The Erdős-Szekeres Theorem is proved in the 1935 paper of Erdős and Szekeres which concerns what was later coined the “happy ending problem” by Erdős. The story is as follows:
Erdős and Szekeres were part of a group of Hungarians who discussed mathematical problems amongst them. Another member was Klein, who proposed the following problem: Any set of 5 points on the plane has a subset of 4 points that form the vertices of a convex quadrilateral. Szekeres then wanted to solve this problem to impress Klein. He eventually did so along with Erdős, and the rumour is that after that Klein was indeed impressed. Erdős then named this problem the “happy ending” problem, as he claims it is what led to Klein and Szekeres getting married. The marriage of the two was reportedly a very happy one, and they were together for pretty much the rest of their (long) lives, as they died within an hour of each other in their 90’s.