What is not patentable subject matter?

You cannot patent naturally occurring things, although you can patent man-made things. So while you could not patent the leaves of different plants, you could patent a pharmaceutical made out of those leaves (as well as the process of making it).

Generally you cannot patent living things, although you can patent certain live matter, such as genetically engineered animals, plants, etc., or the process of extracting a natural product.

You cannot patent laws of nature, mathematical formulas and abstract ideas. Thus, Isaac Newton could not have received a patent for discovery the connection between force and mass (one of those equations you learned in basic physics, F = ma). However, you might be able to patent an application of a mathematical formula or a law of nature, if it otherwise meets the patent requirements.

Finally, you cannot patent a simple idea or suggestion. Rather, the invention must be something real and concrete. So while you can patent a machine, you can not obtain a patent simply for the idea of some machine.