I'm not sure of the connection between nature and ID. Take for example the natural principle that central structures (e.g., nuclei, cells, etc) take prominence in the design strategy employed in the world. Is this a ID requirement? I don't think it is. I can imagine living in a world where there are very few central structures. Perhaps in that world the nature of that world is governed by de-centralized strategies (e.g., ring networks) and we would more likely see free electrons, free protons, and free neutrons all interacting in a big mesh to somehow produce higher structures (who also are governed by de-centralized structures).
The problem with saying that nature is mathematical is that a de-centralized governed universe could be just as mathematical as our universe, and if we lacked the math to describe it, just as long as there is some kind of order I'm sure the potential exists to create a mathematical language which would show how 'mathematical' that natural world happened to be.
Nature that is peculiar to our world is just that, it is the nature or extremely common behavior of our world. As it turns out, the extremely common behavior of our world is one that favors emergent structures that are akin to intelligence at work. In fact, it is so akin to it, that it even produces intelligence that works very similarly to it.
Perhaps it isn't that nature is being ID'd, rather being ID'd is, well, natural.