Does the use of mathematics in economics have limits?

Abstract

Mathematics has played a decisive role in the development of thought, particularly in the field of economics. Over the last few decades, it has become an indispensable tool for constructing theoretical models capable of explaining increasingly complex economic relationships. However, it is logical to exercise caution even while appreciating abstract theories. Sophisticated mathematical models should not be overused, as they can sometimes lead to a “technical escape from reality” or propagate a distorted view of the economy. The connection between mathematics and economics lies not so much in whether specific mathematical results have direct analogs in economic science, but rather in the fundamental similarity of the methodologies used by mathematicians and theoretical economists to address their respective problems.

In this work, after an introduction, we take a brief historical journey through mathematics and its relationship with other sciences. We then focus on its application to the development of economic science. Finally, we highlight certain mathematical theories that, due to their characteristics, can help address current economic challenges.