Mathematical equations representing (approximate) solutions to physics problems are patentable, then? Let's turn the clocks back to 1900 and figure out where we'd be technologically if every such "invention" had a 20-year period of exclusivity.
No, the application of those equations to practical problems is patentable. A physics problem is not necessarily practical (2 frictionless spheres in a vacuum are rolling towards each other...), but practical mechanical problems necessarily have a physical aspect and frequently rely on results of solving mathematical formulae. A patent on a mechanical solution may very well include the solution of such equations, and always have. Funny, doesn't look to me like the mechanical industry is stuck in the 1700s.
That patent is the sort of thing you're tasked with building in a mech-e class, or as an abstract problem in a physics class. If it's patentable, then one could say that the purpose of physics and engineering training is to build things, patent them, and live off of the royalties, rather than to create products people want to buy, competing in an open market.
The premise of your argument relies on the vague notion of what's a "practical" problem and what's not. I don't think that's any more tenable than any other defense of the current patent system I've ever seen. It's all vague, and exchanges like this are pushing me to a more extreme position that all patents are bogus, rather than granting that some "math" patents are connected to specific practical problems and thus patentable.
