Ramsey theory - Bazzi, M (2012)
Ramsey theory is a field of mathematics dating back to approximately 100 years. It intersects with various branches of mathematics, such as combinatorics, number theory, geometry, topology and set theory [16]. Loosely speaking, Ramsey theory can be described as the study of structure which is preserved under partitions – an idea succinctly captured by the statement “complete disorder is impossible” [6, 10]. In this essay we explore Ramsey’s theorems, some of the core results underpinning Ramsey theory and dealing with invariant substructures under finite set partitioning. We then discuss some extensions of these ideas in the case of infinite set partitioning.