Description: The art of paper folding has existed for over fifteen centuries, yet an astonishing 98 percent of new origami designs have been developed within the past fifty years and with rapidly increasing complexity. This modern day origami renaissance has been closely connected to advances in science, technology, and computational mathematics combined with artistic intuition and creativity. How can mathematical methods be applied to develop awesome, creative origami with a purpose? The practice of origami sekkei, or technical origami design, overthrows the traditional freestyle folding process and instead turns to a carefully engineered theoretical model. Students will explore contributions from the pioneers of modern origami, ranging from the fantastically intricate work of NASA physicist Robert J. Lang to the elegant simplicity of origami grandmaster Kiyo Yoshizawa. The course will cover mathematical techniques such as base folding, grafting, circle packing, tree theory, and box pleating through hands-on, interactive exercises. Starting with the very basics, this course is designed to be approachable to beginners in all aspects but also offers topics that may be of additional interest for those in specialized fields of study. Overall, we hope to unfold the mysteries of origami and turn the page to reveal some of the most cutting-edge work in the field.