[azakai]

Yes, the math he shows there from Apple's patent looks very obvious. Anyone looking to implement detection of multiple touches on a touchscreen would end up with basically those equations, or others that are functionally equivalent to them.

I want to give TFA's author more credit, but I worry that he is just copy-pasting some math, in hopes that math will just look incomprehensible and hence novel. But that a patent has some equations in it doesn't make it novel. This math certainly isn't.

If you want an example of a patent that actually does have nontrivial math, then the MP3 patents for example qualify. (Whether you think even that should be patentable is of course still an open question - but at least the math in the MP3 patents isn't obvious.)