The Gauge/Bethe correspondence claims an equivalence between
(1) the vacuum equation of supersymmetric gauge theories with four
supercharges and (2) the Bethe Ansatz equations in quantum integrable
models. While many papers have been written about this subject in
physics and mathematics, it is not yet known how general the
correspondence should hold---at least that has been my opinion for the
past decades. In this talk, I will discuss the general applicability
of the Gauge/Bethe correspondence using the representations of the
quiver BPS algebras, following my research arXiv:2206.13340 [hep-th]
with Dimitry Galakhov and Wei Li.