  Let $\alpha \colon \mathbb{N} \to S^1$ be the Steinhaus multiplicative
function: a completely multiplicative function such that $(\alpha(p))_{p\text{
prime}}$ are i.i.d.~random variables uniformly distributed on $S^1$. Helson
conjectured that $\mathbb{E}|\sum_{n\le x}\alpha(n)|=o(\sqrt{x})$ as $x \to
\infty$, and this was solved in strong form by Harper. We give a short proof of
the conjecture using a result of Saksman and Webb on a random model for the
zeta function.
