Here is a post by Ken Liu with some really fabulous pictures, so I strongly encourage you to click through: The Magic and Mathematics of Paper-Folding.
The origamist-mathematician may be unique in exploring a contemporary branch of mathematics that is as tangible and physical as the geometry of the ancient Greeks. As anyone who has folded a paper crane knows, there is a unique pleasure in working with a flat sheet of paper and through folding, creasing, tucking, and other manipulation, transforming it into something quite magical. The material, at once pliant and rigid, allows the mind to reason with abstract geometry in a way that cannot be replicated through other means.
I’m willing to believe it, given the origami sea turtle, dragon, eagle, horse, katydid, and … get this … T. rex skeleton.
A skeleton. An origami skeleton. I wouldn’t have believed it, honestly.
I admit I skimmed lightly past the math in the post. But wow, those pictures.