Whether bi-infinite geodesics exist has been a significant open problem in first- and last-passage percolation since the mid-1980s. A non-existence proof in the case of directed planar last-passage percolation with exponential weights was posted by Basu, Hoffman and Sly in November 2018. Their proof utilizes estimates from integrable probability. This talk describes an independent proof completed 10 months later that relies on couplings and control of geodesics through planarity and increment-stationary last-passage percolation. Joint work with M'arton Bal'azs and Ofer Busani (Bristol).