Duality theorems and dual variables have played an important role for the development of linear and nonlinear programming – and have also directly and indirectly given raise to discussions of priority, making the question of multiple discoveries a recurrent theme in the history of linear and nonlinear programming. It has been claimed that duality was first discovered by the Russian mathematician Leonid Kantorovich. Others say that it is due to John von Neumann, whereas Albert Tucker at some point felt it should be credited to the work of him, Harold Kuhn and David Gale. Duality also played a significant role for the development in 1950 of the so-called Kuhn-Tucker theorem that led to linear programming’s extension into nonlinear programming. Later it turned out that similar results had been published earlier by William Karush in 1939 and Fritz John in 1948. We will discuss whether and if so in what sense duality and the Kuhn-Tucker theorem can be seen as multiple discoveries. The discussion will be based on ideas of multiple discoveries in literature by Merton, Patinkin and Cozzen from sociology of science. We will trace the occurrence of duality in the history of linear programming and discuss its significance for the development of the Kuhn-Tucker theorem and the emergence of Fenchel’s duality result in nonlinear programming and its influence on the further development of convex analysis. The context of the Second World War and the organization of science support in the post war period in the USA will be taken into account.