For more than ten years, Léon Walras tried in vain to solve the problems of how to derive individual demand curves taking return curves of two individuals as a starting point. Without that key element, the architecture of his theory of general competitive equilibrium was incomplete. At the end of 1872, A. P. Piccard sent a two page memorandum to Walras in which he solved the problem that had stopped the work of the pioneer of general equilibrium. From this procedure, some of the most important results of microeconomics are derived: the transformation of a commodity into another by means of exchange, the marginal rate of substitution and the ratio of prices to the marginal returns of commodities. But even more important, the solution of Piccard became the central hypothesis of the neoclassical theory about the behavior of economic agents: its definition as inexorable return maximizers. This article analyzes the Piccard-Walras relation and from this two basic points to understand the development of incipient mathematical economy are posed: first the turn in language use brought about by Walras was even more radical than he thought, since it implied that mathematical problems should be posed in a mathematical way, creating appropriate room for its formulation and making use of heuristic strategies from mathematics; secondly, and following the later Wittgenstein, if mathematics is a language game the analogies from its field are neither found nor recognized, but constructed.