TITLE: Is there any difference between a math invention and a math discovery?
QUESTION [13 upvotes]: From wikipekia:

The calculus controversy was an argument between 17th-century
  mathematicians Isaac Newton and Gottfried Leibniz (begun or fomented
  in part by their disciples and associates – see Development of the
  quarrel below) over who had first invented calculus. It is a question
  that had been the cause of a major intellectual controversy over who
  first discovered calculus, one that began simmering in 1699 and broke
  out in full force in 1711.

I'm just curious if in the field of mathematics it means one thing to invent and another to discover or if they go totally hand in hand.

REPLY [5 votes]: Connes, the Fields medalist,  and Changeux, a celebrated neurophysiologist, have had an interesting discussion on that subject.
It is this book.
And here is paper commenting on the book.