Tension between Intuitive Infinitesimals and Formal Mathematical Analysis
Mikhail G. Katz, David Tall
TL;DR
This paper explores the historical and conceptual tension between intuitive infinitesimals and formal analysis, examining how mathematical thinking evolved and how visual intuition influenced axiomatic proof development.
Contribution
It provides a historical analysis linking intuitive infinitesimals with formal analysis and discusses their impact on mathematical cognition and proof methods.
Findings
Infinitesimal calculus influenced modern analysis development.
Visual and intuitive approaches shaped axiomatic proof evolution.
Historical perspectives reveal ongoing tension in mathematical foundations.
Abstract
We discuss the repercussions of the development of infinitesimal calculus into modern analysis, beginning with viewpoints expressed in the nineteenth and twentieth centuries and relating them to the natural cognitive development of mathematical thinking and imaginative visual interpretations of axiomatic proof.
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