Is the 4-sphere, up to diffeomorphism, the unique smooth closed simply-connected 4-manifold? Topology says yes; smooth structures say nobody knows — and dimension four is where smoothness goes feral.
The Problems
Not schoolwork — the questions that resisted Erdős, Hilbert, and everyone since. The club keeps three shelves: what is still open, what AI recently settled, and what took humanity centuries.
Tagged 4-manifolds — 1 entry. Clear