*(Part I of this post is here)*

Let denote the partition function, which describes the number of ways to write as a sum of positive integers, ignoring order. In 1918 Hardy and Ramanujan proved that is given asymptotically by

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This is a major plot point in the new Ramanujan movie, where Ramanujan conjectures this result and MacMahon challenges him by agreeing to compute and comparing it to what this approximation gives. In this post I’d like to describe how one might go about conjecturing this result up to a multiplicative constant; proving it is much harder.