I am writing a literature review and I have a couple of questions which amount to "Who did what when?" about the work done in partition theory in the 1900's.

1)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?

2)Who was the first to develop the asymptotic formulae for the distinct parts version of $p(n)?$

Bonus points if someone has a concise chronology of the major results in partition theory in the 20th century.

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?