  We show, by an explicit construction, that a mixture of univariate Gaussian
densities with variance $1$ and means in $[-A,A]$ can have $\Omega(A^2)$ modes.
This disproves a recent conjecture of Dytso, Yagli, Poor and Shamai
\cite{DYPS20} who showed that such a mixture can have at most $O(A^{2})$ modes
and surmised that the upper bound could be improved to $O(A)$. Our result holds
even if an additional variance constraint is imposed on the mixing
distribution. Extending the result to higher dimensions, we exhibit a mixture
of Gaussians in $\mathbb{R}^{d}$, with identity covariances and means inside
$[-A,A]^{d}$, that has $\Omega(A^{2d})$ modes.
