[mejutoco]

> We discover an existing thing.

This is hiding the assumption in plain sight in a different form. The question then would be: was x an existing thing that we "uncovered"/discovered (it has merely hidden) or we created it by thinking it into existence?

At least in terms of Mathematics, I do not think there is an objective answer for this question.

The definitions you provided are, IMO, just moving the problem to further concepts, that are also ill-defined. "Discovery mainly a learning process, Invention mainly a creative process", could mean almost anything. Also, as a rigorous definition, "mainly" does not cut it. It needs to be 100%.

Instead of pretending I know it is my opinion to accept they are merely two ways of looking at the same thing. At least, this is my position for now, until a proper argument emerges.

P.S. I see it as arguing which of 0.5 or 1/2 is the "true" number.