An old question of Erdos asks: Given a set of $N$ points in $R^d$ with no $d+2$ members on a common hyperplane, what is the size of the largest subset of points in general position (i.e., no $d+1$ members on a hyperplane)?  In 2018, Balogh and Solymosi showed that one can use the hypergraph container method to tackle this problem in the plane.  In this talk, I will show how to use the container method to tackle Erdos' question in any dimension.  This is joint work with Ji Zeng.