Abstract

In this paper we study the mathematical object matrix and compare its historical and psychological origins. The literature on history of mathematics tells that this science started with the study of numbers and shapes, giving rise to the fields of arithmetic and geometry. The historical approach has been leading to an interpretation of algebraic structures as secondary concepts, derived from systems of equations representing numerical or geometrical constrains. Our epistemological view supports the argument that matrices originate from a especial form of tabulation, which had and still have a widespread use, appearing in different sciences and forms of expression. Originally, these tables are not numerical and became matrices when numbers were introduced in them. This view leads to the assumption that these algebraic structures are just as fundamental as numbers and figures. Therefore we can assume that algebra is one of the most fundamental domains of mathematics, forming a basic trilogy with the other two fields. This review gives rise to new interpretations in the physical realm, where observational languages are built a priori on suitable mathematical domains. It can show contrasting views between the historical approach and the epistemological view. Observational realism is our guiding epistemology.