Visually Representing the Landscape of Mathematical Structures

TL;DR

This paper develops visual tools to represent and explore relationships among key mathematical structures, making complex concepts more accessible to students and professionals.

Contribution

It introduces a method for categorizing and visually mapping mathematical structures, creating an accessible online resource for understanding their relationships.

Findings

Created 11 visual maps of mathematical structures

Identified 187 unique structures across 10 categories

Provided an online map for public use

Abstract

The information technology explosion has dramatically increased the application of new mathematical ideas and has led to an increasing use of mathematics across a wide range of fields that have been traditionally labeled "pure" or "theoretical". There is a critical need for tools to make these concepts readily accessible to a broader community. This paper details the creation of visual representations of mathematical structures commonly found in pure mathematics to enable both students and professionals to rapidly understand the relationships among and between mathematical structures. Ten broad mathematical structures were identified and used to make eleven maps, with 187 unique structures in total. The paper presents a method and implementation for categorizing mathematical structures and for drawing relationship between mathematical structures that provides insight for a wide audience. The most in depth map is available online for public use [1].