Ramsey Theory

Abstract

Ramsey Theory is the study of how specific patterns inevitably emerge in sufficiently large systems. This paper provides an overview of three key theorems in Ramsey Theory: Ramsey’s Theorem, Van der Waerden’s Theorem, and Rado’s Theorem, which deal with finding patterns in mathematical objects such as graphs, the number line, and systems of linear equations respectively. While each theorem is distinctly different, they share a common objective of discerning order in chaos.