[cma]

Aren't physical machines just math too? We can simulate them on computers, clearly just math, but maybe can't fully mathematically describe the non-idealized versions we produce in reality. Why does that level of completeness of description need to serve as such a sharp line on patentability?

[jandrewrogers]

Yes, and there are theorems to that effect. There is no distinction between "software" and "hardware" in mathematics.