One can read in Wikipedia that the 4-dimensional affine space $\mathbf R^4$ has uncountably many piecewise linear structures (in contrast with other dimensions, where it has exactly one). A reference is given to Milnor's paper, Differential Topology Forty-six Years Later where this fact is indeed printed on the bottom of the first column of page 2.
However, I could not follow the arguments that lead to this conclusion, nor find them in the litterature (eg, Freedman-Quinn's book).
Results of the 60s imply (Theorem 2 of Milnor's quoted paper) that any PL structure on $\mathbf R^4$ gives rise to a well-defined, compatible, smooth structure. Then Freedman classified topological closed 4-manifolds, and Donaldson proved that many of them cannot be smoothed. But how does this help constructing exotic PL structures on $\mathbf R^4$?