Reflections of Mathematical Thought: Contributions ofCore Mathematics to Its Own Advancement

Author: Nupur Sinha

DOI Link: https://doi.org/10.70798/Bijmrd/03060022

Abstract: Mathematics has historically functioned not only as a language for the sciences but also as a self-reflective discipline capable of transforming itself. This article explores how core areas of mathematics—arithmetic, algebra, geometry, calculus, logic, and number theory—have each contributed fundamentally to the advancement of mathematics itself. Through an interdisciplinary review of mathematical developments from antiquity to the digital age, this study underscores how mathematics, by scrutinizing its own foundations, revising its axioms, and expanding its structures, has evolved dynamically. The reflections of mathematical thought are evident in paradigm shifts such as the formalization of calculus, the invention of non-Euclidean geometry, Gödel’s incompleteness theorems, and the abstraction in modern algebra. These self-referential advancements exemplify mathematics as an organic and recursive intellectual pursuit.

Keywords: Mathematics—Arithmetic, Algebra, Geometry, Calculus, Logic, Number Theory

Page No: 208-212