Revealing the hidden beauty of finite groups with Cayley graphs

Abstract

Group theory involves the study of symmetry, and its inherent beauty gives it the potential to be one of the most accessible and enjoyable areas of mathematics, for students and non-mathematicians alike. Unfortunately, many students never get a glimpse into the more alluring parts of this field because "traditional" algebra classes are often taught in a dry axiomatic fashion, devoid of visuals. This article will showcase aesthetic pictures that can bring this subject to life. It will also leave the reader with some (intentionally) unanswered puzzles that undergraduate students, hobbyists, and mathematical artists can explore and answer, and even create new versions themselves.