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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 http://jcer.com/index.php/jcj/article/view/202

The ‘Core’ Concept and the Mathematical Mind: Part II (by Chris King)

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 II of this article includes: 4: Puzzles and Games as an Expression of Human Mathematical Imagination; 5: State Space Graphs and Strategic Topologies; 6: The Brain’s Eye View of Mathematics; 7: The Fractal Topology of Cosmology http://jcer.com/index.php/jcj/article/view/203