I am reading "Basic Manifold Theory" by Yukio Matsumoto:
Even if a differential structure exists on a topological manifold, it is not necessarily unique. The first discovery of an example where the differential structure is not unique, and moreover on a simple manifold such as the 7-dimensional sphere, was made in J. Milnor, "On manifolds homeomorphic to the $7$-sphere", Ann. of Math., Vol. 64, 1956, pp.399-405.
In other fields of mathematics, I feel like such examples are often introduced soon after definitions are given. Why is it so difficult to answer such a basic question in this field?