What makes you think Fischer was the greatest? I mean, he maybe was a Picasso of the chess. Maybe. It because supposedly he has reached the top, but he has stopped before shows his Guernica to the world.
It is a problematic question. But if I needed to answer, it would be Kasparov; although I do not have any decisive argument for that.
Who is (or was) the all time greatest chess player? I think it was Fischer