Tension between Intuitive Infinitesimals and Formal Mathematical Analysis
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2011
- DOI:
- 10.48550/arXiv.1110.5747
- arXiv:
- arXiv:1110.5747
- Bibcode:
- 2011arXiv1110.5747K
- Keywords:
-
- Mathematics - History and Overview;
- Mathematics - Logic;
- 01A85;
- 26E35;
- 03A05;
- 97A20;
- 97C30
- E-Print:
- 19 pages, 5 figures, Chapter in: Bharath Sriraman, Editor. Crossroads in the History of Mathematics and Mathematics Education. The Montana Mathematics Enthusiast Monographs in Mathematics Education 12, Information Age Publishing, Inc., Charlotte, NC, 2011. See http://www.infoagepub.com/products/Crossroads-in-the-History-of-Mathematics