The Gauge/Bethe correspondence of Nekrasov and Shatashvili relates the spectrum of integrable spin chains to the ground states of supersymmetric gauge theories. Up to now, this correspondence has been an observation; the underlying reason for its existence remaining elusive. We argue here that geometrical representation theory is the mathematical foundation of the Gauge/Bethe correspondence, and it provides a framework to study families of gauge theories in a unified way.