>Imagine that Euclid's algorithm was patented? Or Pythagoras theorem? Or the definition of exterior derivative? Or the expression of a function as Fourier serie

>Imagine that Euclid's algorithm was patented? Or Pythagoras theorem? Or the definition of exterior derivative? Or the expression of a function as Fourier series? This is an interesting point and I'm not sure it cuts the way you want it to. The world had to wait thousands of years for each of these algorithms to be developed. There are broad reasons for this, but one of them was probably the fact that nobody had any incentive to develop them. Mankind literally had to wait around for some random nerd to come up with these in his spare time. Now imagine that they were patentable and exploitable for money (for 20 years). Perhaps they would have been developed centuries or millennia earlier. You would have teams of mathematicians from 1000BC onward, working to try to make money inventing theorems and machines and medicines. 20 years under patent seems like a small cost to pay to have something invented possibly thousands of years earlier (or, not kept under trade secret, as e.g. Damascus steel was).