AbstractConsider low-speed potential flow past a ship modelled as a semi-infinite two-dimensional body with constant draught. Is it possible to design the hull in such a way as to eliminate the waves produced downstream of the ship? In 1977, Vanden-Broeck & Tuck had conjectured that a single-cornered piecewise-linear hull will always generate a wake; in this paper, we show how recently developed tools in exponential asymptotics can be used to confirm this conjecture. In particular, we show how the formation of waves near a ship is a necessary consequence of singularities in the ship’s geometry (or its analytic continuation). Comprehensive numerical computations confirm the analytical predictions.