Visually Representing the Landscape of Mathematical Structures

The information technology explosion has dramatically increased the application of areas of mathematics traditionally labeled ?pure” or ?theoretical” to wide ranges of fields, which has created a critical need to make abstract mathematics readily accessible to a broader community. This paper presents a method for categorizing and diagramming mathematical structures that enable students and professionals to rapidly understand relationships among and between mathematical structures. This paper also presents 11 maps diagramming 187 mathematical structures through the method described in the paper.