Erdős–Szekeres convex polygon conjecture

Let $n$ be an integer, and let a set of points in the plane be in general position, meaning that no three points are collinear. Erdős–Szekeres convex polygon conjecture. Every set of $2^{n-2}+1$ points in the plane that are in general position contains $n$ points in convex position, and this bound is tight in the worst case. This is the classical convex polygon problem of Erdős and Szekeres; the assertion concerns the smallest number of points that guarantees $n$ points in convex position, with the stated exponential bound and its tightness.