The ‘Core’ Concept and the Mathematical Mind: Part I

Abstract

Pure mathematics is often seen as an ‘inverted pyramid’, in which algebra and analysis stand at the focal point, without which students could not possibly have a firm grounding for graduate studies. This paper examines a variety of evidence from brain studies of mathematical cognition, from mathematics in early child development, from studies of the gatherer-hunter mind, from a variety of puzzles, games and other human activities, from theories emerging from physical cosmology, and from burgeoning mathematical resources on the internet that suggest, to the contrary, that mathematics is a cultural language more akin to a maze than a focally-based hierarchy; that topology, geometry and dynamics are fundamental to the human mathematical mind; and that an exclusive focus on algebra and analysis may rather explain an increasing rift between modern mathematics and the ‘real world’ of the human population.

Part I of this article include:

1: Introduction

2: Landmarks from Early Childhood and the Noosphere

3: The ε-δ Game, Topology and Two Small Clouds in Classical Analysis