Paper Key : IRJ************392
Author: Prof Nilesh Avinash Joshi
Date Published: 03 Feb 2025
Abstract
Ancient philosophy has significantly influenced the development of modern mathematics, shaping its foundational concepts, logical structures, and abstract reasoning. Greek philosophers such as Pythagoras, Plato, and Aristotle introduced mathematical principles tied to metaphysical and logical thought, establishing the basis for deductive reasoning and formal proofs. The Pythagorean school emphasized numerical harmony and relationships, influencing number theory and geometry, while Platos theory of ideal forms laid the groundwork for abstract mathematical concepts. Aristotles logic provided a systematic approach to reasoning, later formalized in mathematical logic and set theory.Eastern philosophies, including Indian and Chinese traditions, also contributed to modern mathematical advancements. Indian mathematicians introduced the concept of zero and infinity, crucial to calculus and number theory, while Chinese mathematical thought emphasized algorithms and applied problem-solving techniques. The synthesis of these ancient philosophical ideas with modern formalism has led to the evolution of disciplines such as topology, algebra, and mathematical physics.This paper explores how ancient philosophical frameworks have shaped contemporary mathematical thought, demonstrating that mathematics is not merely a technical discipline but a field deeply rooted in logical and philosophical inquiry. Understanding these historical influences provides a richer appreciation of modern mathematical advancements and their conceptual depth
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