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The paper traces the pre-marginalist origins of supply functions, focusing specifically on the contributions of Hermann, Rau, and Mangoldt. Using algebra and geometry, they reinterpreted classical economic theory which had been formulated for a different theoretical context, thus discovering the modern concept of the supply function. Despite their shortcomings, these early contributions to mathematical economics contributed to the development of economics by challenging the classical approach and heralding neo-classical theory. While classical theory held that costs of production depended on highly heterogeneous underlying phenomena, Hermann’s formulas and Rau and Mangoldt’s diagrams propose instead a unifying and symmetric interpretation of the behavior of production costs. In this sense, they anticipated Marshall’s belief that one single law accounts for any shape of the supply curve.