Again, I think you are mixing different levels of abstraction here.
Let's, for simplicity sake, take an extremely simple algorithm as an example: 1+1=2
Person A writes it down as a purely mathematical description, finds out he can draw nice conclusions from it and generally enjoys it in the sphere of pure math. It was created, no doubt.
Person B does not ever spot "1+1=2" anywhere in nature. What person A spots is that if he has one stone in his hand, and he adds a second one, he now has two stones in his hand. That is the natural process. "1+1=2" is not that process, but an abstract description of the process. If person B were to abstract (that is the creative part) and write it down, he would still be creating the 1+1=2 formula.
The difference between these two persons is not that one created and the other discovered. The difference is how their creative process got started.
You discover a new species of snake on your jungle trip. You create a name for it. Same thing with math, really.