Is the House of Mathematics in Order?

Explores the possibility of insights from the ordering of mathematical knowledge as a whole.

[Parts: Next | Last | All] [Links: To-K | From-K | From-Kx ]

Introduction

This paper emerges from the concern that the world of mathematics may hold insights of critical relevance to wider society, but that these insights are effectively withheld because of the nature of that knowledge, the values and dynamics of mathematicians, and their preferences in ordering those insights.

The point is often made that mathematics has many highly specialized branches and few of the people associated with any particular one have any interest in other branches or in mathematics as a whole. Pure mathematicians are proud of the irrelevance of their discoveries to wider society -- although ironically it is also the case that it is the US Department of Defense that employs the majority of professional mathematicians in that country.

This paper is therefore necessarily a naive exploration of a vast terrain to discover whether it holds any insightful answers to questions that maybe of critical importance to wider society.

Implications related to this exploration have subsequently been explored separately in:

• Dynamics of Symmetry Group Theorizing: comprehension of psycho-social implication (2008)
• Towards a periodic organization of the Mathematics Subject Classification (2009)
• Periodic Pattern of Human Knowing: implication of the Periodic Table as metaphor of elementary order (2009)
  • Mathematical knowledge management
  • Missing "map" of mathematics: a self-reflexive "periodic table"?
  • Origin of mathematics and the periodic table -- in human cognition?