In the 1730s two expeditions set out from Paris on extraordinary journeys, the first to Peru, the second towards the Arctic Circle. Their primary objectives were scientific: to determine the Earth's precise shape. Although such information had consequences for navigation and cartography, the motivation was not simply utilitarian. Rather it was part of an intellectual revolution in which advances in mathematics paralleled philosophical strife, and reputations of the living and the dead stood to be elevated or destroyed. In this study, the 'Figure of the Earth' controversy is for the first time comprehensively explored in all its several dimensions.