The nuance with software is that we made up the system in which all of these programs are put together. Just like in math, we made up the constructs and rules

The nuance with software is that we made up the system in which all of these programs are put together. Just like in math, we made up the constructs and rules that define what an algorithm or a theorem or a function can be. Because there is a human-defined limited scope of what even constitutes a valid construct (i.e. an "upper limit" of novelty - "this is everything mathematics can do"), anything that exists within this sandbox is therefore less novel. We establish the baseline novelty of the entirety of mathematics as "really powerful, and world changing - and too important to the common good to lock behind a patent." So if that is the upper limit, no individual piece of it can be more novel. The patent office displays stunning clarity in correctly determining that therefore, any particular instance of maths cannot be patented. Their failure to apply this same reasoning to software (which is, and always will be, reducible to math) baffles me.