of focus here shall be the debut of the Rogers–Ramanujan identities on the mathematical physics stage, in particular their appearance in the hard hexagon model in a paper by Baxter [@B81] in 1981. In this setting the Rogers–Ramanujan identities can be viewed as two different evaluations of the generating function of certain paths which are coined bosonic and fermionic evaluations. Details are discussed in section \[sec:HHM\]. As it turns out the relation between the Rogers–Ramanujan identities and the hard hexagon model is only part of a much bigger picture. In terms of representation theory, the paths that occur in the hard hexagon model are elements of tensor products of crystals associated with the affine Lie algebra $\hat{\mathfrak{sl}}_2$. Crystal bases were introduced by Kashiwara [@K1; @K2] and roughly speaking are bases of representations of quantum universal enveloping algebras $U_q({\mathfrak{g}})$ as the parameter $q$ (not to be confused with the $q$ in the $q$-series!) tends to zero. Here ${\mathfrak{g}}$ is any symmetrizable Kac–Moody algebra. As in the Rogers–Ramanujan case, there are two different ways to evaluate generating functions of tensor products of crystals, thereby giving rise to $q$-identities. Hence crystal base theory provides a natural framework for $q$-identities. Crystal bases, path spaces 