Since the late 1970s, the art of origami (paper folding) has been going through a renaissance, both in terms of technical complexity and artistic expression. Origami artists are now able to fold, from a single, uncut square, things which no one ever would have thought possible, and through this are able to achieve levels of realism and expression never seen before. Mathematics is largely to blame. A small group of mathematicians, physicists, and engineers have been discovering the theorems that govern how paper is folded. Much of this work has led to a deeper understanding of the paper folding process, which has granted artists greater paper folding prowess. This talk will survey the theorems behind flat origami (i.e., origami models that can be pressed in a book without crumpling) and describe (1) how they can be used in complex origami design, (2) how technology has assisted and met pitfalls in this field, and (3) how this, in turn, has found some interesting applications elsewhere in the sciences. The amount of material I will be able to present will depend entirely on how much time I have. But to summarize, I plan on presenting theorems and work of Maekawa, Kawasaki, Meguro, Lang, and myself (skipping most proofs), and give a rough outline of how this work is used in origami designs. This leads directly to Lang's TreeMaker algorithm, which allows basic complex origami design on a computer. This, in turn, branches into two interesting aspects: (1) how parts of Lang's algorithm turn out to have applications in the design of easily-collapsible airbags as well as collapsible materials for use in outer space, and (2) the apparent contradiction that while researchers have been able to model paper crumpling on computers, they have not been completely successful in modeling origami. (There are NP-completeness issues lurking here.) Of course, I will also have numerous pictures and models of super-complex origami which will easily drive home the fact that mathematics has led to increased artistry in the origami field of sculpture. In short, origami is a great example of the interconnectedness between mathematics and art. It also showcases the use of technology in artistic design, although many of the computational problems in modeling origami on a computer remain unsolved. Furthermore, surprising applications of origami design exist in engineering, adding yet another interdisciplinary aspect (in addition to the more obvious cultural ties to Japan) to origami math. Lastly, most mathematicians (and artists) are completely unaware of the interesting and beautiful work being done, both mathematically and artistically, in origami. Thus, including this talk in your session should attract a healthy crowd. A 20 minute talk would suffice to summarize all the main points quickly. Longer would be even better, of course. A computer projector and overhead projector would both be needed. For some examples of the level and style of origami I'm referring to here, see the photos of Satoshi Kamiya's work on my web page: http://web.merrimack.edu/~thull/kamiya/kamiya.html Brief info about the author: I have been practicing origami since I was 8 years old, have authored two origami instruction books, and for the past 12 years have been collecting information about and researching origami mathematics. Last year I organized a conference, the 3rd International Meeting of Origami Mathematics, Science, and Education, and the proceedings of this conference have just been published by A.K. Peters.