The historical context of the usage of mathematics in economics and some other related social sciences is briefly described. This usage is then emphasized in three specific topics: (1) the analysis of a competitive market, regarding in particular the existence of equilibrium and the relations between the concepts of equilibrium and of optimality; (2) in social choice theory, Arrow’s theorem, and results about the strategy-proofness of voting procedures; and (3) in game theory, focusing on cooperative games, the relations between the concepts of core and of competitive equilibrium, and an analysis of Shapley–Shubik voting power index in the case of the voting procedure used within the UN Security Council. The use of mathematics in economics has been questioned. Some responses to this questioning are provided. Finally, the thesis of the “indispensability of mathematics” is defended in the case of the social sciences.