We point out that the half-filled Peierls insulator, celebrated for its soliton excitations andits application to trans(polyacetylene), is an excitonic insulator in which collectively boundelectron–hole pair excitations (excitons) are mixed into the ground state. Unlike the boundelectron pairs of the Bardeen–Cooper–Schrieffer (BCS) superconductor, however, the excitonicpairs can be photoionized leading to the direct observation of the excitonic energy gap2Δ in the optical conductivity. A deeper understanding is provided of the discovery of Kuper in1955 of a BCS-like gap equation describing the thermodynamic properties of the Fröhlich(1954) one-dimensional charge-density-wave state.