Elegance and a (simple) math problem

This is a rant. Remember the title of the blog. You have been warned.

It has always slightly bothered me how sometimes simple arguments are made unnecessarily complicated. Sometimes people do this on purpose, to make themselves look smart. More often, people do this inadvertently, by assuming that, once they have understood something, their way is the only way. This is why, in maths, there is a difference between a proof and an elegant proof, and looking for simpler ways to prove known results is part of the job. Other disciplines (which shall remain unnamed but most readers can easily figure out) could learn a thing or two from that.