The decline of mixed mathematics and the rise of applied mathematics

Abstract

This article aims to outline some elements of the historical process of what were the possible situations that triggered the decline that culminated in the disappearance of mixed mathematics, and consequently, contributed to the emergence and rise of applied mathematics. Through the historical sources of this qualitative research, we provide a brief explanation of how mixed mathematics were conceived through the mathematical classifications of Adrian Van Roomen (1561-1615), Francis Bacon (1561-1626), Diderot (1713-1784) and Jean le Rond d'Alembert (1717- 1783). In the course of the historical investigation presented here, we verified that the physico-mathematics sciences were introduced as a way of getting around the philosophical barriers imposed by metaphysics regarding the approach to topics in the physical world. We conclude that - although there is no final landmark for mixed mathematics and a starting point for applied mathematics - the criticisms formulated by the philosopher Immanuel Kant (1724-1804) in relation to pure knowledge, the creation of the field of Rational Mechanics and the emergence of mathematics applied, may have contributed to the decline of mixed mathematics.

Keywords:
Mixed mathematics; Applied mathematics; Pure mathematics; Philosophy of mathematics; History of mathematics