The Erdős-Szekeres Theorem is a fundamental result in combinatorial mathematics that deals with sequences of numbers. It states that for any sequence of n distinct real numbers, if n is greater than or equal to k \times m , then there exists a subsequence of length k that is either increasing or a subsequence of length m that is decreasing. This theorem highlights the idea that in sufficiently large sets of numbers, certain ordered patterns must appear. It was independently proven by mathematicians Paul Erdős and George Szekeres in 1935, and it has important implications in various fields, including computer science and geometry.