TITLE: Is there any point to Olympiad geometry beyond Olympiads themselves?
QUESTION [5 upvotes]: Is synthetic geometry still relevant in mathematics? I always saw Olympiad geometry as an odd field because while every other Olympiad topic would extend to larger math, geometry seems especially useless. I get that analytic geometry is useful in college but that is heavily discouraged in Olympiad geometry. So what does olympiad geo extend to?

REPLY [5 votes]: Here is a list of open problems in  Euclidean geometry taken from Mathoverflow. Thus, the sentiment that "all of the interesting things (in Euclidean geometry) have been discovered already" is just false. 
Edit 1: At the same time, most MO problems have no connection to the modern research. 
Edit 2. Here is one (admittedly atypical) example. I was told by a person present at the conversation, that the paper W.P.Thurston, "Shapes of polyhedra and triangulations of the sphere" grew out of a conversation about a Brazilian MO problem that Thurston had with a Brazilian grad student in Princeton around 1984 during a lunch break. (Sadly, I do not know the name of the student and the exact MO problem.) According to Google Scholar, Thurston's paper currently has 233 citations. Of course, one has to be William Thurston to accomplish such a feat.