You say that discovery discovers something pre-existing (in the world) whereas inventor comes up with a new idea. But, don't you discover the ideas?
As I understand, there is an abstract world of ideas, where all abstract notions, i.e. ideas, live in. You just discover one or another. They usually tell you how to get from A to B in an optimal way. One way is bad, another is good. And what you do when solve a problem, you find those ways. Mathematicians know very well that solutions are not arbitrary. They exist before you discover them (nobody needs arbitrary solutions as nobody needs garbage). Is desired solution a discovery or an invention? Why do people, particularly academists, insist that there is a distinction between invention and discovery, once you realize that inventors just discover the ideas from the ideal world of ideas/solutions?