In a preprint recently posted to the arXiv, Jineon Baek claims to have solved the moving sofa problem, which asks for the largest area sofa that can be maneuvered through an L-shaped corridor, like this:

The problem was first posed by Leo Moser in 1966. In 1992, Joseph Gerver designed a sofa of area approximately 2.2195 that was believed to be optimal, and indeed what Baek has shown is that Gerver's sofa is the optimal sofa.