What Happened to Euclidean Geometry in Modern Mathematics Curriculums?
It has occurred to me over the course of my first year here at UCLA that mathematicians used to be very good at Euclidean geometry (take the Principia as a prime example, or the early solutions to the Brachistochrone problem)...and over time that has faded. I personally have never taken a course in the subject, and beyond simple facts, I rarely have ever needed it. Though I can see its used in modeling/solving some problems; for example, it was useful in geometric optics/physics problems (but these are mostly lower division/basic problems not requiring a lock of postulates/theorems/etc.).
Yet in looking through some of these forums I've noticed that a good number of people here are actually pretty good at it, and there are many questions pertaining to the subject. So I guess this is now a two-part discussion. Is it worthwhile to become more skilled in Euclidean geometry (i.e. take a rigorous course in foundations of geometry)? And why do you suppose hardly anyone knows the subject anymore?
Re: What Happened to Euclidean Geometry in Modern Mathematics Curriculums?
Well, I can't speak for today's schools but I took a geometry course in High School many years ago and have, in fact, taught Euclidean geometry in college- although as a remedial course. You will certainly need to know basic Euclidean geometry for "Cartesian coordinates" which are a fundamental part of pre-Calculus and Calculus courses. What reason do you have to believe that "hardly anyone knows the subject anymore"?