# Elementary proof of Ramanujan's “most beautiful identity”

Ramanujan presented many identities, Hardy chose one which for him represented the best of Ramanujan. There are many proofs for this identity.

(for example, H. H. Chan’s proof, M. Hirschhorn's proof...)

Is there an elementary proof for Ramanujan's "most beautiful" identity?

$$\displaystyle{\sum_{n=0}^\infty p(5n+4)q^n}=5\frac{(q^5;q^5)^5_\infty}{(q;q)^6_\infty}$$ for $|q|<1$, where $p(n)$ is the partition function, and $(a; q)_\infty := \prod_{n \geq 0} (1 - a q^n)$.