Appears in collection : 2026 - T1 - WS3 - Integrating Research and Illustration in Number Theory

When given a complicated function, one standard technique is to compute a Fourier transform, decomposing the function into simple components that are easier to analyze. On the other hand, the structure of the human ear allows it to mechanistically identify Fourier coefficients of incoming sound waves. We can use this ability to our advantage: we may be able to hear properties of functions that we would never be able to see.

This talk will explore two examples of this ability to hear properties of functions, using the Riemann zeta function as a case study. First, we will try to identify the analytic continuation of the zeta function within the sound of a divergent sum. Second, we will listen to what the primes might sound like if the Riemann hypothesis were false.