  Whole-plane SLE$_\kappa$ is a random fractal curve between two points on the
Riemann sphere. Zhan established for $\kappa \leq 4$ that whole-plane
SLE$_\kappa$ is reversible, meaning invariant in law under conformal
automorphisms swapping its endpoints. Miller and Sheffield extended this to
$\kappa \leq 8$. We prove whole-plane SLE$_\kappa$ is reversible for $\kappa >
8$, resolving the final case and answering a conjecture of Viklund and Wang.
Our argument depends on a novel mating-of-trees theorem of independent
interest, where Liouville quantum gravity on the disk is decorated by an
independent radial space-filling SLE curve.
