We discuss the proof given by M. Haiman of the Macdonald positivity conjecture obtained via the solution to the $n!-$conjecture of Garsia and Haiman. This is obtained from the following remarkable theorem : the Hilbert scheme of $n-$tuples of points in the plane is equal to the $G-$Hilbert scheme of Ito and Nakamura for the action of the symmetric group on the space of such $n-$tuples.