A search for theorems which appear to have very few, if any hypotheses

Theorem. Every group has a terminating transfinite automorphism tower.

Start with any group $G$, compute $\text{Aut}(G)$ and $\text{Aut}(\text{Aut}(G))$ and so on, iterating transfinitely, mapping each to the next via inner automorphisms and taking direct limits at limit stages. Eventually, one arrives at a fixed point, a group that is isomorphic to its automorphism group by the natural map.

• Joel David Hamkins, Every group has a terminating transfinite automorphism tower, Proc. Amer. Math. Soc. 126 (1998), no. 11, 3223--3226.

Every natural number can be written as the sum of four integer squares. (As opposed to the case of three integer squares, which requires certain hypothesis.)

The theorem of Nash and Tognoli says that any compact smooth manifold is diffeomorphic to a nonsingular real algebraic set.