I've heard the discovery vs. invention argument, and there is something too it, but personally, I'm still not clear on how to distinguish between invention and

I've heard the discovery vs. invention argument, and there is something too it, but personally, I'm still not clear on how to distinguish between invention and discovery. Wasn't steel a discovery, elements, or quantum theory? Music and poetry are covered by copyright, currently. But the same problem exists there and Larry Lessig has done a lot to protect culture in an environment of copyright litigation. Re: Mathematics and formulas. A lot of the discoveries or inventions in mathematics are patented. Three dimensional protein folding is a huge industry in pharmaceuticals and math is almost 100% of that knowledge. It's applied math, but nonetheless, still patentable mathematics and a lot of it too. I think one differentiator here is that the multi-touch and the one click amazon patent as another example are something that seems obvious to try to achieve given the current environment. There are other ways as well, like a space elevator or gloves to help protect astronauts in space. Is math a fact? I don't know if facts can be patented or copyrighted, though collections of facts surely can.