The Future of Mathematics in Economics: A Philosophically Grounded Proposal Ricardo Crespo 1 • Fernando Tohme ´ 2 Ó Springer Science+Business Media Dordrecht 2016 Abstract The use of mathematics in economics has been widely discussed. The philo- sophical discussion on what mathematics is remains unsettled on why it can be applied to the study of the real world. We propose to get back to some philosophical conceptions that lead to a language-like role for the mathematical analysis of economic phenomena and present some problems of interest that can be better examined in this light. Category theory provides the appropriate tools for these analytical approach. Keywords Foundations of mathematics Á Universals in singular objects Á Mathematical economics Á Category theory Á Circularity Á Data 1 Introduction The use of mathematics in economics is a debated topic. Numerous voices claim that economics has become excessively mathematical in its formulation. Other, also numerous, voices not only defend but strongly argue for using and refining the mathematical tools applied to economics. The first group, say of ‘‘contrarians’’, sustains that economics, due to its mathematical formalization, has become an abstract discipline detached from reality, or at the very best only able to show an oversimplified picture of facts. The ‘‘partisans’’ maintain, instead, that mathematics provides the right language to express real-world relations and the tools to reason correctly about them. These defenders of the & Ricardo Crespo RCrespo@iae.edu.ar Fernando Tohme ´ ftohme@criba.edu.ar 1 IAE-Universidad Austral and CONICET, Mariano Acosta s/n, 1630 Pilar, Argentina 2 INMABB (CONICET) and Universidad Nacional del Sur, 12 de Octubre y San Juan, 8000 Bahı ´a Blanca, Argentina 123 Found Sci DOI 10.1007/s10699-016-9492-9