Origami is an excellent hobby for mathematicians of all ages. Aside from the obvious geometric connections, origami helps mathematicians in many other areas related to the mathematical practice standards. A few of these are: precision, patience, listening and following directions carefully, perseverance, correcting mistakes and learning from them, helping others and accepting help from others.
I encourage my students to try some of the origami projects posted below. If you need some origami paper, just ask. I have plenty and I will be happy to give you some.