I think you misunderstood my comment. My point wasn't to justify patenting sorting (that would be stupid). It was just an example to clearly show the difference

I think you misunderstood my comment. My point wasn't to justify patenting sorting (that would be stupid). It was just an example to clearly show the difference between an algorithm and an application of an algorithm. In the case of sorting (replace with arbitrary algorithm X if you prefer), its discovering a unique and non obvious mapping from the mathematical entities that are manipulated to the real world that is patentable, rather than the algorithm itself. The point I'm making is simply that patenting an application of an algorithm is fundamentally different than patenting the algorithm itself, so claiming software patents are invalid "because math" is missing the point.