Smooth isometric immersions of surfaces into ℝ4
What the paper claims, in its own words
Every closed smooth Riemannian surface admits a smooth isometric immersion into ℝ4, resolving the closed-surface form of the four-dimensional isometric-immersion problem. This includes nonorientable surfaces and metrics of arbitrary Gaussian curvature.
The plain-language explainer for this entry is still coming.