The "software is mathematics" argument has a few flaws:
1) It is reductio ad absurdum, like saying "machines are metals". It is not the naturally occurring metals that are patentable in physical inventions, it is how you configure and use them. Similarly it's not the mathematics that is patentable, it is the application thereof to a practical problem.
2) More importantly, it misunderstands what abstract math is from a legal perspective. People will invoke the Church-Turing thesis and several related theorems to prove that software being executed is math, but they miss the point.
An abstraction, by definition, cannot affect or effect anything in the real world. An idea in your head is abstract. The moment you act on it in the physical world, it is real. Similarly, if you can run some piece of software and get useful, practical, real world results, it is not abstract.
1) It is reductio ad absurdum, like saying "machines are metals". It is not the naturally occurring metals that are patentable in physical inventions, it is how you configure and use them. Similarly it's not the mathematics that is patentable, it is the application thereof to a practical problem.
2) More importantly, it misunderstands what abstract math is from a legal perspective. People will invoke the Church-Turing thesis and several related theorems to prove that software being executed is math, but they miss the point.
An abstraction, by definition, cannot affect or effect anything in the real world. An idea in your head is abstract. The moment you act on it in the physical world, it is real. Similarly, if you can run some piece of software and get useful, practical, real world results, it is not abstract.