The intersections between origami, mathematics, and science occur at many levels and include many fields of the latter. We can group these intersections into roughly three categories:
These divisions are a bit arbitrary, of course; one genre blends into another. Origami math defines the "ground rules" for computational origami's goal of solving origami design problems (and quantifying their difficulty). The results of computational origami, in turn, can be (and have been) pressed into service to solve technological problems ranging from consumer products to the space program.
In the sections linked above, you'll find examples of all three of these intersecting genres. Feel free to explore; there's no particular order.
Since 1989, there have been several highly successful international scientific conferences exploring the interactions between origami, mathematics, science, and (since 2001) education. The conferences take place at irregular intervals—basically, whenever a general chair and sponsoring organization decide that the time has come for the next. Click here for further information about these meetings.