The moving sofa problem is one of those deceptively simple yet incredibly difficult “real-world” math problems. Despite its straightforward formulation, it has remained unsolved for roughly 60 years—until recently, when Jineon Baek announced a complete solution (arXiv:2411.19826; hopefully, this time the topic I’m blogging about won’t turn out to be incorrect in the end).
In a MathOverflow discussion titled Not especially famous, long-open problems which anyone can understand, the moving sofa problem ranks second on the list. If you’re unfamiliar with it, you can find a detailed explanation on its Wikipedia page. Thanks to its intuitive nature, the problem has captured the interest of both professional mathematicians and science enthusiasts alike, leading to coverage in mainstream science media. For instance, Spektrum.de recently featured an article discussing the new breakthrough.