From the YouTube description:
Origami, the art of paper folding, has been practiced in Japan and all over the world for centuries. The past decade, however, has witnessed a surge of interest in using origami for science. Applications in robotics, airbag design, deployment of space structures, and even medicine and bioengineering are appearing in the popular science press. Videos of origami robots folding themselves up and walking away or performing tasks have gone viral in recent years. But if the art of paper folding is so old, why has there been an increase in origami applications now? One answer is because of mathematics. Advances in our understanding of how folding processes work has arisen due to success in modeling origami mathematically. In this presentation we will explore why origami lends itself to mathematical study and see some of the math that has allowed applications to become so fruitful.