I know Major Macmahon conjectured the formula $$ \prod\_{m=1}^\infty \frac{1}{(1-q^m)^m}=1 + \sum\_{n=1}^\infty PL(n)q^n$$
but who was the first to prove it?



Who proved that the plane partition generating function is valid?
The answer is MacMahon himself, who proved this in his book *Combinatory Analysis* as a corollary of a more general theorem about plane partitions. See Sections IX and X.


There is some additional historical information in the Notes to Chapter 7 of Richard Stanley's book *Enumerative Combinatorics*, volume 2.


