Oral tradition about the thirteenth-century Sun Temple at Konark, Odisha, says that itsimage of the Sun God once floated in the air, held up by a great lodestone set at the top of the tower. The same tradition says this lodestone deflected the compasses of passing ships until sailors removed it. We first review what the historical record does and does not say. The levitation story is a nineteenth-century tradition. It belongs to a long family of similar tales, from Pliny’s unfinished iron statue of Arsinoe to al-Qazwini’s suspended idol of Somnath. We then ask the physical question posed by the first author: what arrangement of magnets could make such a statue float stably? Earnshaw’s theorem, extended by Braunbek, forbids stable levitation by any static arrangement of permanent magnets, soft iron and gravity. We prove the relevant forms of the theorem, including the sum rule kx + ky + kz = 0 for the stiffnesses, and the extension to orientation and to induced magnetism.Following the hint "what gives stability to a boat?", we analyse hydrostatic stability:buoyancy, heave stiffness ρgAw and the metacentre. We show that buoyancy evades Earnshaw because it is a contact force exerted by matter, not a field in free space. The magneticanalogue is a magnetic boat. Lift comes from a magnet overhead, acting at the statue’s crown,above a low centre of gravity; this plays the role of the metacentre. A pair of diamagneticplates (graphite or bismuth) plays the role of the water and supplies the missing verticalstiffness. We derive the complete set of stability conditions, evaluate them for lodestone, ferrite, samarium—cobalt and neodymium—iron—boron magnets, and give a worked design. A neodymium arrangement holds a 10 kg statue 15 cm below a 20 cm magnet, with graphiteplates at gaps of about 12 mm. Lodestones fall short of the required forces by two to sixorders of magnitude. A 52-tonne lodestone would also have deflected a compass by less thanabout 10−3 degree at one kilometre, even if fully magnetised, so the sailors’ story cannotbe literally true. Finally we survey the dynamic loopholes to Earnshaw: spin stabilisation,feedback, superconductivity and oscillating fields.