Roger Penrose – Is Mathematics Invented or Discovered? [video]
The question assumes that there is a difference between invention and discovery.  There isn't.  Invention is a kind of discovery.  The apparent distinction arises from our separation of physical and mental processes.  But this is a purely artificial separation, a human conceit, because (unless you're a dualist) mental processes <i>are</i> physical processes.  Specifically, mental processes are <i>computational</i> processes, which are physical.  So it's not surprising that the structure of the physical world should be reflected back on itself in the structure of mental processes.  It's universal Turing machines all the way down.