision of Ken Ono. His primary research interests lie in partition theory, analytic number theory, combinatorics and physics; he is also a professional composer, musician and indie record producer, and is interested as in using ideas from mathematics to seek new modes of expression in music.