The sticking point is that patent law does not apply to natural laws. You cannot discover the law of gravity and own it. You cannot develop a new mathematical theorem and patent it. At least, that is the broad claim. Some exceptions exist.

First, with mathematics, as I showed, Penrose Tiles were patented in the US, UK, and Japan because Roger Penrose claimed that they could be used to make interesting patterns in floor tile. That converted his mathematical diversion into a practical invention.

A little before that, the first software patent was granted not on the code, but on the fact it created an array of gates and switches in computer hardware, so it was the hardware configuration that was patented.

From there, it gets crazy...

One standard for patentability is that the process must not be obvious to the skilled practitioner. (Dale Halling does not like the "obviousness" standard. I could agree but he would disagree with the conclusions I draw from that.) So, with software, with a million people banging out work in a new field of knowledge, what is known or knowable? An egregious example was the patenting of Screen X-or, which was known before it was claimed.

“Ever since Autodesk had to pay $25,000 to “license” a patent which claimed the invention of XOR-draw for screen cursors (the patent was filed years after everybody in computer graphics was already using that trick), at the risk of delaying or cancelling our Initial Public Offering in 1985, I've been convinced that software patents are not only a terrible idea, but one of the principal threats to the software industry. " --
http://www.fourmilab.ch/autofile/www/cha...

As it is, software is protected by copyright.

Well 9 Supreme Court justices just did.