<< But if we trust in Plato and Kant as to that ideas exist "outside, before and independently from a human-being", then all mathematical achievements are certainly scientific discoveries :-) >>
<< From this point of view, there is a quite interesting question: whether G.Cantor was an inventor or a discoverer of his famous diagonal argument and his minimal transfinite integer "OMEGA"? :-) >>
Since you brought up Kant in this connection, I will seize the occasion to ask any philosophically minded participants in this virtual get-together whether they interpret Kant to have held that mathematical ideas exist independently of humans, in the manner which Plato did. I take him to have proposed something more like this: Humans are so constituted that they must understand the world in certain restrictive ways. He used as an example a proposed necessity for humans to interpret space using a euclidean geometry, presumably including its notorious parallel postulate. Legions of commenters thereafter have derogated old Kant for having missed the boat on non-euclidean geometries, which have turned out, it appears, to have some relevance in interpreting space (and time), at least on large enough scales. (This has happened since Einstein through us a curve -- pardon me, Alexander, if this attempt at humor doesn't get through to you in Russia, since it's based on the sport of American baseball.)
My own belief, of some standing, is that while Kant chose an unfortunate example to illustrate his theories of the transcendental aesthetic, and how people necessarily perceive space and time and such things, his arguments can still be cogently taken to apply to such propositions as: humans necessarily perceive and conceive of space in terms of _some_ geometry_ our brains, minds, or whatever, being the way they are.
Somehow I'm reminded of Rainer Rilke's fantasy (in his prose piece Malte Laurid Brigge) of the fellow who had to take to his bed permanently because he became aware of our earth's motion around our sun, and it made him dizzy.