Infinitely many closed geodesics on Riemannian spheres and closed three-manifolds
What the paper claims, in its own words
Proves that every smooth Riemannian metric on Sn, n ≥ 2, has infinitely many prime closed geodesics with pairwise distinct images. The same conclusion holds on every closed manifold admitting a finite smooth spherical cover and on every closed three-manifold, without orientability or nondegeneracy restrictions.
The plain-language explainer for this entry is still coming.