In 1935, Erd\H{o}s and Szekeres proved that for every integer $n\geq 3,$ there is a minimal integer $ES(n)$ such that any set of $ES(n)$ points in the plane in general position contains $n$ points in convex position. They showed that $ES(n)\geq 2^{n-2}+1$ and conjectured this to be sharp.

There are many different variations of Erd\H{o}s-Szekeres Conjecture. Babai and Moran said:"Since the creation of formal systems, the element of interaction in the proof process has been ignored in mathematics." In this paper, for the first time, the Interactive Proof Method was introduced to investigate the Erd\H{o}s-Szekeres Conjecture. The connection of this method to the design of randomized and deterministic algorithms to find the convex hull of $n$ points for a given point set is also discussed.