in 1831, goldschmidt wrote a mathematical treatise in latin, "determinatio superficiei minimae rotatione curvae data duo puncta jungentis circa datum axem ortae" ("determination of the surface-minimal rotation curve given two joined points about a given axis of origin"). the paper dealt with the problem in the calculus of variations of determining the minimal surface of revolution, the surface of revolution of the planar curve between two given points which minimizes surface area. solutions to the problem exist which are not continuous; such discontinuous solutions are known as goldschmidt solutions in honor of goldschmidt's discovery of them.