Understanding Mega-paradigms in the History of Western Thought, Euro-centrism, Indian Mathematical Proofs and Gödel's Incompleteness Theorems

Abstract

This paper explains the evolution of western thought through three major paradigms (pre-modern, modern, and post-modern) and their profound implications for knowledge, education, and mathematical philosophy. The pre-modern paradigm emphasized cosmic harmony and essentialist truths, while the modern era ushered in a mechanistic and empirical worldview. The post-modern shift, influenced by quantum physics and Gödel’s incompleteness theorems, embraces uncertainty, contextuality, and socially constructed realities. Within this intellectual framework, the traditional Eurocentric narrative of mathematical history is critically examined. Contrary to the dominant view that centers Greek and European contributions, the paper highlights the significant advancements made by Indian mathematicians, particularly those from the Kerala school, who developed foundational ideas in calculus and infinite series long before similar European discoveries. Their approach, rooted in intuitive reasoning and demonstrative methods (upapattis), contrasts with the formal deductive traditions of the West. Gödel’s incompleteness theorems serve as a pivotal point in the discourse, revealing intrinsic limits within formal mathematical systems and challenging the absolutist belief in complete and consistent foundations. Together, these threads present a more inclusive and philosophically nuanced understanding of mathematics as a dynamic, culturally shaped, and epistemologically contested field.