Was mathematics invented or discovered?
To be more precise, does mathematics describe the physical world or does it describe a mental representation of the physical world? If the latter is true, then an empirical science, physics namely, tries to describe mental phenomena via what is believed to be the physical world and its behavior?
Thanks for the suggestions. Actually, my question refers to reality or the physical world, and not to mathematics. Whether mathematics was invented or not is a different question, I believe. Anyway, I think that my question is most likely unanswerable. ... That mathematics is real and that it is capable of describing our understanding of things in a systematic and very efficient way, for me is out of question. But, consider the following situation: there is a huge sculpture in the middle of a room. There is also a wall before the sculpture. Johnny has never seen a sculpture and he has been told that sculptures are solid and white; that's all he knows about sculptures. So, Johnny stands in front of the wall and thinks that it is a sculpture, as the wall is solid and white. For the sake of this stupid argument, let's assume that Johnny is a prolific mathematician. As he contemplates the wall which he believes is a sculpture, he starts to generate a number of very accurate mathematical formulations that indeed describe the reality of the wall. Then, Johnny is describing a reality (the mathematics he produces describe a real thing), but they fail to describe what is being intended in this case, the sculpture. In this way, if one substitutes the wall for mental representation and the sculpture for the physical world, then (at this point I am feeling quite ashamed) does the conclusion stated above hold? I really hope this was easy to understand; I surely tried.