An Analytical Perspective On The Nature And Scope Of Mathematics
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Abstract
Mathematics is one of the most substantial accomplishments of human thought both as an abstract axiomatic science and as an art of human creation as well as the universal language to explain natural and social phenomena. The paper is an analytic investigation on nature and extent of mathematics in the form of formal definitions, axiomatic foundations, representative theorems with proofs, and illustrative problem solutions. Platonism, Formalism, Logicism and Constructivism are the philosophical aspects of mathematics that are critically discussed to explain the ontological and epistemological position of mathematics knowledge. Moreover, the growing range of mathematics in both the pure theory and the applied sciences, computational technologies, social systems, and life sciences, are explored systematically. Through the combination of the logical rigor and practical modeling, this paper shows that mathematics is more than simple numerical calculations: it is a framework that can be used to reason, innovate and solve problems across disciplinary boundaries. The paper has concluded with the finding that mathematics is not only eternal in the truths but dynamic in its uses and that it cannot be done away with in the process of science and development of society.
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