Ontological and Epistemological Disparities between Abstract and Applied Mathematics

This study explores the distinction between mathematics as an abstract entity and its applications in the real world, as well as the implications of this distinction for the development of contemporary science. Abstract mathematics is understood as a reality that exists independently of the physical world, while applied mathematics is used to solve concrete problems across various disciplines, such as physics, biology, and technology. By examining key philosophical approaches, including Platonism, Formalism, and Constructivism, this research delves into the ontological status of mathematics and how each perspective interprets the relationship between mathematics and reality. The methodology employed involves an analysis of current scientific and philosophical literature to assess the role of mathematics in modeling and predicting real-world phenomena. The findings reveal that while abstract mathematics provides a robust theoretical foundation, its application in science is often constrained by practical limitations, such as uncertainties in data and computational constraints. The conclusion drawn is that abstract and applied mathematics differ not only in their nature and objectives but also in the ways they interact with the real world. This distinction has significant implications for how we understand and advance science and technology in the modern era.