In the 1880s Henri Poincaré did important work on the shape of the Earth regarded as a stably rotating mass of fluid. This led him into a correspondence with the younger Russian mathematician Liapunov, that revealed important differences in their attitudes to rigour in mathematics, and in what it meant for mechanical systems to be stable. In the years after 1900 Poincaré was also heavily involved in the direction of the French geophysical expedition to Peru to measure longitude, and when that concluded he became interested in the motion of the tides and ocean currents. This mixture of often highly innovative work and attention to his patriotic duty provides a revealing insight into the life and work of one of France’s leading mathematicians and scientists.