Mathematical Conversations

The Möbius function $\mu(n)$ measures the parity of number of prime factors of $n$ (if $n$ is square free). Understanding the randomness in this function (often referred to as the Möbius randomness principle) is a fundamental and very difficult problem. A basic conjecture concerns the disjointness of this sequence from observables in zero entropy dynamical systems. We review the formulation, intuition, and a few of the many recent advances around the conjecture.